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Nowcasting GDP in Greece: The impact of data revisions and forecast origin on model selection and performance
The Journal of Economic Asymmetries ∎ (∎∎∎∎) ∎∎∎–∎∎∎
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Nowcasting GDP in Greece: The impact of data revisions and forecast origin on model selection and performance Dimitra Lamprou Department of Economics, School of Management and Economics, University of Peloponnese, Tripolis Campus, 22100, Greece
a r t i c l e i n f o
abstract
Article history: Received 27 June 2016 Accepted 25 July 2016
In this paper we consider ways to forecast and nowcast the evolution of the growth rate of the Greek Real Gross Domestic Product (GDP). We explore information in more timely indicators that are available at a higher frequency to improve the forecast of quarterly output growth and, more importantly, examine the effect of data revisions in model selection. In our analysis we focus on three kinds of models, benchmarks, bridge models and factor analysis models trying to understand the effect that the crisis had on both data, informational content of explanatory variables and predictive ability of various models. Our results suggest that not only do we observed large changes in the informational content due to data revisions but the models with highest predictive ability are varying based on both the predictive variables being used and the point in time of the forecast origin. It is therefore important to consider an array of models when nowcasting, especially under periods of higher volatility and data revisions, as in the case of Greece. & 2016 Published by Elsevier B.V.
JEL classification: C52 C53 E01 E27 Keywords: Nowcasting GDP Data revisions Greece
1. Introduction In policy institutions such as Central Banks, business, government, financial markets and others, nowcasting GDP growth is an important task to inform decision makers about the current state of the economy. Nowcast models typically consider specific data irregularities: whereas GDP is sampled at quarterly frequency and with a considerable delay only, many business cycle indicators are available at a higher frequency and more timely, for example, monthly industrial production or high-frequency financial data. The accuracy of such quarterly or lower frequency forecasts can thus have important repercussions on the policy measures taken. GDP is, however, only available on a quarterly basis. In addition, first official estimations are only published after a time span of 2 or 3 months (around 45 days or later after the end of the reference quarter for the main European countries) and these first GDP estimations are often revised significantly. The aim of this paper is to highlight the importance of the data revisions and changes in information content of predictive variables in nowcasting the Greek Real Growth Rate, by exploiting the particular structure of data on the Greek economy. Greek data are released routinely since 2000 that makes our data sample quite limited. Our work is potentially interesting because of the examination we make for the problems of the data themselves and the importance of growth assessments and forecasts during and after the context of the deep fiscal crisis faced by the Greek economy. Nowcasting is a relatively new method whose main advantage is the use of new information as it comes in, and the generation of updates at a higher frequency than the frequency of observation of the variable of interest. Until recently, nowcasting had received very little attention in the academic literature, although it was routinely conducted in policy E-mail address: [email protected] http://dx.doi.org/10.1016/j.jeca.2016.07.006 1703-4949/& 2016 Published by Elsevier B.V.
