RETRACTED: Investigating the efficiency in oil futures market based on GMDH approach

Expert Systems with Applications 36 (2009) 7479–7483

Contents lists available at ScienceDirect

Expert Systems with Applications journal homepage: www.elsevier.com/locate/eswa

Mohsen Mehrara a,*, Ali Moeini b, Mehdi Ahrari a, Ali Erfanifard a b

Faculty of Economics, University of Tehran, Kargar-e-Shomali, Tehran, Iran Department of Algorithms and Computation, Faculty of Engineering, University of Tehran, Tehran, Iran

a r t i c l e

i n f o

Keywords: GMDH neural network Futures market Oil prices

1. Introduction

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Investigating the efficiency in oil futures market based on GMDH approach

a b s t r a c t

If the crude oil futures market is not efficient in the Fama sense, profitable trading opportunities may exist. This paper uses a GMDH neural network model with moving average crossover inputs to predict price in the crude oil futures market. The predictions of price are used to construct buy and sell signals for traders. Compared to those of benchmark models, cumulative returns, year-to-year returns, returns over a market cycle, and Sharpe ratios all favor the GMDH model by a large factor. The significant profitability of the GMDH model casts doubt on the efficiency of the oil futures market. Ó 2008 Elsevier Ltd. All rights reserved.

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As oil prices have climbed, the financial news has been filled with accounts of diverse types of investors from individuals and pension funds to investment banks and hedge funds joining the ‘‘black gold rush”.1 The futures market for oil is the preferred trading arena for hedgers and speculators wishing to place their bets on that market’s next move. The hundreds of millions of dollars wagered by these new players in the futures market is said to have resulted in higher prices and increased volatility. Futures markets are differentiated from actual asset markets by the fact that futures are a zero sum game, where for every long position there must be a short position. Every price movement in a futures market that creates a profit for one participant will result in an equal loss for another participant. With heavy participation of informed traders on both sides, futures trading should perform particularly well as a price discovery mechanism based on the known market fundamentals. Thus neoclassical economic theory suggests that futures markets should be highly efficient, with no room for excess returns. What then explains traders’ enthusiasm for short-term bets on oil futures? An explanation for the behavior of traders may be rooted in the belief that there are anomalies in asset pricing which persist, at least in the short-run. In the scholarly literature, proponents of behavioral finance have provided empirical evidence as well as theoretical explanations of price patterns inconsistent with the efficient market hypothesis, such as evidence of negative serial correlation of stock returns explained by an over-reaction of traders to changes in market fundamentals. In other words, traders in the oil

* Corresponding author. Tel.: +98 21 88029007; fax: +98 21 88633744. E-mail address: [email protected] (M. Mehrara). 1 See Times Newspapers Inc., September 20 (2004). 0957-4174/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.eswa.2008.09.055

futures market may believe that anomalies in pricing persist and that price movements contain predictable patterns which can be exploited for profitable returns. Long before the contributions of behavioral finance, technical analysts have claimed the ability to generate excess returns solely on the basis of interpretations of historical price patterns.2 Technical analysis has evolved from looking for patterns on price charts to using computer programs based on a variety of weighted and unweighted price averages, to the current state of the art which employs artificial intelligence [AI] techniques. A branch of AI technology that has been experiencing strong expansion in its application to commodity trading is the field of group method of data handling (GMDH) neural networks. If historical price patterns can indeed be used to predict future prices, the market would not fit the strict definition of efficient markets laid out by Fama (1970). If inefficiencies exist, there could be profitable trading opportunities. The purpose of this paper is to examine the possibility that the oil futures market is not an efficient market in that subtle price patterns that can be exploited for profitable trading. To explore this question we estimate an GMDH neural network model for the price of nearby oil futures with technical analysis rules as inputs. We find that, without transaction costs and disregarding slippage, the GMDH model can produce profitable trading signals for several years, thus casting doubt on the efficiency of the oil market. In Section 2 below, we reference selected literature as background, including studies which have used neural network models in technical analysis. Section 3 provides a general discussion of GMDH neural network modeling and describes a network with technical analysis rules as inputs. Benchmark models are given in

2

See, for example, Hoyle (1898).

