Forecasting commodity prices out-of-sample: Can technical indicators help?

International Journal of Forecasting xxx (xxxx) xxx

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Forecasting commodity prices out-of-sample: Can technical indicators help? ∗

Yudong Wang a , , Li Liu b , Chongfeng Wu c a

School of Economics and Management, Nanjing University of Science and Technology, China School of Finance, Nanjing Audit University, China c Antai College of Economics and Management, Shanghai, China b

article

info

Keywords: Forecasting Commodity price Technical indicators Predictive regression Forecast combination

a b s t r a c t Economic variables are often used for forecasting commodity prices, but technical indicators have received much less attention in the literature. This paper demonstrates the predictability of commodity price changes using many technical indicators. Technical indicators are stronger predictors than economic indicators, and their forecasting performances are not affected by the problems of data mining or time changes. An investor with mean–variance preference receives utility gains of between 104.4 and 185.5 basis points from using technical indicators. Further analysis shows that technical indicators also perform better than economic variables for forecasting the density of commodity price changes. © 2019 International Institute of Forecasters. Published by Elsevier B.V. All rights reserved.

1. Introduction Both market participants and policy makers require real-time forecasts of asset prices. In recent years, commodities have emerged as a popular equity-like asset for many financial institutions due to the financialization of commodity markets (Gorton, Hayashi, & Rouwenhorst, 2013; Gorton & Rouwenhorst, 2006; Tang & Xiong, 2012). Commodity prices provide instantaneous information about the state of the economy (Gospodinov & Ng, 2013; Marquis & Cunningham, 1990), and therefore, it is not surprising that a growing number of papers are detecting predictability in commodity prices. Macroeconomic and financial variables are used commonly in the literature for forecasting commodity prices. The fundamental variables that are used to predict commodity prices include exchange rates (Chen, Rogoff, & Rossi, 2010; Groen & Pesenti, 2011), interest rates (Bessembinder & Chan, 2016), open interests in futures markets (Hong & Yogo, 2012), global economic activity ∗ Corresponding author. E-mail address: [email protected] (Y. Wang).

(Baumeister & Kilian, 2012, 2015), futures prices (Alquist & Kilian, 2010; Coppola, 2008), inventory (Ye, Zyren, & Shore, 2005, 2006), and other commodity-specific variables (Ahumada & Cornejo, 2016; Baumeister, Kilian, & Zhou, 2018; Wang, Liu, & Wu, 2017). Gargano and Timmermann (2014) use a series of fundamental variables that reflect the stock market and real economic activity to forecast commodity prices, and find that commodity currencies have some predictive power over short forecast horizons. Technical indicators have received much less attention than economic variables for forecasting commodity prices. Technical rules identify future price trends according to past prices or volume patterns. Many studies have examined the profitability of various technical rules, such as the momentum strategy (Fuertes, Miffre, & Rallis, 2010; Miffre & Rallis, 2007; Moskowitz, Ooi, & Pedersen, 2012; Shen, Szakmary, & Sharma, 2007) and the moving average and channel strategy (Szakmary, Shen, & Sharma, 2010) in commodity futures trading. However, these studies do not show explicitly whether technical variables predict commodity spot and futures price changes directly. We fill this gap in the literature.

https://doi.org/10.1016/j.ijforecast.2019.08.004 0169-2070/© 2019 International Institute of Forecasters. Published by Elsevier B.V. All rights reserved.

Please cite this article as: Y. Wang, L. Liu and C. Wu, Forecasting commodity prices out-of-sample: Can technical indicators help?. International Journal of Forecasting (2019), https://doi.org/10.1016/j.ijforecast.2019.08.004.

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This study conducts a comprehensive investigation of the predictive ability of technical indicators for World Bank commodity price indices. We use five trading rules (momentum, filtering, moving average, oscillator trading and support-resistance) to generate a total of 105 technical indicators. Because each trading rule yields many technical indicators, we use the equal-weighted average forecasts produced by technical indicators from the same rule. For the sake of comparison, nine economic variables are also used to forecast the prices of eight commodity indices. We find little evidence of out-of-sample predictability using economic models. In contrast, technical models outperform the prevailing mean benchmark significantly for all commodities. The combination of technical models produces more accurate forecasts than the combination of economic models. This predictability using technical information is robust to data mining considerations, the time considered and an alternative benchmark model. We show that the predictability of commodity price changes based on technical information is robust to the source of the commodity price data, and go on to predict the Standard & Poor’s–Goldman Sachs (S&PGS) spot commodity indices. These indices are based on front-end futures contracts. Our results indicate that the combination of technical models significantly outperforms the benchmark model which assumes no predictability. However, the predictive ability of technical indicators for the S&PGS indices is moderately weaker than their predictive ability for the World Bank commodity indices. One plausible explanation for this result is that commodity futures markets are more efficient than spot markets because of the high liquidity of futures contracts. We demonstrate the economic significance of the predictability in commodity price changes by imagining an investor with mean–variance preference who allocates her wealth between S&PGS commodity indices and a riskfree asset. The optimal weight on the commodity indices in her portfolio is determined ex-ante by the forecasts of commodity price changes. An agent with a risk aversion coefficient of two who uses technical forecasts to allocate wealth between a commodity index and the risk-free asset increases her certainty equivalent returns (CER) by between 104.4 and 185.5 basis points. The CER gains of the portfolio formed using the technical model forecasts are much larger than those of the portfolio formed using the economic model forecasts. As another contribution, we investigate predictions of the densities of commodity price changes. Unlike ‘‘point forecasts’’, ‘‘density forecasts’’ or ‘‘distribution forecasts’’ are independent of the loss function (Gneiting, 2011). Our technical models predict the commodity price densities significantly. Technical indicators also outperform economic indicators for density prediction. According to Neely, Rapach, Tu, and Zhou (2014), there are several economic theories that can explain the predictive ability of technical information. Theoretical explanations include differences in the time taken for investors to receive information (Brown & Jennings, 1989; Treynor & Ferguson, 1985), different responses to information by heterogeneous investors (Cespa & Vives, 2012) and investor initial under-reaction and delayed over-reaction

(De Long, Shleifer, Summers, & Waldmann, 1990; Hong & Stein, 1999; Moskowitz et al., 2012). The remainder of this paper is organized as follows. Section 2 briefly describes data on the predictors and commodity prices. Section 3 shows the methodology of predictive regressions and the evaluation methods. Section 4 gives the main forecasting results. Section 5 executes a series of robustness tests. Section 6 shows the results of density prediction. Section 7 investigates the predictability of commodity prices from an alternative source. The last section concludes the paper. 2. Data 2.1. Commodity prices We obtain monthly data on the prices of eight commodity indices from the World Bank’s website.1 The World Bank classifies commodities into two categories: energy and non-energy commodities. The energy index is the weighted average of the prices of coal, crude oil and natural gas, where the weight on the price of oil is 84.6%. The non-energy commodity index is the weighted average of sub-group indices, including agriculture, beverage, food, raw materials, metals and minerals, and precious metals.2 Our sample goes from January 1982 to December 2017, and Fig. 1 plots the commodity prices over that period. Commodity prices are volatile and follow similar paths. Popular commodities such as energy and food experienced large spikes from 2007 to mid-2008, then had large crashes during the subsequent financial crisis. A plausible explanation for this co-movement is that commodity prices share fundamentals such as global economic activity and interest rates. Excess co-movement between commodity prices beyond these fundamental reasons is also documented in the literature (Deb, Trivedi, & Varangis, 1996; Pindyck & Rotemberg, 1990). In the predictive regressions, we use changes in log prices as the dependent variables because they are stationary. The equation can be written as rt +1 = log (Pt +1 ) − log(Pt ),

(1)

where Pt denotes a commodity price in month t. 2.2. Macroeconomic variables For a comparison, we use eight macroeconomic variables to predict commodity price changes. These are the predictors that were used by Gargano and Timmermann (2014) for commodity forecasting, and can be classified into two groups. The first group contains five variables reflecting financial market activity, namely the dividend price ratio (the log of dividends from the S&P 500 index minus the log of stock prices, DP), the Treasury bill rate (the second market rate of 3-month U.S. Treasury 1 http://www.worldbank.org/en/research/commodity-markets. 2 For details on these indices, see the World Bank’s website, http://pubdocs.worldbank.org/en/550191549309123169/CMO-PinkSheet-February-2019.pdf.