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institutions either through a judgmental process or on the basis of simple models. It was first introduced by Evans (2005) for a limited number of time series and evolved by Giannone, Reichlin, and Small (2008) for a larger number of series to produce real-time GDP estimates, combining the idea of linking high-frequency indicators to low-frequency GDP data and the idea of using real-time data within a single statistical framework. In recent years, there have been many applications of this method for several countries and variables thus enhancing and expanding this methodology. For example, Lahiri and Monokroussos (2013) in the United States, who study the role of survey data in nowcasting; Angelini, Camba-Mendez, Giannone, Reichlin, and Rünstler (2011); Banbura and Rünstler (2011); Camacho and Perez-Quiros (2010), in the euro area; Barhoumi, Darné, and Ferrara (2010) in France, who compare several factor extraction techniques; Marcellino and Schumacher (2008) in Germany, who proposed an approach that combines mixed-data sampling techniques with a factor model; D’Agostino, McQuinn, and O’Brien (2008) in Ireland, Yiu and Chow (2010) in China using a large data set, Urasawa (2014) in Japan and Bragoli, Metelli, and Modugno (2014) in Brazil . The current literature has provided several general findings which indicate a clear gain from developing a model to early assess the ongoing economic activities. A statistical model that does not include a judgment process performs as well as institutional forecasts that are allowed to incorporate their own judgment. Thus, nowcasting becomes progressively more accurate toward the end of the quarter, when the amount of relevant information increases, and timely data —which by definition are more promptly available— tend to improve forecast performance. In addition, exercises using factor models have been implemented in several institutions, including the European Central Bank (ECB, 2008) and the International Monetary Fund (Matheson, 2011). Until recently, the approach used to obtain an early estimate of GDP was based on judgment combined with simple models called Bridge Models (BM), Baffigi, Golinelli, and Parigi (2004). BM are essentially regressions relating quarterly GDP growth to one or a few monthly variables aggregated to quarterly frequency. Since, only partial monthly information is available for the target quarter, the monthly variables are forecasted using auxiliary models. In order to exploit information from several monthly predictors BM are sometimes pooled, Kitchen and Monaco (2003). To the best of our knowledge, Banerjee, Marcellino, and Masten (2005), Banerjee and Marcellino (2006), Antipa, Barhoumi, Brunhes-Lesage, and Darne (2012) are the only studies that compare the forecasting performance of the automatically selected BM and the DFMs – for Eurozone, US and German GDP growth, respectively. These studies, however, only use factor models following Stock and Watson (2002a), (2002b), for which results are not conclusive in favor of one or the other. In order to have better forecasts, factor models have proved to be a very useful tool for short-term forecasting of real activity. The use of dynamic factor models (DFM) has been further improved by recent advances in estimation techniques proposed by Stock and Watson (2002a), (2002b), Forni, Hallin, Lippi, and Reichlin (2003) or Giannone et al. (2008), who have put forward the advances in estimation techniques that allow improving their efficiency. This type of model is particularly appealing as it can be applied to large data sets as by Angelini et al. (2011), Barhoumi et al. (2010), Schumacher and Breitung (2008). The DFMs are based on static and dynamic principal components. The static principal components are obtained as in Stock and Watson (2002a), (2002b). The dynamic principal components are based on either time domain methods, as in Doz, Giannone and Reichlin (2011, 2012), or frequency domain methods, as in Forni et al. (2003). DFMs have so far never been used for forecasting Greek GDP growth rates. Unlike DFMs, Time Series Factor Analysis (TSFA) Gilbert and Meijer (2005) obviates the need for explicitly modeling the process dynamics of the underlying phenomena. It also differs from standard factor models (FM) in important respects: the factor model has a non-trivial mean structure, the observations are allowed to be dependent over time, and the data does not need to be covariance stationary as long as differenced data satisfies a weak boundedness condition. TSFA is suitable for a relatively small number of series and therefore relies on somewhat stronger model assumptions. TSFA is useful when measurement and modeling are being used simultaneously, because specific assumptions about factor dynamics are usually much more fragile than the assumption that factors exist. What is important to note is that TSFA is very well suited for the data used in this paper. The rest of the paper is organized as follows. In Section 2, we give a summary of the data set used in our paper, in Section 3, a brief presentation of the bridge and TSFA models. In Section 4, we discuss the results of our forecasting analysis and Section 5 offers some concluding remarks for future research.
2. Data set Our dependent variable is obtained from the, seasonally adjusted, quarterly real GDP series expressed as annual growth rate. As explanatory variables we consider the quarterly Gross Capital Formation (GCF), the Gross Fixed Capital Formation (GFCF) and the Exports (EXP) and the monthly economic activity indicators, namely the index of industrial production (IPI), the total turnover of retail sales (RSTOT) and the volume of retail sales (RSVOL). All variables are from seasonally adjusted indices and expressed in real terms as annual growth rates. Additionally, we used aggregation of the variables (A-IPI, A-RSTOT, A-RSVOL) using the average of the three months of the quarter. All variables are obtained from the Greek Statistical Authority website (www.statistics.gr) and we consider two vintage series, a first and second revision from 2013 data, and the latest release as of the time of writing of this paper from 2015.