M. Mehrara et al. / Expert Systems with Applications 36 (2009) 7479–7483

Section 4. Empirical results are presented in Section 5, and concluding remarks in Section 6. 2. Background

GMDH neural networks are based on the concept of pattern recognition, and in that sense such networks are a refinement of traditional methods of technical analysis. GMDH neural networks, which are highly flexible, semi parametric models, have been applied in many scientific fields, including biology, medicine and engineering. For economists, neural networks represent an alternative to standard regression techniques and are particularly useful for dealing with non-linear univariate or multivariate relationships. By means of GMDH algorithm a model can be represented as set of neurons in which different pairs of them in each layer are connected through a quadratic polynomial and thus produce new neurons in the next layer. Such representation can be used in modelling to map inputs to outputs. The formal definition of the identification problem is to find a function ^f so that can be approx^ for imately used instead of actual one, f, in order to predict output y a given input vector X = (x1, x2, x3, . . . , xn) as close as possible to its actual output y. Therefore, given M observation of multi-input-single-output data pairs so that

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The literature investigating the predictability of financial asset prices is vast and diverse. The econometrics used to test the efficient market hypothesis and important empirical results of prominent researchers can be found in Campbell, Lo, and MacKinlay (1997) and the references therein. Behavioral finance, which is part of the broader study of behavioral economics, seeks to translate the psychology of investors into testable hypotheses. Seminal articles in behavioral finance include DeBondt and Thaler (1985) and Shleifer and Vishny (1997). Shleifer (2000) provides an overview of this field. A formal study of the predictive power of technical analysis rules in linear and non-linear models is given by Neftci (1991). Brock, Lakonishok, and LeBaron (1992) provide some of the earliest support for the use of technical analysis and suggest the need for a non-linear model. Gencay (1996) use foreign exchange markets to pioneer the use of technical analysis rules as inputs for neural networks, which are flexible, non-linear models with powerful pattern recognition properties. In a series of articles, Gencay (1998a), Gencay (1999) and Gencay and Stengos (1998) show that simple technical rules result in significant forecast improvements for current returns over a random walk model for both foreign exchange rates and stock indices. Franses and van Griensven (1997), Gencay (1998b), Fernandez-Rodriquez, Gonzalez-Martel, and SosvillaRivero (2000) shift the focus of the approach from forecast accuracy to profitability to reflect the buy and sell outcomes which are the goals of technical analysis. Trippi and Turban (1996) summarize other work along this line for various stocks and commodities. In the energy economics literature, Gulen (1998) examines efficiency in the futures market for crude oil, while Fleming and Ostdiek (1999) investigate oil futures and spot market volatility. Sanders, Boris, and Manfredo (2004) examine the relationship between the positions of commercial and noncommercial traders and prices in energy markets. There is a large body of GA3 work in the computer science and engineering fields but little work has been done concerning economics related areas. Latterly, there has been a growing interest in GA use in financial economics, but so far there has been little research concerning automated trading. To our knowledge the first published paper linking genetic algorithms to investments was from Bauer and Liepins (1992). Bauer (1994) in his book ‘‘Genetic Algorithms and Investment strategies” offered practical guidance concerning how GAs might be used to develop attractive trading strategies based on fundamental information. These techniques can be easily extended to include other types of information such as technical and macroeconomic data as well as past prices. According to Allen and Karjalainen (1999), genetic algorithm is an appropriate method to discover technical trading rules. Fernández-Rodrı´guez, González-Martel, and Sosvilla-Rivero (2001) by adopting genetic algorithms optimization in a simple trading rule provide evidence for successful use of GAs from the Madrid Stock Exchange. Some other interested studies are those by Mahfoud and Mani (1996) that presented a new genetic algorithm based system and applied it to the task of predicting the future performances of individual stocks; by Neely, Weller, and Ditmar (1997) that applied genetic programming to foreign exchange forecasting and reported some success.