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Fig. 1. Commodity prices.

bills, TBL), the long-term yield (the long-term government bond yield, LTY), exchange rates (trade-weighted exchange rates of the U.S. dollar, EX) and stock excess returns (returns to S&P 500 index, RET). The motivation for using these variables comes from the financialization of commodity markets, which has led to closer links between commodities and other financial markets (Gorton et al., 2013; Gorton & Rouwenhorst, 2006; Tang & Xiong, 2012). Some financial predictors themselves are fundamental determinants of commodity prices. For example, storage cost theory suggests that an increase in the interest rate will lead to a decrease in commodity prices. All commodity prices are denominated in U.S. dollars. Therefore, an appreciation in the dollar will result in a lower demand outside the U.S., thus decreasing commodity prices. The financial data are available from the homepage of Amit Goyal.3 The second group of predictors consists of three macroeconomic variables: inflation (the log growth in the consumer price index for all urban consumers, INFL), industrial production in the U.S. (IP) and global real economic activity as proxied for by Kilian’s index (KI). For CPI and IP, an extra lag is used to account for the delayed release of the data. We collect the IP and INFL data from the website of the Federal Reserve Bank of 3 http://www.hec.unil.ch/agoyal.

Saint Louis4 and the KI data from the homepage of Lutz Kilian.5 2.3. Technical indicators We use five popular technical trading rules to generate technical indicators for forecasting commodity prices. The first is the momentum rule (MOM), which depends on whether the current price Pt is higher than the lagged price Pt −k with

{ St ,MOM =

1, if Pt ≥ Pt −k 0, if Pt < Pt −k ,

(2)

where k is the look-back period. We choose k = 1, 3, 6, 9 and 12, resulting in five momentum indicators. The second rule for generating technical indicators is the filtering rule (FR) (Alexander, 1961). This rule produces a buying signal whenever the price has risen above its most recent low by more than a given percentage and a selling signal whenever the price has dropped below its most recent high by more than a given percentage. These buying and selling indicators can be written as buy

St ,FR = {St ,FR , Stsell ,FR },

(3)

4 https://fred.stlouisfed.org/. 5 http://www-personal.umich.edu/~lkilian/.

Please cite this article as: Y. Wang, L. Liu and C. Wu, Forecasting commodity prices out-of-sample: Can technical indicators help?. International Journal of Forecasting (2019), https://doi.org/10.1016/j.ijforecast.2019.08.004.

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Y. Wang, L. Liu and C. Wu / International Journal of Forecasting xxx (xxxx) xxx buy

St ,FR

(

{ =

1,

if Pt ≥ 1 +

η )

∗ min(Pt −1 , Pt −2 , . . . , Pt −k ) 100 0, otherwise, (4)

buy

Stsell ,FR

(

{ =

where k = 1, 3, 6, 9 and 12 and η = 5 and 10. A total of 20 indicators correspond to this rule. The last technical rule is the support-resistance rule (SR). This rule generates a buying or selling indicator by comparing the current price with the support or resistance level, with

1,

if Pt ≤ 1 −

St ,SR = {St ,SR , Stsell ,SR },

η )

∗ max(Pt −1 , Pt −2 , . . . , Pt −k ) 100 0, otherwise, (5)

where the look-back period k = 1, 3, 6, 9 and 12. We choose threshold values η = 5 and 10, and therefore obtain a total of 20 indicators. The third technical rule is the moving average (MA) rule. This rule gives a buying (selling) signal when the short-term MA of prices (MAs,t ) is higher (lower) than the long-term MA (MAl,t ), so

{ St ,MA =

1,

(6)

otherwise,

where MAj,t =

( )∑ j−1 1 j

i=0

Pt −i , j = s, l. Here, s and l are

the short and long look-back periods for comparing moving averages, respectively. We analyze monthly moving average rules for s, l = 1, 3, 6, 9 and 12 (s < l), resulting in 10 technical indicators. Our fourth rule is the oscillator trading rule (OSLT). Oscillators reflect whether the price increases or decreases in a recent period have been too rapid. The oscillator rule generates a buying or selling signal based on the relative strength indicator (RSI) (Levy, 1967), defined as RSI (m) = 100[

Ut (m) Ut (m) + Dt (m)

],

(7)

where Ut (k) and Dt (k) are the cumulative ‘‘upward movement’’ and ‘‘downward movement’’, respectively, of prices over the most recent k months, with Ut (k) =

k−1 ∑

I(Pt −j − Pt −j−1 > 0)(Pt −j − Pt −j−1 ),

(8)

j=0

Dt (k) =

k−1 ∑

I(Pt −j − Pt −j−1

(9)

where I(.) is an indicator variable that is equal to one when the condition in the parentheses is satisfied. The oscillator indicators expect a reversal in trend, and can be written as buy

St ,OSLT = {St ,OSLT , Stsell ,OSLT },

buy

{

1,

(

{ =

1,

if Pt ≥ 1 +

η )

∗ max(Pt −1 , Pt −2 , . . . , Pt −k ) 100 0, otherwise, (14)

Stsell ,SR

(

{ =

1,

if Pt ≤ 1 −

η )

∗ min(Pt −1 , Pt −2 , . . . , Pt −k ) 100 0, otherwise,

where k = 1, 3, 6, 9 and 12 and η = 1, 2, 3, 4 and 5, resulting in 50 support-resistance indicators. 3. Forecasting methodology 3.1. Predictive regression We follow the literature (e.g., Gargano & Timmermann, 2014) and use the following predictive regression to detect predictability: rt +1 = α + β xt + εt +1 , εt +1 ∼ N 0, σε2 ,

(

)

0,

if RSI ≤ 50 + η otherwise,

(10)

(11)

(16)

where rt denotes commodity price changes, xt is a predictor variable, and εt is the disturbance term which is assumed to be independently and identically distributed. A recursive estimation window (expanding window) is used to generate out-of-sample forecasts. We divide the sample of T observations for rt and xt into an insample part with the first M observations and an outof-sample part with the remaining T – M observations. Out-of-sample forecasts are given by rˆk+1 = αˆ k + βˆ k xk ,

⏐ ⏐ < 0) ⏐Pt −j − Pt −j−1 ⏐ ,

j=0

St ,OSLT =

buy

St ,SR

(15)

MAs,t ≥ MAl,t

0,

(13)

(17)

where αˆ k and βˆ k are the ordinary least squares estimates of α and β , respectively. These estimates are obtained by −1 regressting {rt }kt=2 on a constant and {xt }kt = 1 (k ≥ M). Repeating this procedure for k = M , . . . , T − 1 yields a time series{of}T – M one-step-ahead forecasts, which we T denote by rˆk k=M +1 . Each trading rule generates many technical indicators which result in different forecasts via Eq. (17). One must then determine which forecast from these technical indicators should be used. For simplicity, we consider the equal-weighted average of forecasts from technical indicators that correspond to the same rule, so the forecast is P

Stsell ,OSLT =

{

1,

if RSI ≥ 50 + η 0, otherwise,

(12)

rˆj,t =

j 1 ∑

Pj

rˆi,j,t , j = MOM , FR, MA, OSLT , SR,

(18)

i=1

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where rˆi,j,t denotes the forecast of commodity price changes from the ith technical indicator of the jth trading rule. Pj is the total number of technical indicators generated by Rule j. 3.2. Forecast combination It is well-known that it is dangerous to rely on a single model’s forecasts due to the problem of model uncertainty. Model uncertainty recognizes that forecasters do not know which predictors should be incorporated in the predictive regression because the relevant variables for commodity prices change over time. The inclusion of irrelevant variables in a predictive model worsens the forecasting performance. One of the techniques that is used to deal with model uncertainty is that of forecast combination, which takes the weighted average of forecasts from potential models in order to create the forecast

rˆt ,comb =

N ∑

wj,t rˆj,t ,

(19)

where wj,t is the weight assigned to the jth model’s forecast and N is the number of predictive models. We have N = 8 when using the macroeconomic model and N = 5 when using the technical model. Eq. (19) implies that the key procedure in forecast combination is the computation of the weights wj,t . We use an equal-weighted combination in our forecasting analysis (i.e., wj,t = 1/N). This simple weighting scheme performs quite well for economic and financial forecasting (Rapach, Strauss, & Zhou, 2010; Wang et al., 2017).6 3.3. Forecast evaluation Following the literature (e.g., Campbell & Thompson, 2007), we use the percentage out-of-sample R2 (R2OoS ) to evaluate the forecasting performance.

( = 100 × 1 −

MSPEmodel MSPEbench

)

,

(20)

where MSPEmodel and MSPEbench are the mean squared prediction errors of the given model and the benchmark model, respectively: MSPEi =

1 T −M

We assess the significance of predictability by using the Clark and West (2007) method (CW) to test the null hypothesis that MSPEbench is less than or equal to MSPEmodel (H0 : MSPEbench ≤ MSPEmodel ) against the upper-tail alternative hypothesis that MSPEbench is greater than MSPEmodel (MSPEbench > MSPEmodel ). The original (Diebold & Mariano, 1995) statistic does this by defining a series of forecasting losses between the tested and benchmark models as lt = (rt − r t )2 − rt − rˆt

(

)2

.

(22)

A significantly positive mean of the lt series indicates that MSPEbench is greater than MSPEmodel . Clark and West (2007) demonstrate that the Diebold and Mariano (1995) statistic is not suitable for comparing the forecasting performance of two nested models, such as we have here. Instead, they propose a corrected series of the loss differences by adding an adjustment term to Eq. (22): Lt = (rt − r t )2 − rt − rˆt

(

)2

( )2 + r t − rˆt .