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The industrial production index is a well-known business cycle indicator which measures monthly changes in the priceadjusted output of industry. The industrial production index is one of the most important short-term statistics indicators. It is used to identify turning points in the economic development at an early stage and to assess the future development of GDP. It is available on a monthly basis in a detailed activity breakdown and with a rather short delay little more than one month. Total turnover of retail sales (RSTOT) is the objective of the turnover index to show the development of the market for goods and services. Comprises the totals invoiced by the observation unit during the reference period, and this corresponds to market sales of goods or services supplied to third parties. Turnover also includes all other charges (transport, packaging, etc.) passed on to the customer, even if these charges are listed separately in the invoice. It excludes VAT and other similar deductible taxes directly linked to turnover as well as all duties and taxes on the goods or services invoiced by the unit. The volume of sales (RSVOL) represents the value of turnover in constant prices and as such is a quantity index. It is normally calculated as turnover at current prices, deflated by the deflator of sales. While turnover shows sales in current prices, the volume of sales indicates the situation once price changes have been removed. The index of the volume of retail trade is a business indicator which measures the monthly changes of the deflated turnover of retail trade. Trade volume data are available on a monthly basis, in working-day adjusted and seasonally adjusted form, in our example we used the second one. Gross capital formation (GCF) is measured by the total value of the gross fixed capital formation, changes in inventories and acquisitions less disposals of valuables for a unit or sector. Gross fixed capital formation (GFCF) consists of resident producers’ acquisitions, less disposals, of fixed assets during a given period plus certain additions to the value of nonproduced assets realised by the productive activity of producer or institutional units. GFCF includes acquisition less disposals of, e.g. buildings, structures, machinery and equipment, mineral exploration, computer software, literary or artistic originals and major improvements to land such as the clearance of forests. Exports (EXP) consist of transactions in goods and services (sales, barter, gifts or grants) from residents to non-residents. An export of a good occurs when there is a change of ownership from a resident to a non-resident. Change of ownership does not necessarily imply that the good in question physically crosses the frontier. If goods cross the border due to financial leasing, as deliveries between affiliates of the same enterprise or for significant processing to order or repair national accounts impute a change of ownership even though in legal terms no change of ownership takes place. Export of services consists of all services rendered by residents to non-residents. Any direct purchases by non-residents in the economic territory of a country are recorded as exports of services; therefore all expenditure by foreign tourists in the economic territory of a country is considered as part of the exports of services of that country. Real GDP Gross Capital formation, Gross Fixed Capital formation and exports are available in quarterly basis and released three to six weeks after the end of the quarter of examination. 2.1. Analysis of data used in our models To make things specific, we used three different data sets. The first two are from January 2000 until December 2013 (Table 1) this is due to a data revision made by the Greek Statistical Authority one month after the original publication of the data in September 2014. These datasets include the quarterly variable of Real GDP the index of industrial production (IPI), the total turnover of retail sales (RSTOT) and the volume of retail sales (RSVOL). The data set 3 contains data from January 2000 until Jun 2015 (Table 2) gathered in November 2015. In this data set we obtained three more variables than the previous data sets the Gross Capital Formation (GCF), the Gross Fixed Capital Formation (GFCF) and the Exports (EXP). We present some descriptive statistics for Data Set 3 in Table 3, for the full sample we have. The Real GDP Growth rate varies from 0.046 at the first quarter of 2009, which is the trough, to the peak 0.033 at the first quarter of 2006. Note that, because of the crisis, the growth rate is negatively skewed but has kurtosis close to 3. It also has medium first order autocorrelation. The IPI in every lag has a negative autocorrelation and on the contrast the RSTOT has a positive one. The volume of retail sales on March 2008 presents the highest price and April 2013 the lowest and has kurtosis over than 3 and negative skewness.