3. Modelling using GMDH neural networks

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yi ¼ f ðxi1 ; xi2 ; xi3 ; . . . ; xin Þ ði ¼ 1; 2 . . . ; MÞ:

It is now possible to train a GMDH-type neural network to predict ^i for any given input vector X = (xi1, xi2, xi3 ,. . . , xin), the output values y that is

^i ¼ ^f ðxi1 ; xi2 ; xi3 ; . . . ; xin Þ ði ¼ 1; 2 . . . ; MÞ: y

The problem is now to determine a GMDH-type neural network so that the square of difference between the actual output and the predicted one is minimised, that is M X ½^f ðxi1 ; xi2 ; xi3 ; . . . ; xin Þ  yi 2 ! min : i¼1

General connection between inputs and output variables can be expressed by a complicated discrete form of the Volterra functional series in the form of

y ¼ a0 þ

i¼1

Genetic algorithm.

ai xi þ

n X n X i¼1

aij xi xj þ

j¼1

n X n X n X i¼1

aijk xi xj xk þ   

ð1Þ

j¼1 k¼1

Which is known as the Kolmogorov–Gabor polynomial (Farlow, 1984; Iba, deGaris, & Sato, 1996; Ivakhnenko, 1971; Nariman-Zadeh, Darvizeh, & Ahmad-Zadeh, 2003; Sanchez, Shibata, & Zadeh, 1997). This full form of mathematical description can be represented by a system of partial quadratic polynomials consisting of only two variables (neurons) in the form of

^ ¼ Gðxi ; xj Þ ¼ a0 þ a1 xi þ a2 xj þ a3 xi xj þ a4 x2i þ a5 x2j : y

ð2Þ

In this way, such partial quadratic description is recursively used in a network of connected neurons to build the general mathematical relation of inputs and output variables given in Eq. (1). The coefficient ai in Eq. (2) are calculated using regression techniques (Farlow, 1984; Nariman-Zadeh et al., 2003) so that the difference between ^, for each pair of xi, xj as actual output, y, and the calculated one, y input variables is minimized. Indeed, it can be seen that a tree of polynomials is constructed using the quadratic form given in Eq. (2) whose coefficients are obtained in a least-squares sense. In this way, the coefficients of each quadratic function Gi are obtained to optimally fit the output in the whole set of input–output data pair, that is

PM 3

n X

E¼

 Gi ðÞÞ2 ! min : M

i¼1 ðyi

ð3Þ

M. Mehrara et al. / Expert Systems with Applications 36 (2009) 7479–7483

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In the basic form of the GMDH algorithm, all the possibilities of two independent variables out of total n input variables are taken in order to construct the regression polynomial in the form of Eq. (2) that best fits the dependent observations (yi,i = 1, 2, . . . , M) in a   n ¼ nðn1Þ neurons will be least-squares sense. Consequently, 2 2 built up in the first hidden layer of the feedforward network from the observations {(yi, xip, xiq); (i = 1, 2 . . . , M)} for different p, q 2 {1, 2, . . . , n}. In other words, it is now possible to construct M data triples {(yi, xip, xiq); (i = 1, 2. . . , M)} from observation using such p,q 2 {1, 2, . . . , n} in the form

hidden nodes and a direct connection between the lagged moving average crossovers and return. The price data are NYMEX crude oil futures contracts obtained from EIA.4 Observations are the daily nearby oil futures contract prices. Predicted prices from the model are compared with the actual prices for January 1, 2003 through December 31, 2007. Prices are converted to returns using the daily difference in the logs of the prices.

2

In addition to the GMDH model, three benchmark models are used for comparison purposes. The first benchmark model, referred to as the buy-and-hold [BH] model, simply assumes that the nearby contract is purchased and rolled over as a new contract month becomes the nearby contract. The second benchmark model [TA for ‘‘twenty-day average”] is a simple moving average crossover model where a long position is established when the price exceeds the 20-day moving average by one standard deviation, and a short position is taken when the price is at least one standard deviation below the 20-day moving average. This second model has been popular with technical analysts, who believe it has the ability to capture and profit from trending markets. The third model [RW for ‘‘random walk”] incorporates a naïve trading rule based on the current day’s movement. If the price is above the previous day’s closing price, the trader goes long. If the price is below the previous day’s price, the trader goes short. The BH model is a useful yardstick because it allows comparisons with other models on a very primitive level. It is likely that inflation, shrinking reserves and increasing demand will lead to long-run increases in oil prices. Oil companies exploit this by buying or leasing and holding underground reserves. Because of storage costs and the availability of refining profits the buy and hold strategy is not as popular for aboveground oil holdings. Presumably, excess profits generated from this strategy would reflect the relative risk of the strategy. In an efficient market risk-adjusted excess profits generated from other strategies would be expected to be similar. We use the TA model as a benchmark because it is representative of a broad category of technical trading models that have been in use over the years. Such models are all based on rules using moving averages of recent prices. A typical moving average is simply the sum of the closing prices for the last n number of days divided by n, where n may be from 1 to 200 days. Some traders prefer more sophisticated moving average tools like exponentially or geometrically smoothed moving averages. The rules for using these tools are very similar and usually involve making a decision when a short-term average crosses over a long-term average. For example, the rule may be to buy when the 5-day moving average exceeds the 50-day moving average and to sell when the 5-day average is below the 50-day average. To minimize false starts and whipsaw reversals, many traders use a no-trade or no-reversal band around the long-term moving average whereby a trade is initiated only when the short-term average lies outside the band. The RW model is used as a benchmark because it is the most basic representative of linear data generating processes. The model assumes that the best predictor of tomorrow’s return is today’s return. In all of the models except TA, the trader always has a position and the position is assumed to be taken at the close of the day based on information obtained up to and including that point. We further assume that there are no transaction costs. These assumptions are, of course, unrealistic on several counts. There