(23)

Lt TM +1

j=1

R2OoS

5

T ∑

(rˆi − rt )2 , i = benchmark, model.

t =M +1

(21) The average of commodity price changes, r t +1 = ∑historical t 1 r , is taken as the natural benchmark. This model j j = 1 t is equivalent to a regression on a constant. A positive R2OoS means that MSPEmodel is less than MSPEbench , meaning that predictability can be tested by simply observing the sign of R2OoS . 6 As a robustness check, though, we also consider alternative combination strategies.

By regressing { } on a constant, we obtain the CW statistic, which is equivalent to the t-statistic of the constant. The p-value for the upper-tail test with the Student t-distribution is then used to determine significance. 4. Empirical results This section provides the main forecasting results for the economic variables and technical indicators. We use a recursive estimation window to generate forecasts of commodity price changes from January 1992 to December 2017. In addition to the individual models, we compare the performances of the equal-weighted forecast combination of technical models (EW-T) and the combination of the macro models (EW-M). The EW-T and EW-M forecasts and the realized commodity price changes are plotted in Fig. 2. 4.1. Forecasting results Table 1 shows the forecasting results evaluated by the out-of-sample R2 (R2OoS ). We begin by looking at the results for the individual models. The forecasting performances of the macroeconomic variables differ greatly by commodity. DP predicts price changes of energy commodities with an R2OoS of 0.473%, which is statistically significant at the 10% level. However, it fails to outperform the historical average benchmark when forecasting the prices of the other seven commodities, as is evidenced by its negative R2OoS values. INFL predicts the prices of only one of the eight commodities (precious metals). Two interest rates (TBL and LTY) underperform the benchmark model when forecasting the prices of any single commodity. The IP model has a positive R2OoS for six out of eight commodities, but the CW tests do not show significant differences in MSPE relative to the benchmark model. The RET and KI models outperform the historical average benchmark for four out of the eight commodities, while EX predicts the commodity prices significantly in six out of the eight cases. The performances of the technical models are more encouraging. We find that the MOM, OSLT and SR indicators result in significantly positive

Please cite this article as: Y. Wang, L. Liu and C. Wu, Forecasting commodity prices out-of-sample: Can technical indicators help?. International Journal of Forecasting (2019), https://doi.org/10.1016/j.ijforecast.2019.08.004.

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Fig. 2. Forecasts of commodity price changes.

R2OoS values for all eight commodities. The FR and MV indicators also lead to positive R2OoS values for all eight commodities, and the R2OoS values are significant in seven of the eight cases. In summary, these results suggest that the technical indicators have more predictive content than the economic variables. Turning to the performances of forecast combinations, we find that the EW-M method performs significantly better than the benchmark for six out of eight commodity prices, with R2OoS values ranging from −0.184% (raw materials) to 2.881% (non-energy). Using the EW-T strategy, we find significant predictability at the 1% level for all commodities. The R2OoS values range from 0.930% (precious metals) to 6.789% (non-energy). Interestingly, EW-T’s R2OoS is higher than that of the corresponding EW-M method for each commodity. This result indicates that combining technical information leads to stronger predictions for commodity prices than combining macroeconomic information. When forecasting with many predictors, it is necessary to control for data mining (or data snooping), and White’s (2000) reality check is a powerful tool for addressing this problem. We use this method to test the null hypothesis that the benchmark forecast’s MSPE is less than or equal to a given model’s forecast MSPE. We perform 5000 bootstraps and report the p-values in Table 2. The bootstrapped p-values suggest that the predictive ability of economic variables is very weak after accounting for

data mining. Exchange rates predict four out of eight commodities significantly, while the other seven economic variables have p-values above 0.1 in most cases, implying an absence of predictability. The performance of EWM is affected less by data mining, with p-values below 0.1 for five of the eight commodities. In sharp contrast, the bootstrapped p-values of the technical models and their combination are below 0.1 in most cases. This result indicates that the predictability of commodity prices by technical models cannot be explained by data mining. We assess the forecasting results further by considering an alternative evaluation criterion, success probability (SP). SP computes the number of times that a model forecasts the direction of changes in oil prices correctly relative to the total number of forecasts. If a model’s success ratio is above 0.5, then price changes are predictable. We conduct the test of Pesaran and Timmermann (2009) with the null hypothesis that the probability of predicting the direction of change in commodity prices correctly is less than or equal to 0.5. The results are reported in Table 3. Panel A of Table 3 lists the SPs of economic models. The directional accuracy of economic variables varies greatly by commodity. For example, the success probability of the DP model when forecasting energy prices is 0.613, which is significantly larger than 0.5. However, we cannot reject the null hypothesis of no directional predictability when forecasting the other commodity prices using DP.

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Table 1 Out-of-sample forecasting results. Energy

Non-energy

Agriculture

Beverage

Food

Raw materials

Metals & minerals

Precious metals

−3.340 −1.341 −2.149 −0.985 −0.398 −0.462

−0.773 −2.018 −0.910 −0.923

−0.110 −0.478 −0.213

Panel A: Forecasting results of economic variables DP TBL LTY INFL IP RET KI EX EW-M

0.473*

−0.723 −0.500 −0.441

−1.178 −2.298 −1.102 −1.017

−1.483 −1.825 −1.126 −0.721

−1.265 −0.190 −1.028 −1.016

−1.425 −2.471 −1.266 −0.697

0.117 −2.696 −0.300 3.790*** 0.568*

2.067 3.290*** 1.603** 7.508*** 2.881***

0.550 0.901* 1.736** 4.784*** 1.967***

0.350 −0.317 −0.304 0.042 0.147

0.323 0.955** 1.174** 3.902*** 1.748***

3.798*** 3.222*** 3.907*** 3.979*** 3.862*** 3.873***

4.149*** 2.697*** 2.987*** 3.805*** 3.852*** 3.700***

0.367* 0.828 −0.184

1.401 5.576*** −0.597 5.595*** 1.995***

2.603** −0.757 −0.234 −4.729 1.407** 0.794*

7.122*** 3.676*** 6.826*** 7.245*** 7.187*** 6.677***

4.894*** 5.839*** 5.679*** 4.822*** 4.766*** 5.378***

1.249** 0.404 0.468 1.207** 1.197** 0.930**

Panel B: Forecasting results of technical variables MOM FR MV OSLT SR EW-T

1.642*** 3.389*** 2.258*** 1.856*** 1.735*** 2.263***

6.451*** 5.103*** 8.006*** 6.447*** 6.367*** 6.789***

5.759*** 2.555*** 5.838*** 5.896*** 5.744*** 5.419***

Notes: The table shows the out-of-sample forecasting results of univariate models with economic variables and technical indicators, as well as of forecast combinations. EW-M and EW-T denote the equal-weighted combinations for macroeconomic and technical models, respectively. The forecasting performance is evaluated using the out-of-sample R2 (R2OoS ),

(

R2OoS = 100 × 1 −

MSPEmodel MSPEbench

)

,

where MSPEmodel and MSPEbench are the mean squared prediction errors of the given model and the benchmark model, respectively. ∑t The historical average of the commodity return, r t +1 = 1t j=1 rj , is taken as a natural benchmark. The full sample period is from January 1982 to December 2017, and the out-of-sample period for forecast evaluation starts in January 1991. The numbers in bold indicate that the corresponding model outperforms the benchmark model. We use the Clark and West (2007) method (CW) to test the null hypothesis that MSPEbench is less than or equal to MSPEmodel against the one-sided (upper-tail) alternative hypothesis that MSPEbench is greater than MSPEmodel . *, ** and *** denote rejections of the null hypothesis at the 10%, 5% and 1% significance levels, respectively. Table 2 Bootstrapped p-values. Energy

Non-energy

Agriculture

Beverage

Food

Raw materials

Metals & minerals

Precious metals

1.000 1.000 1.000 1.000 0.358 1.000 1.000 0.473 0.367

1.000 1.000 1.000 1.000 0.378 0.174 0.405 0.090 0.065

1.000 1.000 1.000 1.000 1.000 1.000 0.325 0.191 1.000

1.000 1.000 1.000 1.000 0.281 0.085 1.000 0.100 0.057

1.000 1.000 1.000 0.119 1.000 1.000 1.000 0.131 0.187

0.011 0.002 0.005 0.005 0.010 0.004

0.023 0.045 0.105 0.022 0.018 0.027

0.000 0.006 0.001 0.000 0.000 0.000

0.008 0.015 0.014 0.006 0.008 0.006

0.032 0.202 0.236 0.030 0.033 0.069

Panel A: Forecasting results of economic variables DP TBL LTY INFL IP RET KI EX EW-M

0.319 1.000 1.000 1.000 0.409 1.000 1.000 0.060 0.073

1.000 1.000 1.000 1.000 0.266 0.106 0.334 0.069 0.028

1.000 1.000 1.000 1.000 0.365 0.164 0.338 0.072 0.062

Panel B: Forecasting results of technical variables MOM FR MV OSLT SR EW-T

0.025 0.014 0.031 0.014 0.016 0.012

0.001 0.024 0.007 0.001 0.001 0.001

0.003 0.035 0.014 0.004 0.003 0.004

Notes: The table shows the testing results for the null hypothesis that the mean squared prediction error (MSPE) of the benchmark ∑t model is less than or equal to that of the given model. We take the historical average of the commodity return, r t +1 = 1t j=1 rj , as a natural benchmark. The full sample period is from January 1982 to December 2017, and the out-of-sample period for forecast evaluation starts in January 1991. The numbers reported in the table are the bootstrapped p-values based on the White (2000) reality check. We perform 50,000 bootstraps.