Table 1 Data series used in our analysis—Data Set 1 and 2.Source: ELSTAT Data series
Full-sample period
Data collection period/ reporting frequency
Number of observations with reporting lag of 1 month or quarter
RGDP IPI RSVOL RSTOT
1Q 2000 4Q 2013 Jan 2000 - Dec 2013 Jan 2000- Dec 2013 Jan 2000 - Dec 2013
Quarterly Monthly Monthly Monthly
56 168
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Number of observations with reporting lag of 2 months
168 168
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Table 2 Data series used in our analysis—Data Set 3.Source: ELSTAT Data series
Full-sample period
Data collection period/ reporting frequency
Number of observations with reporting lag of 1 month or quarter
RGDP GCF GFCF EXP IPI RSVOL RSTOT
1Q 2000 2Q 2015 1Q 2000 2Q 2015 1Q 2000 2Q 2015 1Q 2000 2Q 2015 Jan 2000-Jun 2015 Jan 2000-Jun 2015 Jan 2000-Jun 2015
Quarterly Quarterly Quarterly Quarterly Monthly Monthly Monthly
62 62 62 62 186
Number of observations with reporting lag of 2 months
186 186
We split the data into a training period up to 2007 and use the post-crisis data as our evaluation period. To examine robustness, we then proceed to move the training period up to 2008 and 2009, particularly for seeing whether the post crisis period provides us with different models than when including in our evaluation period the 2008 observations. An important point we should make is that we use our data aligned correctly and taking account of release lags. This is important for making the exercise realistic. For example, we always use a two-month lag on the aligned monthly data: if we are at the end of the 4th quarter we use monthly data for October. So, if the real GDP for the 4th quarter is released, for example, in mid-February and the monthly variable is released in November or December we always use past data correctly in producing the forecasts.
.
3. Bridge and TSFA models 3.1. Bridge models The general specification of a bridge model is that of an autoregressive-distributed-lag (ARDL) for q explanatory variables and is given as follows: m
Yt = a +
q
k
∑ βiYt − i + ∑ ∑ δj, iXj, t −1 + εt i=1
j=1 i=1
where m is the number of autoregressive parameters, q is the number of explanatory variables, and k is the number of lags for the explanatory variables. Note that under the restriction that now monthly variables appear above, we see that the equation collapses to a standard autoregression – which thus becomes the natural benchmark to compare forecasting performance. In our analysis we consider models that use each monthly variable, a pair of monthly variables and all three monthly variables together, all the previous combinations aggregated and factor analysis. These models are benchmarked against an AR(1) model and an AR(AIC) model. 3.2. TSFA models The factors k for a sample of T time periods will be indicated by ξit, t ¼1,…, T, i¼1,…, k. The indicators M will be denoted by yit, t¼1,…, T, i¼1,…, M. The factors and indicators for period t are collected in the vectors ξt and yt , respectively. It is assumed there is a measurement model relating the indicators to the factors given by:
yt = α + Bξt + εt Please cite this article as: Lamprou, D. (2016), http://dx.doi.org/10.1016/j.jeca.2016.07.006i
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Table 3 Summary of statistics — Data Set 3.
RGDP GCF GFCF EXP RSTOT (0) RSTOT ( 1) RSTOT ( 2) RSVOL (0) RSVOL ( 1) RSVOL ( 2) IPI (0) IPI ( 1) IPI ( 2)
Average
Std. Dev.
Min
Max
Skewness
Kurtosis
ACF, lag 1
0,0001 0,0083 0,0099 0,0047 0,0036 0,0038 0,0040 0,0022 0,0021 0,0018 0,0053 0,0050 0,0049
0,0162 0,1122 0,0728 0,0463 0,0371 0,0345 0,0315 0,0385 0,0330 0,0323 0,0298 0,0339 0,0280
0,0329 0,3275 0,1634 0,1096 0,0924 0,1052 0,0456 0,1011 0,0884 0,0402 0,0532 0,0819 0,0729
0,3592 0,0219 0,1236 0,2569 0,8136 0,2344 1,2559 0,4576 0,8386 1,1688 0,1872 0,2246 0,2026
3,0717 3,7839 2,8013 3,7781 5,0531 3,9694 4,1758 4,6890 5,7582 3,5453 2,6257 3,1759 3,0030
0,3798 0,2117 0,0597 0,0705 0,0225 0,1640 0,0538 0,1333 0,2944 0,0648 0,4088 0,4812 0,3647
0,0465 0,2952 0,1814 0,1430 0,1249 0,1012 0,0995 0,1102 0,1261 0,0870 0,0777 0,0870 0,0738
The variables (0),( 1)( 2) refer to the growth rates of the current month, the previous and two months back, respectively.