6 4 x2p xMp

x1q x2q xMq

3

y1

7 y2 5: yM

Aa ¼ Y;

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Using the quadratic sub-expression in the form of Eq. (2) for each row of M data triples, the following matrix equation can be readily obtained as

where a is the vector of unknown coefficients of the quadratic polynomial in Eq. (2)

a ¼ fa0 ; a1 ; a2 ; a3 ; a4 ; a5 g;

ð4Þ

and

Y ¼ fy1 ; y2 ; y3 ; . . . ; yM gT ;

is the vector of output’s value from observation. It can be readily seen that

2

1 x1p 6 A¼6 4 1 x2p 1 xMp

x1q

x1p x1q

x21p

x2q

x2p x2q

x22p

xMq

xMp xMq

x2Mp

x21q

3

7 x22q 7 5: 2 xMq

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The least-squares technique from multiple-regression analysis leads to the solution of the normal equations in the form of

a ¼ ðAT AÞ1 AT Y;

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x1p

4. Other trading strategies

ð5Þ

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which determines the vector of the best coefficients of the quadratic Eq. (2) for the whole set of M data triples. It should be noted that this procedure is repeated for each neuron of the next hidden layer according to the connectivity topology of the network. However, such a solution directly from normal equations is rather susceptible to round off errors and, more importantly, to the singularity of these equations. Our approach is to construct a GMDH neural network model using a technical analysis rule as an input. We assume that technical analysis rules may have merit because there may be exploitable patterns which can result in profitability. The patterns may not be identifiable by traditional means but may be uncovered by the pattern recognition capabilities of GMDH neural networks. Empirical evidence of profitability will be confirmation of this approach and evidence of inefficiencies in the crude oil futures market. As input variables to the neural network, we use five lags of the 5- and 50-day moving average crossover. Moving average crossovers have long been used as buy–sell signals for trend-following trading systems. The assumption that a short-term moving average is higher than a long-term moving average indicates that prices are trending higher, thus signaling an uptrend. The opposite case signals a downtrend. First we use the neural network with moving average crossover inputs to forecast what will happen to futures prices. A long position is taken when prices are predicted to be higher, and a short position when prices are predicted to be lower. Then profitability is calculated from actual returns based on these positions. For tractability, we utilize a neural network with two

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Energy Information Administration.

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M. Mehrara et al. / Expert Systems with Applications 36 (2009) 7479–7483 Table 3 Statistical comparisons 2003–2007

Description

Strategy Take a long position if forecast from the network is that price will increase; take a short position if forecast is that price will decrease Go long and continuously roll position over Take a long position if price exceeds the 20-day moving average by one standard deviation; take a short position if price is at least one standard deviation below the 20-day moving average Take a long position if price is above previous day’s price; take a short position if price is below previous day’s price Measure equal to change in log price of 90-day Treasury bill

Group method of data handling

Inputs to the network are the differences between the 5- and the 50-day moving average of price (1–5 lags)

BH

Buy and hold rule Technical analysis rule

Assumes price will always increase Conventional moving average crossover rule

RW

Random walk rule

Na trading rule

T-bill

90-day Treasury bill

Risk-free rate

TA

are always transaction costs and one cannot be guaranteed the settlement price. In fact, it would be unusual to receive very many executions exactly at the settlement price. Also, there would be many occasions where market action would preclude being able to make decisions at or near the close. Therefore, the GMDH, TA and RW models are likely to be strongly biased toward showing greater profitability than is possible in actual trading. Table 1, below summarizes the artificial neural network given in Section 3 as well as the benchmark trading strategies discussed in this section.