Similar results are present for each of the other economic variables. Not surprisingly, the directional accuracy of the combination of economic models (EW-M) is not strong, with an SP that is significantly larger than 0.5 for only two of the eight commodities (non-energy and metals and minerals).

Panel B of Table 3 shows the directional forecasting results for the technical models and their combination. All technical models have SPs larger than 0.5, regardless of which commodity price is predicted. The Pesaran and Timmermann (2009) test results suggest significant directional predictability for almost all commodities. The

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Y. Wang, L. Liu and C. Wu / International Journal of Forecasting xxx (xxxx) xxx Table 3 Directional forecasting results. Energy

Non-energy

Agriculture

Beverage

Food

Raw materials

Metals & minerals

Precious metals

0.413 0.523 0.452 0.465 0.471 0.465 0.497 0.587* 0.503

0.484 0.465 0.484 0.452 0.484 0.497 0.703 0.561 0.529

0.458 0.535 0.490 0.445 0.580 0.529 0.548 0.561 0.497

0.580 0.574* 0.548 0.561 0.548 0.677*** 0.574 0.593* 0.574*

0.523 0.523 0.471 0.574 0.490 0.593* 0.523 0.580* 0.523

0.645*** 0.619** 0.658*** 0.670*** 0.670*** 0.651***

0.619** 0.593* 0.632*** 0.645*** 0.632*** 0.606**

0.651*** 0.638*** 0.683*** 0.677*** 0.670*** 0.664***

0.715*** 0.748*** 0.735*** 0.703*** 0.722*** 0.748***

0.574* 0.542 0.510 0.568 0.580 0.574*

Panel A: Forecasting results of economic variables DP TBL LTY INFL IP RET KI EX EW-M

0.613** 0.555 0.574* 0.407 0.510 0.555 0.529 0.548 0.555

0.555 0.574* 0.523 0.477 0.523 0.600 0.677*** 0.619** 0.613**

0.477 0.516 0.439 0.458 0.561 0.497 0.670 0.548 0.542

Panel B: Forecasting results of technical variables MOM FR MV OSLT SR EW-T

0.574* 0.606** 0.587* 0.600** 0.568 0.600**

0.709*** 0.651*** 0.683*** 0.658*** 0.677*** 0.696***

0.690*** 0.613** 0.677*** 0.683*** 0.683*** 0.683***

Notes: The table shows the directional forecasting results of univariate models with either economic variables or technical indicators, as well as those of forecast combinations. EW-M and EW-T denote the equal-weighted combinations for macroeconomic and technical models, respectively. We report the probability that the model of interest predicts the directions of commodity price changes correctly. The full sample period is from January 1982 to December 2017, and the out-of-sample period for forecast evaluation starts in January 1991. The numbers in bold indicate that the corresponding model outperforms the benchmark of no predictability. We use the Pesaran and Timmermann (2009) statistic to test the null hypothesis that the success probability is equal to 0.5, the probability of tossing a coin. *, ** and *** denote rejections of the null hypothesis at the 10%, 5% and 1% significance levels, respectively.

only exceptions are the SPs of the FR, MV, OSLT and SR models, which are not significantly different from 0.5 when forecasting precious metals. The SP values of the EW-T models range from 0.574 to 0.748. The forecasting accuracy of this equal-weighted combination strategy is statistically significant for all eight commodities. 4.2. Forecasting performance over time We investigate forecasting performances over time by computing the cumulative sum of the squared predictive error difference (CSSED), defined as CSSEDt =

T ∑

(e2bench,t − e2model,t ),

(24)

t =M +1

where emodel,t and ebench,t are the forecast errors of the model of interest and the benchmark model, respectively. Intuitively, an increase from CSSEDt −1 to CSSEDt implies that the given model produces more accurate forecasts relative to the benchmark forecasts at time t. Fig. 3 plots the evolution of CSSEDs over time. The CSSEDs of the EW-M and EW-T strategies increase with time for six of the eight commodities. Relative to the benchmark forecasts, the forecasts from these two strategies become more accurate over time. There is a small upward jump in the CSSED values around the 2008 financial crisis. For the other two commodities (beverages and raw materials), the CSSEDs of EW-M are close to zero and nearly constant, while those of EW-T display a prominent increasing pattern. For all commodities except precious metals, EW-T has higher CSSEDs than EW-M most of time. Before 2015, the EW-M forecasts for precious metals prices are at least as accurate as the EW-T forecasts; after 2015, the EW-T forecasts outperform the EW-M forecasts.

Clearly, the performances of the technical models are more robust over time than those of the macro models. We also plot the recursive R2OoS values of the equalweighted combination strategies for the six commodity indices in Fig. 4. With the exception of the precious metals index, the R2OoS values of EW-M change around zero, while EW-T has R2OoS values that are significantly greater than zero. For precious metals, EW-M and EW-T have positive R2OoS values most of time and their forecasting performances are close. In summary, the predictive ability of combining technical information is affected less by time than that of combining economic information. The significant commodity price predictability of EW-T is robust to the evaluation period. 4.3. Combining information vs. combining forecasts We forecast commodity price changes using many explanatory variables, including technical and economic indicators. There are generally two directions in which one could go with high-dimensional information: combine forecasts (CF) or combine information (CI). CF combines the forecasts generated by individual models with a subset of information, whereas CI incorporates the entire information set into one predictive model in order to produce forecasts. There is no consensus on the optimal forecasting method for dealing with multivariate information (Hendry & Hubrich, 2011; Huang & Lee, 2010). We find significant commodity price predictability using the CF approach. As has been discussed, an alternative way of generating forecasts is to combine information. A popular way of performing CI is to reduce the dimensionality using principal components analysis and then use these factors to forecast price changes. There is a small but growing body of literature that forecasts commodity

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Fig. 3. Cumulative sum of squared predictive error.

prices using commodity-specific factors (e.g., Giampietro, Guidolin, & Pedio, 2018; Gorton et al., 2013; Guidolin & Pedio, 2018). The CI method is also found to work well in forecasting stock returns (Baetje & Menkhoff, 2016; Neely et al., 2014). Thus, it is interesting to compare the forecasting performances of the CF and CI methods.7 We use the first principal components drawn from the macroeconomic indicators (PC-M) and from the technical indicators (PC-T) to predict commodity price changes. The forecasting results are reported in Table 4. We find that PC-M has negative R2OoS values for all commodities except precious metals, while PC-T has significantly positive R2OoS values in all cases. This result confirms our main finding on the existence of commodity price predictability using technical information. Compared with the results reported in Table 1, the relative performances of the combination of information and the combination of forecasts depend on the choice of predictors. PC-M generally performs worse than EW-M. In contrast, PC-T and EW-T have similar outof-sample performances. That is, the significant predictive ability of technical information for commodity price changes is robust to different methods of dealing with high-dimensional predictors.

7 We thank an anonymous referee for this valuable suggestion.

4.4. Long-horizon forecasting results We have explored the one-month-ahead predictability of commodity prices using technical indicators. This subsection evaluates the forecasting performance for longer horizons. The price change over a horizon of h months is defined as rt +h = log (Pt +h ) − log(Pt ).

(25)

We consider horizons of h = 3 and 6 months and present the forecasting results in Table 5. The forecasting performances of the economic and technical models for long horizons are generally consistent with those for h = 1. We find little evidence of long-term price predictability using univariate economic models. The combination strategy EW-M outperforms the benchmark model significantly for six of the eight commodities when h = 3 and for five commodities when h = 6. All technical model forecasts are significantly more accurate than the benchmark forecasts for all commodities except energy. The technical model combination strategy (EW-T) for these commodities has R2OoS values ranging from 1.224% to 5.029% when h = 3 and from 1.135% to 5.200% when h = 6. Therefore, the price predictability by technical models is robust to the forecasting horizon used. Furthermore, the R2OoS values of the technical models are higher than those of the economic models in most cases, indicating that technical information has a higher predictive content than economic information over long horizons.