where α is an M-vector of intercept parameters, B is an M k matrix parameter of factor loadings or simply loadings, and εt is a random M-vector of measurement errors, disturbances, and unique or idiosyncratic factors. This is a standard FA model except that indicators are indexed by time and intercepts are explicitly included, whereas in FA means are usually subtracted. A slightly more general variant of the previous equation is:
yt = at + Bξt + εt where at is a possibly time-varying intercept vector, but loadings are assumed time-invariant. Many time series integrate of order 1 so the variances of the indicators increase with time. This violates assumptions for standard estimators where parameters are constant and moments converge in probability to finite limits (Wansbeek and Meijer, 2000). In order to find the most suitable models we run for every one of the three data sets 24 models making all possible combinations changing the frequency from year-on-year, Y-o-Y, to quarter-on-quarter, Q-o-Q (F), the back month (M) to use for two months and five months, the maximum autoregressive lag (L) and three different choices of principal components (C) used by the TSFA. We narrowed down the best 5 models for each data set for the purposes of presentation and further understanding.
4. Discussion of results To evaluate our forecasting results, and considering the relatively short evaluation we have, we use the standard measures of mean squared error and mean absolute error of each variable or combination of them, expressed in ratios over the benchmark models AR(1) and AR(AIC). Additional results on tests of predictive ability (Diebold & Mariano, 1995) tests and predictive (Mincer-Zarnowitz type) regressions are also available on request. 4.1. Forecasting results for Data Set 1 The Data Sets 1 and 2, as mentioned before, include the first and second revision of the data from Q1 2000 to Q4 2013 for the three monthly variables of IPI, RSTOT, RSVOL. After applying all the 24 different combination of models in data set 1 we concluded that most models perform better with Q-o-Q frequency. The factor analysis performs better than the rest of the variables when the number of the principal components is 2 and 2 lags. As it can be seen in Table 4 the impact on changing the frequency and the components from 2 to 6 the best Table 4 Forecasting results Data Set 1 for the Top 5 Models. Training Period Ends 31/12/2007
A-IPI ALL 3 FA A-RSVOL A-RSVOL
AR (1)-bench-greece-2013-rev1
AR (AIC)-bench-greece-2013-rev1
Top 5 Performing Combinations
RMSE
MAE
RMSE
MAE
F
M
L
C
1,0429 11.544 1,1366 1,1546 1,1493
1,0859 1,1235 1,1821 1,1526 1,1021
1,0505 1,1628 1,0762 1,0474 1,0882
1,1055 1,1438 1,1386 1,0378 1,0616
Y-o-Y Y-o-Y Q-o-Q Q-o-Q Q-o-Q
2 5 5 2 2
2 4 2 4 2
2 6 2 2 6
Frequency (F), the back month (M), the maximum autoregressive lag (L) and principal components (C)
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performing model is changing from A-IPI to A-RSVOL. A-RSVOL is the best performing model when the back month set to 2 both in the combinations of 4 lags and 2 components and 2 lags and 6 components. Finally, the model performing better in Y-o-Y frequency with back month set to 5 and the principal components are set to 6 is that of the combination of the three variables together followed by the A-IPI. 4.2. Forecasting results for Data Set 2 While examining the results of the second data set, we came up with the following Table 5. The use of 5 back months, on Y-o-Y frequency shows the combination of the three variables perform better with the combination RSVOL&IPI following. The A-RSVOL performs better in Q-o-Q frequency and two principal components in FA. In contrast with results of the first data set the FA underperforms in all cases. In both data sets 1 & 2 on Y-o-Y frequency, back month 5, 4 lags and 6 components the combination of the IPI, RSVOL and RSTOT perform better than the rest.