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5. Empirical results

Average daily return (%) Standard deviation Coefficient of variation Sharpe ratio t-Statistic Correct (%) a

TA

BH

RW

T-bill

0.23 0.0282 12.09 0.0775 2.34a 64.4

0.13 0.0229 17.61 0.0503 1.60 63.2

0.10 0.0189 19.48 0.0435 1.45 52

0.04 0.0092 20.82 0.0641 1.24 47.7

0.01 0.0017 11.51 NA 2.45* NA

Significant at 5% level.

through January 22, 2007 as a bear market. During this time period, oil prices decline from over $77 per barrel to about $50 per barrel. The period from January 22, 2007 through December 31, 2007 is defined as a bull market. The bull market saw prices rose from about $50 to over $96. As might be expected, the BH model does very well in the bull market, with a return of 65%. But the BH model does very poorly in the bear market, losing 37%. The TA model gains, while the RW one loses in both periods. The GMDH model is profitable in both markets and more profitable than TA. Although the gains of the GMDH model during the bull period are lower than those of BH, the GMDH model more than makes up for the shortfall during the bear period. Over the entire market cycle, the GMDH model returns approximately 80% while the BH strategy returns approximately 30%. In sum, GMDH has the best overall return with no losing years and consistently good returns over an entire market cycle. But the strategy does not necessarily deliver the best returns for each period. It is a mistake, however, to try to compare returns from different strategies based on profitability alone. It is important to compare these returns as they relate to risk. Table 3 offers some additional means of comparison. In Table 3 the average daily returns from the trading strategies and T-bills (all in percent) for the 5 years under examination are presented. All other strategies are dominated by the GMDH model’s 0.23%. The nearest competitor, TA, returned slightly more than half of those profits. RW bring up the rear with returns of 0.04 per day. However, a key factor in comparing returns is the volatility of the returns. Volatility is typically measured using the standard deviation of the returns. From Table 3 it can be seen that the volatility of the returns generated by GMDH and TA are similar and quite high relative to T-bill and RW. But, a popular statistic for measuring comparative risk/reward is the coefficient of variation [CV], defined as the standard deviation divided by the average return. A low CV is indicative of small risk, while a high CV indicates high risk. The CV of about 12 for the GMDH strategy rivals that of the ‘‘risk-free” T-bill, indicating a very low relative risk associated with the strategy. The other strategies have relatively high risk associated with their returns, with coefficients of approximately 17–20. Another popular method of comparing returns relative to risk is the Sharpe ratio, defined as the ratio of excess return (investment return less risk-free return) divided by standard deviation. Here we use the 90-day T-bill rate as the risk-free return. The Sharpe ratio for the GMDH return, about 0.08, is higher than those of the other returns, indicating that GMDH produces much better return for risk than the other strategies.

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GMDH

GMDH

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Table 1 Summary of trading strategies

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Trading signals from the four models are used to generate daily profit and loss expressed as percent returns. Table 2 summarizes the returns for each strategy. With cumulative returns of over 290% over a 5-year period, the GMDH model generates much better overall returns than the other models. Cumulative returns for the TA and BH models are slightly more than 160% and 120%, respectively, with cumulative returns of 18% on a Treasury bill. During the same time period, the cumulative return for the RW model is just 55%. When profitability is examined on a year-to-year basis, benchmark models all have at least one losing year. In contrast, the GMDH model is a profitable strategy for each of the 5 years. In all of the year-to-year comparisons, the GMDH model is also more profitable than any of the other models. While the cumulative and year-to-year performances of the GMDH model are impressive, it is also useful to compare the relative performances of the models in time periods when prices were generally falling (bear market) or generally rising (bull market). Using historical prices, we define the period from July 14, 2006