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Y. Wang, L. Liu and C. Wu / International Journal of Forecasting xxx (xxxx) xxx

Fig. 4. Recursive out-of-sample R2 . Table 4 Forecasting results of the first principal components. PC-M PC-T

Energy

Non-energy

Agriculture

Beverage

Food

Raw materials

Metals & minerals

Precious metals

−0.064

−0.973

−0.891

−0.498

−1.299

−1.745

−0.988

2.423***

6.928***

5.059***

4.940***

2.116***

7.662***

5.730***

1.113** 1.297**

Notes: PC-M and PC-T denote the first principal components for macroeconomic and technical indicators, respectively. The forecasting performance is evaluated by the out-of-sample R2 (R2OoS ),

(

R2OoS = 100 × 1 −

MSPEmodel MSPEbench

)

,

where MSPEmodel and MSPEbench are the mean ∑t squared prediction error of the given model and the benchmark model, respectively. The historical average of the commodity return, r t +1 = 1t j=1 rj , is taken as a natural benchmark. The full sample period is from January 1982 to December 2017, and the out-of-sample period for forecast evaluation starts in January 1991. The numbers in bold indicate that the corresponding model outperforms the benchmark model. We use the Clark and West (2007) method (CW) to test the null hypothesis that MSPEbench is less than or equal to MSPEmodel against the one-sided (upper-tail) alternative hypothesis that MSPEbench is greater than MSPEmodel . *, ** and *** denote rejections of the null hypothesis at the 10%, 5% and 1% significance levels, respectively.

5. Robustness analysis We execute two checks in order to demonstrate the robustness of commodity price predictability by technical information. First, we use several different weighting schemes to combine forecasts. Second, an alternative benchmark model is used to evaluate the forecast accuracy. 5.1. More sophisticated combinations Our main prediction analysis uses an equal-weighted strategy to combine forecasts from different models. The

results support the superiority of combining technical models relative to economic models. Here, we consider alternative weighting schemes. This is of interest because the outcomes of combination forecasts depend on the weighting methodology. We use three forecast combinations. The first two methods build on Stock and Watson’s (2004) discounted MSPE (DMSPE), which assigns weights according to

wi,t = φi−,t1−1 /

N ∑

φj−,t1−1 ,

(26)

j=1

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Forecasting horizon h = 3 Energy

Nonenergy

Forecasting horizon h = 6

Agriculture Beverage Food

Raw materials

Metals & minerals

Precious metals

−4.629 −2.251 −3.623 −0.485

−1.076 −3.008 −1.256 −1.265

0.137 −0.673 0.658 −0.601 −0.127

0.074 2.070 −1.137 5.190*** 1.054**

0.315 0.967** 0.614** 0.265 −2.023 −0.771 −5.508 0.550 1.161**

5.587*** 2.254*** 5.212*** 5.639*** 5.575*** 5.029***

3.517*** 5.093*** 4.892*** 3.855*** 3.557*** 4.340***

1.364** 1.245** 2.389*** 1.618*** 1.636*** 1.709***

Energy

Nonenergy

Agriculture Beverage

Food

Raw materials

Metals & minerals

Precious metals

0.439**

−1.469 −3.741 −1.454 −0.256

−1.990 −3.481 −1.721

−2.401 −5.636 −2.562

−5.048 −2.661 −4.039 −0.888 −0.264 −1.076

−0.921 −2.851 −1.101 −1.110 0.227 2.220** −0.982 5.336*** 1.205**

1.602** 2.246*** 1.897*** 1.553** −0.706 0.530 −4.146 1.834** 2.437**

1.126* 1.295* 0.421* 1.137* 1.056* 1.135*

5.209*** 1.862** 4.832*** 5.260*** 5.196*** 4.649***

3.665*** 5.238*** 5.038*** 4.002*** 3.705*** 4.487***

2.637*** 2.520*** 3.649*** 2.888*** 2.906*** 2.978***

Panel A: Forecasting results of economic variables DP TBL LTY INFL IP RET KI EX EW-M

1.098*** −0.793 −0.331 −0.695 0.600 −0.018 −0.575 2.759*** 0.983**

−1.698 −3.975 −1.683 −0.482 0.720 0.303 1.340* 5.008*** 1.940***

−2.004 −3.496 −1.736 0.061 −0.449 −0.322 2.211** 2.387** 1.723**

−1.747 0.337** −1.817 −0.886 −0.983 −0.052 −0.070 0.267 0.464

−2.308 −5.540 −2.469 0.263 −0.788 −0.362 1.560 2.699*** 1.559**

−1.464 −0.999 −1.366 −0.063 −0.685 −1.245 2.111** 0.323

0.943* 0.527 1.562* 5.222*** 2.161**

0.076 −0.434 −0.307 2.225** 2.401** 1.737**

−3.241 −1.126 −3.311 −2.367 −2.465 −1.521 −1.539 −1.197 −0.997

4.613*** 4.049*** 6.683*** 4.933*** 4.699*** 5.200***

3.649*** 1.690** 3.185*** 3.567*** 3.477*** 3.239***

1.773*** 0.412* 1.356** 1.726*** 1.748*** 1.498**

0.173 −0.880 −0.453 1.471** 0.259* 2.611*** −1.004 1.470** −0.528

Panel B: Forecasting results of technical variables MOM FR MV OSLT SR EW-T

0.034 0.677** −0.586 0.132 0.047 0.106

4.398*** 3.832*** 6.473*** 4.719*** 4.484*** 4.986***

3.635*** 1.676*** 3.171*** 3.553*** 3.463*** 3.224***

3.194*** 1.853*** 2.783*** 3.147*** 3.169*** 2.923***

1.216** 1.385** 0.511* 1.227** 1.145** 1.224**

−0.633 0.015 −1.257 −0.534 −0.619 −0.559

Notes: The table shows the out-of-sample forecasting results for long horizons. EW-M ( and EW-T) denote the equal-weighted combinations for macroeconomic and technical models, respectively. The forecasting performance is evaluated by the out-of-sample R2 (R2OoS ), R2OoS = 100 × 1 −

1 t

MSPEmodel MSPEbench t j=1 rj ,

∑

, where MSPEmodel and MSPEbench are the mean squared prediction errors of the given model and the

benchmark model, respectively. The historical average of the commodity return, r t +1 = is taken as a natural benchmark. The full sample period is from January 1982 to December 2017, and the out-of-sample period for forecast evaluation starts in January 1991. The numbers in bold indicate that the corresponding model outperforms the benchmark model. We use the Clark and West (2007) method (CW) to test the null hypothesis that MSPEbench is less than or equal to MSPEmodel against the one-sided (upper-tail) alternative hypothesis that MSPEbench is greater than MSPEmodel . *, ** and *** denote rejections of the null hypothesis at the 10%, 5% and 1% significance levels, respectively.

Y. Wang, L. Liu and C. Wu / International Journal of Forecasting xxx (xxxx) xxx 11

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Table 5 Long-horizon forecasting results.

12

Y. Wang, L. Liu and C. Wu / International Journal of Forecasting xxx (xxxx) xxx

where N is the number of individual models and φi,t = ∑ t t −j (rt − rˆi,t )2 . We consider δ = 1 and δ = 0.9. j=1 δ Baumeister and Kilian (2015) use the DMSPE method to forecast the price of crude oil, one of the most important commodities. The third alternative combination is the method proposed by Yang (2004). Yang (2004) demonstrates that linear forecast combinations can perform far worse than the single best forecasting model due to the large variability in estimates of combination weights. With this motivation, the author introduces the nonlinear weights

πi exp(−λ

wi,t = ∑N

∑t −1

π exp(−λ

j=1 ( j

ˆ 2 k=1 (rk − ri,k ) )

∑t −1

k=1 (rk

− rˆj,k )2 ))

.