Table 5 Forecasting results Data Set 2 for the Top 5 Models. Training Period Ends 31/12/2007
ALL 3 ALL 3 A-RSVOL A-RSVOL A-RSVOL
AR (1)–bench-greece-2013-rev2
AR (AIC)–bench-greece-2013-rev2
Top 5 Performing Combinations
RMSE
MAE
RMSE
MAE
F
M
L
C
1,1508 1,1518 1,1433 1,1468 1,1433
1,1372 1,1308 1,1786 1,1400 1,1786
1,1508 1,1602 1,0826 1,0404 1,0826
1,1372 1,1512 1,1353 1,0264 1,1353
Y-o-Y Y-o-Y Q-o-Q Q-o-Q Q-o-Q
5 5 5 5 5
2 4 2 4 2
6 6 2 2 6
Frequency (F), the back month (M), the maximum autoregressive lag (L) and principal components (C)
4.3. Forecasting results for Data Set 3 The third data set includes data from Q1 2000 to Q2 2015. The best performance is that of the FA while the frequency is Q-o-Q and the principal components are set to 6. As it can be seen in Table 6 the values of the forecasting results on Q-o-Q frequency, 2 lags and 2 components is better for the RSVOL. On Q-o-Q frequency with back month 5 and 4 lags we can see that by changing the number of the principal components from 6 to 8 we can see that the best performing model changes from the FA to the combination of the three variables. Moreover, in change of frequency to Y-o-Y with 2 components the IPI model distinguishes. We have to mention than when the number of the components are set to 8, on Q-o-Q frequency with back month 5 and 2 lags the combination of RSVOL with the IPI is performing better than the other variables.
Table 6 Forecasting results Data Set 3 for the Top 5 Models. Training Period Ends 31/12/2007
IPI RSVOL FA ALL 3 RSVOL&IPI
AR (1)–bench-greece-2015
AR (AIC)–bench-greece-2015
Top 5 Performing Combinations
RMSE
MAE
RMSE
MAE
F
M
L
C
0,9205 1,0911 1,0189 0,7814 1,0964
0,9605 1,128 0,991 0,7586 1,1162
1,0346 1,0087 1,3445 1,0311 1,0136
1,0148 0,9928 1,4121 1,0810 0,9824
Y-o-Y Q-o-Q Q-o-Q Q-o-Q Q-o-Q
5 5 5 5 5
4 2 4 4 2
2 2 6 8 8
Frequency (F), the back month (M), the maximum autoregressive lag (L) and principal components (C)
We have to highlight that on the one hand the FA performs better in the third data set but on the other hand applying the models on the second revision data the FA underperforms in most combinations. As mentioned before we have split the data into a training period up to 2007 and use the post-crisis data as our evaluation period. By changing the training period and splitting the data firstly up to 2008 and secondly up to 2009.
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In order to examine robustness we then proceed to move the training period up to 2008 and 2009, particularly for seeing whether the post crisis period provides us with different models than when including in our evaluation period the 2008 observations. In Table 7 we can see that the same combinations perform better. After 2009 there is a trending growth which makes it natural that the models regain their predicting ability. It probably means that in periods of trending growth and lower volatility we need to use more information in terms of back month, lags and numbers of components. The IPI and RSVOL are directly infected by the crisis.