Table 2 Comparison of profitability

Period Period Period Period Period

return return return return return

GMDH BH TA RW T-bill

2003

2004

2005

2006

2007

Bear

Bull

Cumulative

0.6858 0.0414 0.4312 0.0373 0.0103

0.7629 0.2587 0.5738 0.1711 0.0314

0.4633 0.3710 0.1855 0.1122 0.0302

0.3955 0.0456 0.2543 0.0373 0.0463

0.6088 0.5875 0.5514 0.1952 0.0664

0.2502 0.3727 0.2298 0.1370 0.0243

0.5614 0.6511 0.4821 0.1823 0.0617

2.9163 1.2130 1.6252 0.5532 0.1846

M. Mehrara et al. / Expert Systems with Applications 36 (2009) 7479–7483

Opportunity cost (%)

% Correct

Overall return

0.005 0.010 0.015

76.58 78.81 82.64

2.36 1.29 1.25

References Allen, F., & Karjalainen, R. (1999). Using genetic algorithms to find technical trading rules. Journal of Financial Economic, 51, 245–271. Bauer, R. J. (1994). Genetic algorithms and investment strategies. New York: John Wiley & Sons Inc. Bauer, R. J., & Liepins, G. E. (1992). Genetic algorithms and computerized trading strategies. In D. E. O’Leary & P. R. Watkins (Eds.), Expert systems in finance. Amsterdam, The Netherlands: Elsevier Science Publishers. Brock, W. A., Lakonishok, J., & LeBaron, B. (1992). Simple technical trading rules and the stochastic properties of stock returns. Journal of Finance, 47, 1731–1764. Campbell, J., Lo, A., & MacKinlay, A. C. (1997). The econometrics of financial markets. Princeton, NJ: Princeton University Press. DeBondt, W., & Thaler, R. (1985). Does the stock market overreact? Journal of Finance, 40(3), 793–805. Fama, E. (1970). Efficient capital markets: A review of theory and empirical work. Journal of Finance, 25, 383–417. Farlow, S. J. (Ed.). (1984). Self-organizing method in modelling: GMDH type algorithm. MarcelDekker Inc.. Fernández-Rodrı´guez, F., González-Martel, C., & Sosvilla-Rivero, S. (2001). Optimisation of technical rules by genetic algorithms: Evidence from the Madrid stock market. Working Papers 2001-14, FEDEA. Fernandez-Rodriquez, F., Gonzalez-Martel, C., & Sosvilla-Rivero, S. (2000). On the profitability of technical trading rules based on artificial neural networks: Evidence from the Madrid stock market. Economics Letters, 69(1), 89–94. Fleming, J., & Ostdiek, B. (1999). The impact of energy derivatives on the crude oil market. Energy Economics, 21(2), 135–167. Franses, P. H., & van Griensven, K. (1997). Forecasting exchange rates using neural networks for technical trading rules. Studies in Nonlinear Dynamics and Econometrics, 2(4), 108–114. Gencay, R. (1996). Non-linear prediction of security returns with moving average rules. Journal of Forecasting, 15(3), 165–174. Gencay, R. (1998a). The predictability of security returns with simple technical trading rules. Journal of Empirical Finance, 5(4), 347–359. Gencay, R. (1998b). Optimization of technical trading strategies and the profitability in security markets. Economics Letters, 59(2), 249–254. Gencay, R. (1999). Linear, non-linear and essential foreign exchange rate prediction with simple technical trading rules. Journal of International Economics, 47(1), 91–107. Gencay, R., & Stengos, T. (1998). Moving average rules, volume and the predictability of security returns with feedforward networks. Journal of Forecasting, 17(5–6), 401–414. Gulen, G. S. (1998). Efficiency in the crude oil futures market. Journal of Energy Finance & Development, 3(1), 13–21. Hoyle (1898). The game in Wall Street, and how to play it successfully. Reprinted by Frazer Pub. Co., Flint Hill, Virginia, 1968. Iba, H., deGaris, H., & Sato, T. (1996). A numerical approach togenetic programming for system identification. Evolutionary Computation, 3(4), 417–452. Ivakhnenko, A. G. (1971). Polynomial theory of complex systems. IEEE Transactions on Systems Man and Cybernetics, SMC-1, 364–378. Mahfoud, S., & Mani, G. (1996). Financial forecasting using genetic algorithms. Journal of Applied Artificial Intelligence, 10(6), 543–565. Nariman-Zadeh, N., Darvizeh, A., & Ahmad-Zadeh, R. (2003). Hybrid genetic design of GMDH-type neural networks using singular value decomposition for modelling and prediction of the explosive cutting process. Proceedings of the I MECH E part B. Journal of Engineering Manufacture, 217, 779–790. Neely, C., Weller, P., & Ditmar, R. (1997). Is technical analysis in the foreign exchange market profitable? A genetic programming approach. In C. Dunis, & B. Rustem (Eds.), Proceedings, forecasting financial markets: Advances for exchange rates, interest rates and asset management. London. Neftci, S. N. (1991). Na trading rules in financial markets and Wiener–Kolmogorov prediction theory: A study of technical analysis. Journal of Business, 64, 549–571. Sanchez, E., Shibata, T., & Zadeh, L. A. (1997). Genetic algorithms and fuzzy logic systems. World Scientific. Sanders, D. R., Boris, K., & Manfredo, M. (2004). Energy Economics, 26(3), 425–445. Shleifer, A. (2000). Inefficient markets: An introduction to behavioral finance. Clarendon lectures. Oxford University Press. Shleifer, A., & Vishny, R. (1997). The limits of arbitrage. Journal of Finance, 52(1), 35–55. Times Newspapers Inc., September 20 (2004). Special report. Speculators hijack oil market. Trippi, R. R., & Turban, E. (Eds.). (1996). Neural networks in finance and investing. using artificial intelligence to improve real-world performance. BurrRidge, IL: Irwin Professional PublishingCo.