(27)

For the sake of simplicity, we use weighting parameters π = λ = 1. Table 6 shows the forecasting results for the alternative combinations. When using the economic models, the performances of the combinations change with the weighting scheme. The DMSPE method with δ = 0.9 has higher R2OoS values than the other combination strategies, including the equal-weighted one. For example, if the equal-weighted method is replaced by DMSPE when forecasting energy prices, the R2OoS improves from 0.568% to 0.676%. In contrast, the performances of the technical model combinations are influenced less by the weighting methodology, with their R2OoS values being much closer together. More importantly, we find consistent evidence that combining technical information improves the predictability of all commodity prices significantly, and that the predictability is stronger than that from combining economic information. This result does not rely on the way in which predictor information is combined, and therefore, we conclude that our main empirical finding is robust to the selection of weights.

main results, the individual technical models show significant predictability in almost all cases. The two exceptions are the FR and MV forecasts, which are statistically indistinguishable from the no-change forecasts, although their R2OoS values are positive. The significance of predictability in the EW-T model is observed for all commodities. In summary, the predictability of commodity prices is not sensitive to the choice of benchmark. 6. Forecasting density We have demonstrated the predictability of commodity prices using technical information. In addition to point forecasts, market participants are also interested in predicting the distributions of prices (e.g., Diebold, Schorfheide, & Shin, 2017; Segnon, Gupta, Bekiros, & Wohar, 2018). Density forecasts have important implications for risk management, as they give an appropriate estimate of the probability distribution of forecasts. The density prediction of commodity prices has been analyzed in a few studies (Høg & Tsiaras, 2011; Ielpo & Sévi, 2014; Lombardi & Ravazzolo, 2012; Wang et al., 2017). however, to the best of our knowledge, technical information has not been used to forecast densities. A normal distribution is characterized by its mean and variance. When constructing density forecasts, we use the mean forecasts from different models and the same five-year rolling window forecasts of volatility. Thus, the accuracy of density forecasts is determined uniquely by the mean forecasts of the commodity prices. One problem when evaluating the accuracy of density forecasts is that the true density is not observed, even ex-post. However, an evaluation measure based on the well-known Kullback–Leibler information criterion (KLIC) addresses this issue without needing the true distribution (Mitchell & Hall, 2005). The KLIC measures the distance between the true and predictive densities, and is given by

5.2. Alternative benchmark model

KLICi = E [ln ft (yt ) − ln fi,t (yt )],

It is crucial to choose an appropriate benchmark model for evaluating the forecast performance, as a bad benchmark can cause artificial findings of predictability. Our main analysis follows Gargano and Timmermann (2014) in using the prevailing mean that assumes no predictability as the benchmark. This benchmark is equivalent to regression on a constant. Here, we consider an alternative benchmark model, the no-change forecast, which assumes that the best prediction of the commodity price in the future is the current price. Baumeister and Kilian (2012, 2015) use the no-change model as their benchmark when analyzing the oil market predictability. The relative performances of the economic and technical models are independent of the benchmark model. Table 7 reports the evaluation results. None of the individual economic models beats the no-change forecast model significantly for all commodities, and their combination, EW-M, outperforms the benchmark significantly for only five of the eight commodities. In particular, the individual exchange rate model beats the benchmark model significantly for six commodities, and works even better than EW-M in seven cases. Consistent with our

where E is the expectation operator, ft and fi,t are the true and predictive densities of the ith model, respectively, and yt is the realized value of the commodity price changes. We use the predictive density fi,t , characterized by the mean forecasts Rˆ t +1 and volatility forecasts σˆ t2+1 , along with yt , to compute fi,t (yt ). Intuitively, a larger KLIC value implies that model i’s density forecasts are less accurate. Even though the true density is unknown, we only need to compute the last term of the expectation in Eq. (28) in order to compare the accuracies of the density forecasts of two different models. This term allows us to determine the expected logarithmic score (lnS), E [ln Si ] = E ln fi,t (yt ) .

[

]

(28)

(29)

lnS chooses the model that gives the highest probability, on average, [ to] events that occur. It is easy to see that E [ln Si ] > E ln Sj is equivalent to KLICi > KLICj . E [ln Si ] can be estimated by the average of the sample logarithmic scores, with E [ln Si ] =

1 T −M

T ∑

ln fi,t (yt ),

(30)

t =M +1

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13

Table 6 More advanced combination strategies. Energy

Non-energy

Agriculture

Beverage

Food

Raw materials

Metals & minerals

Precious metals

0.147 0.149 0.182 0.147

1.748*** 1.853*** 2.256*** 1.754***

−0.184 −0.210 −0.076 −0.183

1.995*** 2.048*** 2.213*** 2.022***

0.794* 0.816* 0.898** 0.800*

3.873*** 3.874*** 3.875*** 3.873***

3.700*** 3.744*** 3.744*** 3.700***

6.677*** 6.694*** 6.697*** 6.679***

5.378*** 5.378*** 5.373*** 5.378***

0.930** 0.930** 0.931** 0.931**

Panel A: Forecasting results of economic variables Mean DMSPE(1) DMSPE(0.9) Yang

0.568* 0.621* 0.676* 0.584*

2.881*** 2.956*** 3.262*** 2.890***

1.967*** 2.013*** 2.450*** 1.971***

Panel B: Forecasting results of technical variables Mean DMSPE(1) DMSPE(0.9) Yang

2.263*** 2.263*** 2.265*** 2.266***

6.789*** 6.779*** 6.794*** 6.789***

5.419*** 5.438*** 5.441*** 5.420***

Notes: The table shows the out-of-sample forecasting results of alternative combination strategies. The forecasting performance is evaluated by the out-of-sample R2 (R2OoS ),

(

R2OoS = 100 × 1 −

MSPEmodel MSPEbench

)

,

where MSPEmodel and MSPEbench are the mean squared prediction errors of the given model and the benchmark model, respectively. ∑t The historical average of the commodity return, r t +1 = 1t j=1 rj , is taken as a natural benchmark. The full sample period is from January 1982 to December 2017, and the out-of-sample period for forecast evaluation starts in January 1991. The numbers in bold indicate that the corresponding model outperforms the benchmark model. We use the Clark and West (2007) method (CW) to test the null hypothesis that MSPEbench is less than or equal to MSPEmodel against one-sided (upper-tail) alternative hypothesis that MSPEbench is greater than MSPEmodel . *, ** and *** denote rejections of the null hypothesis at the 10%, 5% and 1% significance levels, respectively. Table 7 Random walk without drift as the benchmark. Energy

Non-energy

Agriculture

Beverage

Food

Raw materials

Metals & minerals

Precious metals

−2.137 −1.053 −1.899 −1.886 −0.508 −1.181 −1.168 −0.818 −0.713

−1.671 −2.719 −1.511 −0.941

−0.855 −2.101 −0.992 −1.005

−0.298 −0.034

0.082 0.715 0.935** 3.670*** 1.510**

−3.705 −1.699 −2.510 −1.342 −0.753 −0.818

2.969*** 2.388*** 3.079*** 3.152*** 3.034*** 3.045***

3.917*** 2.462*** 2.752*** 3.572*** 3.619*** 3.467***

Panel A: Forecasting results of economic variables DP TBL LTY INFL IP RET KI EX EW-M

−0.093 −1.296 −1.072 −1.013 −0.451 −3.280 −0.871 3.243*** 0.003

−1.216 −2.336 −1.139 −1.055

−1.655 −1.998 −1.297 −0.892

2.030* 3.254*** 1.566** 7.473*** 2.845***

0.381 0.733 1.569** 4.622*** 1.801**

0.069

2.777**

0.015 0.477 −0.538

1.321 5.500*** −0.679 5.518*** 1.916**

1.584** 0.972*

6.794*** 3.335*** 6.496*** 6.917*** 6.858*** 6.348***

4.816*** 5.762*** 5.602*** 4.744*** 4.688*** 5.301***

1.426** 0.583 0.647 1.384** 1.374** 1.108*

−0.576 −0.054 −4.542

Panel B: Forecasting results of technical variables MOM FR MV OSLT SR EW-T

1.083** 2.839*** 1.702*** 1.297** 1.176** 1.707***

6.416*** 5.068*** 7.972*** 6.412*** 6.332*** 6.754***

5.599*** 2.390*** 5.678*** 5.736*** 5.584*** 5.258***

Notes: The table shows the out-of-sample forecasting results of univariate models with economic variables and technical indicators, as well as of forecast combinations. EW-M and EW-T denote the equal-weighted combinations for macroeconomic and technical models, respectively. The forecasting performance is evaluated using the out-of-sample R2 (R2OoS ),

(

R2OoS = 100 × 1 −

MSPEmodel MSPEbench

)

,

where MSPEmodel and MSPEbench are the mean squared prediction errors of the given model and the benchmark model, respectively. The no-change price forecast, r t +1 = 0, is taken as a natural benchmark. The full sample period is from January 1982 to December 2017, and the out-of-sample period for forecast evaluation starts in January 1991. The numbers in bold indicate that the corresponding model outperforms the benchmark model. We use the Clark and West (2007) method (CW) to test the null hypothesis that MSPEbench is less than or equal to MSPEmodel against the one-sided (upper-tail) alternative hypothesis that MSPEbench is greater than MSPEmodel . *, ** and *** denote rejections of the null hypothesis at the 10%, 5% and 1% significance levels, respectively.

where T is the total number of full sample periods and M is the number of in-sample periods, as defined above. We examine whether the difference in lnS between two different models is statistically significant using the test suggested by Mitchell and Hall (2005). This test is similar to the t-test for comparing the difference between two sample means. Table 8 shows the gains in lnS, which are the differences between the lnS values of the given model and the

benchmark model. None of the economic variables except the exchange rate beat the benchmark model significantly for forecasting the densities of any commodity prices. The exchange rate generates significantly more accurate density forecasts than the benchmark forecasts for five commodities. The EW-M model performs well for density prediction for four commodities out of eight. The technical models demonstrate a stronger density predictability than the economic models, and significantly so in almost