Table 7 Forecasting result by changing the training period. Training Period Ends 31/12/2008
AR (1)-bench-greece-2015
AR (AIC)-bench-greece-2015
Top 5 Performing Combinations
RMSE
MAE
RMSE
MAE
F
M
N
C
IPI RSVOL FA ALL 3 RSVOL&IPI
0,9012 1,1203 1,2086 0,8809 1,1257
0,9563 1,1786 1,1945 1,0163 1,1596
1,0241 1,027 1,2486 0,9101 1,0319
0,9932 1,0164 1,1486 0,9773 1,0001
Y-o-Y Q-o-Q Q-o-Q Q-o-Q Q-o-Q
5 5 5 5 5
4 2 4 4 2
2 2 6 8 8
Training Period Ends31/12/2009
AR(1)-bench-greece-2015 RMSE MAE 0,7954 0,9289 1,1661 1,2604 1,4897 1,4181 0,8735 1,1374 1,2518 1,2525
IPI RSVOL FA ALL 3 RSVOL&IPI
AR(AIC)-bench-greece-2015 RMSE MAE 1,0536 1,0664 1,0098 1,0290 1,4148 1,1466 0,8296 0,9195 1,0840 1,0226
Top 5 Performing Combinations F M N C Y-o-Y 5 4 2 Q-o-Q 5 2 2 Q-o-Q 5 4 6 Q-o-Q 5 4 8 Q-o-Q 5 2 8
5. Concluding remarks In the preceding analysis we have presented the use of Bridge Models and Time Series Factor Analysis in order to nowcast the GDP growth rate of Greece. Obviously, revisions must be therefore considered an important issue. We highlighted the importance of them and the changes in information content of predictive variables in nowcasting the Greek real growth rate, by exploiting the particular structure of data on the Greek economy. Exercises to evaluate the performance of factor models in the presence of data revisions are still relatively scarce, with the exceptions of Schumacher and Breitung (2008) for Germany, Camacho and Perez-Quiros (2010) for the euro area, and Bańbura et al. (2013) and Lahiri and Monokroussos (2013) for the US. Moreover, we found that it is possible to get reasonably good estimates of current quarterly GDP growth in anticipation of the official release. We considered three data sets, two vintage series, a first and second revision from 2013 data, and the latest release as of the time of writing of this paper from 2015. Comparing 24 different models for every data set varying by frequency, back month, lags and components for each data set gave us a multitude of results. Our results suggest that not only do we observed large changes in the informational content due to data revisions but the models with highest predictive ability are varying based on both the predictive variables being used and the point in time of the forecast origin. We concluded that it is important to consider an array of models when nowcasting, especially under periods of higher volatility and data revisions, as in the case of Greece.
Appendix A See Fig. A1.
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Fig. A1. Graphs of each time series in comparison with the Real GDP Growth.
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Fig. A1. (continued)
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Nowcasting GDP in Greece: The impact of data revisions and forecast origin on model selection and performance Dimitra Lamprou Department of Economics, School of Management and Economics, University of Peloponnese, Tripolis Campus, 22100, Greece
a r t i c l e i n f o
abstract
Article history: Received 27 June 2016 Accepted 25 July 2016
In this paper we consider ways to forecast and nowcast the evolution of the growth rate of the Greek Real Gross Domestic Product (GDP). We explore information in more timely indicators that are available at a higher frequency to improve the forecast of quarterly output growth and, more importantly, examine the effect of data revisions in model selection. In our analysis we focus on three kinds of models, benchmarks, bridge models and factor analysis models trying to understand the effect that the crisis had on both data, informational content of explanatory variables and predictive ability of various models. Our results suggest that not only do we observed large changes in the informational content due to data revisions but the models with highest predictive ability are varying based on both the predictive variables being used and the point in time of the forecast origin. It is therefore important to consider an array of models when nowcasting, especially under periods of higher volatility and data revisions, as in the case of Greece. & 2016 Published by Elsevier B.V.