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6. Concluding remarks

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One criticism of previous studies comparing GMDH to alternative models is that no evidence of significance of returns had been presented. To address this, in Table 3 we present the t-statistic for the null hypothesis that average daily return equals zero for the overall 5-year period. GMDH and T-bills are the only strategies where the daily returns are significantly different from zero at the 5% level. In sixth row of Table 3 the percentage of correct trades is presented for each strategy. GMDH is correct 64% of the time, only slightly better than TAs 63%. The other two strategies are correct about half the time. This leads to the conclusion that, for GMDH, the successful trades produce more profits than the unsuccessful trades produce losses. To examine this we alter the trading rules somewhat to find out if we can improve on the percentage correct. The rule is altered such that trades are only initiated if the profit predicted by the GMDH model exceeds some arbitrary percent. This means that no trade is initiated if the opportunity cost is too high. When we set this opportunity cost parameter at 0.005%, the average daily T-bill return, the percentage of profitable trades indeed increases, but the overall profitability decreases. Percentage correct increases to 76%, but overall return drops to 236%. Table 4 contains comparisons of returns and percentage correct for three opportunity cost filters. Increasing the parameter consistently increases the percentage correct and decreases the overall return. This appears to occur because some of the trades that are eliminated turn out to be more profitable than predicted. Overall we find that GMDH dominates the other trading strategies examined. The risk/reward relationship for GMDH is similar to the T-bill. In fact, GMDH and the T-bill are the only strategies with significant returns.

non-linear, semiparametric means. A note of caution is warranted, however. Transaction costs and slippage may substantially reduce the returns available in actual trading from those found here.

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Table 4 Effect of opportunity cost filter trading rule on GMDH

Efficient market theory claims that current prices reflect the efficient use of all available information. Strictly speaking, if markets are efficient, exploitable historical price patterns should not exist. Technical analysis, on the other hand, depends upon the ability to identify patterns and profit from their repetition. GMDH neural networks are especially well-suited to identifying patterns and making predictions based on those patterns. In this paper, we trained an GMDH neural network model for nearby oil futures prices with technical analysis crossover rules as inputs. By contrasting this model with a buy-and-hold strategy, a traditional technical trading strategy, a naïve ‘‘random walk” strategy and the return on Treasury bills, we were able to show that superior returns are possible using the network. Overall returns, yearto-year returns, returns over a market cycle, and Sharpe ratios all favor the GMDH model by a large factor. Additionally, daily returns using the GMDH and TA models appear to be significantly different than zero, while the returns from the other models are not. All of this indicates that the oil futures market is not efficient in the Fama sense. The exploitable patterns are not obvious and are difficult to detect using conventional linear models, but can be found using

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