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14

Y. Wang, L. Liu and C. Wu / International Journal of Forecasting xxx (xxxx) xxx Table 8 Density forecast results. Energy

Non-energy

Agriculture

Beverage

Food

Raw materials

Metals & minerals

Precious metals

−0.0059 −0.0016 −0.0060 −0.0070

−0.0069 −0.0067

−0.0137

−0.0040 −0.0008

−0.0031

Panel A: Forecasting results of economic variables DP TBL LTY INFL IP RET KI EX EW-M

−0.0027 −0.0058 −0.0062 −0.0007 0.0012 −0.0145 −0.0009 0.0236*** 0.0025

−0.0161

−0.0136

0.0030 0.0005 −0.0022 0.0085 0.0033 0.0132 0.0181* 0.0156***

0.0016 0.0009 −0.0029 0.0055 −0.0001 0.0186 0.0127* 0.0138**

0.0012 −0.0019 −0.0021 0.0053 0.0015

0.0003 −0.0028 0.0008 0.0006 0.0203 0.0120* 0.0124**

0.0003 −0.0031 −0.0078 0.0015 −0.0033 0.0001 0.0032 0.0012

0.0000 0.0005 0.0092 0.0137 −0.0019 0.0162* 0.0098***

0.0006 0.0009 0.0069 −0.0039 −0.0019 −0.0397 0.0032 0.0021

0.0213*** 0.0166*** 0.0236*** 0.0225*** 0.0217*** 0.0219***

0.0285*** 0.0125** 0.0172* 0.0247*** 0.0256*** 0.0231***

0.0367*** 0.0189*** 0.0346*** 0.0372*** 0.0374*** 0.0346***

0.0345*** 0.0347*** 0.0409*** 0.0324*** 0.0328*** 0.0362***

0.0063** 0.0005 0.0012 0.0058** 0.0062** 0.0041*

Panel B: Forecasting results of technical variables MOM FR MV OSLT SR EW-T

0.0120*** 0.0228*** 0.0165*** 0.0137*** 0.0127*** 0.0160***

0.0444*** 0.0271*** 0.0516*** 0.0444*** 0.0441*** 0.0450***

0.0354*** 0.0154*** 0.0399*** 0.0379*** 0.0355*** 0.0347***

Notes: The table shows the out-of-sample forecasting results of the density of commodity price changes. We consider univariate models with economic variables and technical indicators, as well as forecast combinations. EW-M and EW-T denote the equalweighted combinations for macroeconomic and technical models, respectively. The forecasting performance is evaluated by the expected logarithmic score (lnS). We report the gains in lnS; that is, the differences ∑t in lnS values between the given model and the benchmark model. The historical average of the commodity return, r t +1 = 1t j=1 rj , is taken as a natural benchmark. The full sample period is from January 1982 to December 2017, and the out-of-sample period for forecast evaluation starts in January 1991. The numbers in bold indicate that the corresponding model outperforms the benchmark model. We test the significance of predictability by using the method given by Mitchell and Hall (2005). *, ** and *** denote rejections of the null hypothesis at the 10%, 5% and 1% significance levels, respectively.

all cases. The forecasting gains from using the technical models are always greater than those from using the economic models. That is, the superiority of technical information is also evident for density prediction. 7. Alternative commodity prices This section investigates the predictive ability of technical indicators for commodity indices from different sources. Our motivation for this exercise comes from the work of Groen and Pesenti (2011), who find that the predictability of commodity prices by exchange rates depends heavily on the source of the price index. Furthermore, market participants are more concerned with economic predictability than with the statistical predictive ability of technical indicators for commodity prices. That is, they are more interested in the economic gains from the predictability of commodity prices. Market investors are more likely to trade futures contracts than spot contracts because of their high liquidity and low transaction costs. Thus, it is not surprising that finance researchers tend to consider futures contracts with favor (Dolatabadi, Narayan, Nielsen, & Xu, 2018; Guidolin & Pedio, 2018; Liu, Wang, & Yang, 2018). Based on these considerations, we follow Giampietro et al. (2018) and Bae, Kim, and Mulvey (2014) and forecast the Standard & Poor’s–Goldman Sachs (S&PGS) spot commodity indices.8 These indices are built using frontend futures in order to exploit the proximity of traded future prices to spot prices, and therefore can be simply replicated by market investors. In addition to the overall 8 We thank an anonymous referee for this valuable suggestion.

commodity index, we use the category commodity indices, namely S&PGS agriculture, S&PGS reduced energy PI, S&PGS light energy spot and S&PGS livestock spot. For these financial indices, we focus on the prediction of log price changes, i.e., the price returns.9 The sample period goes from January 1970 to December 2017.10 7.1. Statistical predictability Table 9 reports the forecasting results for S&PGS commodity price returns after January 1980. We find little evidence of economic indicators having significant predictive ability for S&PGS commodity returns. The only exceptions are that industrial production, Kilian’s economic activity index and the equal-weighted combination of macroeconomic models (EW-M) have significantly positive R2OoS values. The technical indicators perform much better, with positive R2OoS values in almost all cases. The significance of the return predictability for each type of technical indicator changes with the S&PGS commodity index used. The MOM, OSLT and SR rules outperform the historical average benchmark significantly when forecasting returns to the S&PGS overall commodity index and the reduced energy index. When forecasting agriculture index returns, the OSLT and SR rules demonstrate significant predictability. Nevertheless, we find that the equal-weighted combination of technical models (EW-T) predicts returns for 9 This section uses the terms ‘commodity returns’ and ‘commodity price changes’ interchangeably. 10 The data are from Datastream.

Please cite this article as: Y. Wang, L. Liu and C. Wu, Forecasting commodity prices out-of-sample: Can technical indicators help?. International Journal of Forecasting (2019), https://doi.org/10.1016/j.ijforecast.2019.08.004.

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Table 9 Forecasting results for Standard & Poor’s-Goldman Sachs spot commodity indices. Overall index

Agriculture

Reduced energy

Light energy

Livestock

−0.522 −1.053 −0.730 −0.469 −0.291 −0.470

−0.615 −1.265 −0.837 −0.510 −0.304 −0.481

0.253

−0.010

0.470 0.080

−0.682 −0.883 −1.137 −0.498 −0.081 −0.578 −0.894 −0.443

0.313* 0.458* 0.208 0.262 0.317* 0.331*

0.235 0.584* 0.348* 0.201 0.282 0.350*

0.761** 0.801** 1.363*** 0.897** 0.850** 0.993**

Panel A: Forecasting results of economic indicators DP TBL LTY INFL IP RET KI EW-M

−0.471 −0.929 −0.648 −0.421 −0.350 −0.491

−0.828 −2.044 −0.803 −0.495 0.454* −0.124 0.614* 0.462*

0.067 −0.076

Panel B: Forecasting results of technical indicators MOM FR MV OSLT SR EW-T

0.259* 0.250 0.040 0.285* 0.306* 0.246*

0.176 0.108 −0.043 0.244* 0.244* 0.181*

Notes: The table shows the out-of-sample forecasting results for the Standard & Poor’s-Goldman Sachs spot commodity indices. EW-M and EW-T denote the equal-weighted combinations for the macroeconomic and technical models, respectively. The forecasting performance is evaluated by the out-of-sample R2 (R2OoS ),

(

R2OoS = 100 × 1 −

MSPEmodel MSPEbench

)

,

where MSPEmodel and MSPEbench are the mean squared prediction errors of the given ∑t model and the benchmark model, respectively. The historical average of the commodity return, r t +1 = 1t j=1 rj , is taken as a natural benchmark. The full sample period is from January 1970 to December 2017, and the out-of-sample period for forecast evaluation starts in January 1980. The numbers in bold indicate that the corresponding model outperforms the benchmark model. We use the Clark and West (2007) method (CW) to test the null hypothesis that MSPEbench is less than or equal to MSPEmodel against the one-sided (upper-tail) alternative hypothesis that MSPEbench is greater than MSPEmodel . *, ** and *** denote rejections of the null hypothesis at the 10%, 5% and 1% significance levels, respectively.

all commodity indices significantly. Therefore, the performance from combining technical information is robust to the source of commodity prices and trading markets. The R2OoS values of technical indicators for S&PGS commodity prices are moderately lower than those for the World Bank commodity spot indices reported in Table 2. This is because commodity futures markets are more efficient than spot markets due to the much higher liquidity of futures contracts. 7.2. Economic gains of predictability We analyze the economic significance of the predictability of commodity returns by technical information by following the literature and using a simple portfolio strategy (e.g., Dolatabadi et al., 2018; Rapach et al., 2010). This exercise imagines that an investor with mean–variance preferences allocates her wealth between the commodity index and a risk-free asset, where the optimal weight of the commodity index in this portfolio is determined ex-ante by the mean and volatility forecasts of commodity returns. The utility from investing in this portfolio is 1 γ v ar(ωt Rt + rt ,f ), (31) 2 where ωt is the weight on the commodity index in the portfolio and Rt is the returns to the commodity index in excess of the risk-free rate. The risk-free rate rt ,f is proxied for by the 3-month Treasury bill rate. The coefficient γ measures the investor’s aversion to risky assets (i.e., the commodity index). Ut = E ωt Rt + rt ,f −

(

)

We obtain the optimal weight on the commodity index by maximizing Ut , with

ωt = ∗

1

γ

(

Rˆ t +1

σˆ t2+1

) ,

(32)

where Rˆ t +1 and σˆ t2+1 are the mean and volatility forecasts of commodity returns, respectively. For simplicity, we use a five-year rolling window to generate the volatility forecasts, following Neely et al. (2014) and Rapach et al. (2010). After calculating the ωt∗ , the portfolio return is given by Rt +1,p = ωt∗ Rt +1 + rt +1,f − τ ⏐ωt∗+1 − ωt ⏐ ,

⏐

⏐

(33)

where the transaction costs are τ percentage points of the value traded. Note that transaction costs in futures markets range from 0.0004% (low cost) to 0.033% (high cost) (Locke & Venkatesh, 1997), which are much lower than the conservative 0.5% estimate of Jegadeesh and Titman (1993). We use the high cost of 0.033%. We use two popular criteria to evaluate the portfolio performance. The first is the Sharpe ratio. We compute the Sharpe ratio gains, defined as the difference between the Sharpe ratios of the portfolio formed by the given model forecasts and the portfolio formed by the √ benchmark forecasts. This difference is multiplied by 12 in order to calculate the annualized value. The second criterion is the certainty equivalent return (CER). We calculate the CER gains, defined as the difference between the CERs of the given portfolio and the benchmark portfolio.

Please cite this article as: Y. Wang, L. Liu and C. Wu, Forecasting commodity prices out-of-sample: Can technical indicators help?. International Journal of Forecasting (2019), https://doi.org/10.1016/j.ijforecast.2019.08.004.

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Y. Wang, L. Liu and C. Wu / International Journal of Forecasting xxx (xxxx) xxx

Table 10 Portfolio performance (γ = 2). Sharpe ratio gains Overall index

Agriculture

Certainty equivalent return gains Reduced energy

Light energy

Livestock

Overall index

Agriculture

Reduced energy

Light energy

Livestock

0.045 0.111 0.145 −0.090 0.040 0.076 0.189 0.085

−0.121 0.033 0.005 −0.001 0.043 −0.071 −0.049 −0.060

−0.186 −1.499 −1.363 −0.668 −0.455

−0.602 −0.982 −1.239 −0.284

−0.140 −1.136 −0.326 −0.503

−0.918 −1.750 −1.593 −1.381

0.170 1.294 0.001

2.034 0.539 2.708 1.882

0.412 0.528 1.900 0.227

0.312 0.249 0.793 −1.022 0.594 0.672 2.162 0.513

0.150 −0.749 −1.899 −1.230

0.097 0.090 0.078 0.076 0.083 0.085

0.211 0.196 0.293 0.226 0.237 0.234

1.343 0.312 0.823 1.786 1.752 1.253

1.701 1.636 1.278 1.802 1.943 1.855

1.580 0.904 0.886 1.407 1.579 1.348

1.152 1.184 0.932 0.901 1.014 1.044

1.352 0.991 2.233 1.328 1.563 1.516

Panel A: Portfolio performance of economic indicators DP TBL LTY INFL IP RET KI EW-M

0.112 0.060 0.125 −0.063 −0.022 0.148 0.174 0.085

0.011 0.067 0.100 −0.082 0.200 0.110 0.265 0.194

0.050 0.061 0.138 −0.060 0.028 0.094 0.189 0.077

Panel B: Portfolio performance of technical indicators MOM FR MV OSLT SR EW-T

0.134 0.010 0.075 0.166 0.163 0.112

0.177 0.170 0.153 0.182 0.195 0.186

0.127 0.067 0.067 0.113 0.125 0.104

Notes: The table shows the out-of-sample forecasting results for Standard & Poor’s-Goldman Sachs spot commodity indices. EW-M and EW-T denote the equal-weighted combinations for macroeconomic and technical models, respectively. In each period, a mean-variance investor allocates wealth between the commodity ) index and the T -bill based on return and volatility forecasts. In this framework, the commodity index is assigned the ( weight ωt∗ =

( ) 1

γ

Rˆ t +1

σˆ t2+1

, where γ denotes the risk aversion degree, and Rˆ t +1 and σˆ t2+1 are the mean and volatility forecasts of commodity returns,

respectively. We consider 5-year rolling window volatility forecasts and use γ = 2. The optimal weight of the commodity index is restricted to be between 0 and 1.5. The Sharpe ratio gains are defined as the differences in Sharpe √ ratios between the portfolio formed by given model forecasts and that formed by the benchmark forecasts. This difference is then multiplied by 12 to denote the annualized value. The certainty equivalent return (CER) gains are defined as the differences in CERs between the given portfolio and the benchmark portfolio. This difference is further multiplied by 12,000 to denote the annualized percentage value. The full sample period is from January 1970 to December 2017, and the out-of-sample period for forecast evaluation starts in January 1980. The numbers in bold indicate that the corresponding model outperforms the benchmark model.

This difference is multiplied by 12,000 to determine the annualized percentage value. Columns 2–6 of Table 10 report the Sharpe ratio gains for γ = 2.11 The performances of individual economic indicators change greatly with the commodity index used. The same pattern is also found for the EW-M strategy, which has Sharpe ratio gains between –0.060 (livestock) and 0.194 (agriculture). In contrast, the Sharpe ratio gains of EW-T are positive for all commodity indices and range from 0.085 (light energy) to 0.234 (livestock). For the agriculture commodity index, EW-T has slightly lower Sharpe ratio gains than EW-M. For the other commodity indices, EW-T has higher Sharpe ratio gains than the EW-M. The CER gains reported in columns 7–11 of Table 10 are consistent. Under this criterion, the performance of the EW-T strategy is much less sensitive to the choice of commodity index than that of the EW-M. The CER gains of EW-T range from 104.4 basis points (light energy) to 185.5 basis points (agriculture). Such economic gains from investing in commodities are also greater than those from investing in a stock index, as has been reported in the literature (e.g. Neely et al., 2014; Rapach et al., 2010). In summary, our results suggest that the predictability of commodity returns by technical information is economically significant. Investors can form more reliable and better performing portfolios by combining technical information instead of economic information. 11 As a robustness check, we also considered an alternative γ of 6. To save space, we report the results in the appendix rather than the main text.

8. Conclusions The number of papers on the issue of forecasting commodity prices is growing. We contribute to the literature by using technical indicators to improve the accuracy of predictions of commodity prices. Using spot price data on eight commodity indices from 1982 to 2017, we show that a combination of 105 technical indicators drawn from five trading rules have significant predictive content for the eight commodity prices. Technical information leads to stronger and more robust predictability than the traditional economic information that is used widely. The success of technical variables is also found in forecasting densities. We also use technical indicators to forecast returns to Standard & Poor’s–Goldman Sachs (S&PGS) spot commodity indices. The commodity return forecasts are also applied to a portfolio exercise. Our findings confirm the economic significance of commodity price predictability. Technical indicators perform better than economic indicators for portfolio allocation.

Acknowledgment The authors acknowledge the financial support from the National Natural Science Foundation of China under the grant numbers Nos. 71722015, 71501095 (Yudong Wang), 71771124 (Li Liu), and 71790592 (Chongfeng Wu).

Please cite this article as: Y. Wang, L. Liu and C. Wu, Forecasting commodity prices out-of-sample: Can technical indicators help?. International Journal of Forecasting (2019), https://doi.org/10.1016/j.ijforecast.2019.08.004.

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Yudong Wang, is a professor of economics and finance in Nanjing University of Science and Technology. He is a specialist in economic forecasting and energy economics. He has published more than 50 papers in economics and management journals such as Management Science, International Journal of Forecasting, Journal of Banking and Finance, Journal of Empirical Finance, Journal of Forecasting, Journal of Comparative Economics and Energy Economics.

Li Liu, is an associate professor of finance at School of Finance, Nanjing Audit University. She is interested in the area of economic forecasting and energy finance. She has published more than 20 papers in international journals including Journal of Empirical Finance and Energy Economics.

Chongfeng Wu, is a professor of finance in Shanghai Jiao Tong University. He is a specialist in financial economics. He has published many papers in economics and finance journals such as Management Science, Journal of Banking and Finance, International Journal of Forecasting, Journal of Empirical Finance and Journal of Comparative Economics.

Please cite this article as: Y. Wang, L. Liu and C. Wu, Forecasting commodity prices out-of-sample: Can technical indicators help?. International Journal of Forecasting (2019), https://doi.org/10.1016/j.ijforecast.2019.08.004.