JEL classification: C52 C53 E01 E27 Keywords: Nowcasting GDP Data revisions Greece
1. Introduction In policy institutions such as Central Banks, business, government, financial markets and others, nowcasting GDP growth is an important task to inform decision makers about the current state of the economy. Nowcast models typically consider specific data irregularities: whereas GDP is sampled at quarterly frequency and with a considerable delay only, many business cycle indicators are available at a higher frequency and more timely, for example, monthly industrial production or high-frequency financial data. The accuracy of such quarterly or lower frequency forecasts can thus have important repercussions on the policy measures taken. GDP is, however, only available on a quarterly basis. In addition, first official estimations are only published after a time span of 2 or 3 months (around 45 days or later after the end of the reference quarter for the main European countries) and these first GDP estimations are often revised significantly. The aim of this paper is to highlight the importance of the data revisions and changes in information content of predictive variables in nowcasting the Greek Real Growth Rate, by exploiting the particular structure of data on the Greek economy. Greek data are released routinely since 2000 that makes our data sample quite limited. Our work is potentially interesting because of the examination we make for the problems of the data themselves and the importance of growth assessments and forecasts during and after the context of the deep fiscal crisis faced by the Greek economy. Nowcasting is a relatively new method whose main advantage is the use of new information as it comes in, and the generation of updates at a higher frequency than the frequency of observation of the variable of interest. Until recently, nowcasting had received very little attention in the academic literature, although it was routinely conducted in policy E-mail address: [email protected] http://dx.doi.org/10.1016/j.jeca.2016.07.006 1703-4949/& 2016 Published by Elsevier B.V.
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institutions either through a judgmental process or on the basis of simple models. It was first introduced by Evans (2005) for a limited number of time series and evolved by Giannone, Reichlin, and Small (2008) for a larger number of series to produce real-time GDP estimates, combining the idea of linking high-frequency indicators to low-frequency GDP data and the idea of using real-time data within a single statistical framework. In recent years, there have been many applications of this method for several countries and variables thus enhancing and expanding this methodology. For example, Lahiri and Monokroussos (2013) in the United States, who study the role of survey data in nowcasting; Angelini, Camba-Mendez, Giannone, Reichlin, and Rünstler (2011); Banbura and Rünstler (2011); Camacho and Perez-Quiros (2010), in the euro area; Barhoumi, Darné, and Ferrara (2010) in France, who compare several factor extraction techniques; Marcellino and Schumacher (2008) in Germany, who proposed an approach that combines mixed-data sampling techniques with a factor model; D’Agostino, McQuinn, and O’Brien (2008) in Ireland, Yiu and Chow (2010) in China using a large data set, Urasawa (2014) in Japan and Bragoli, Metelli, and Modugno (2014) in Brazil . The current literature has provided several general findings which indicate a clear gain from developing a model to early assess the ongoing economic activities. A statistical model that does not include a judgment process performs as well as institutional forecasts that are allowed to incorporate their own judgment. Thus, nowcasting becomes progressively more accurate toward the end of the quarter, when the amount of relevant information increases, and timely data —which by definition are more promptly available— tend to improve forecast performance. In addition, exercises using factor models have been implemented in several institutions, including the European Central Bank (ECB, 2008) and the International Monetary Fund (Matheson, 2011). Until recently, the approach used to obtain an early estimate of GDP was based on judgment combined with simple models called Bridge Models (BM), Baffigi, Golinelli, and Parigi (2004). BM are essentially regressions relating quarterly GDP growth to one or a few monthly variables aggregated to quarterly frequency. Since, only partial monthly information is available for the target quarter, the monthly variables are forecasted using auxiliary models. In order to exploit information from several monthly predictors BM are sometimes pooled, Kitchen and Monaco (2003). To the best of our knowledge, Banerjee, Marcellino, and Masten (2005), Banerjee and Marcellino (2006), Antipa, Barhoumi, Brunhes-Lesage, and Darne (2012) are the only studies that compare the forecasting performance of the automatically selected BM and the DFMs – for Eurozone, US and German GDP growth, respectively. These studies, however, only use factor models following Stock and Watson (2002a), (2002b), for which results are not conclusive in favor of one or the other. In order to have better forecasts, factor models have proved to be a very useful tool for short-term forecasting of real activity. The use of dynamic factor models (DFM) has been further improved by recent advances in estimation techniques proposed by Stock and Watson (2002a), (2002b), Forni, Hallin, Lippi, and Reichlin (2003) or Giannone et al. (2008), who have put forward the advances in estimation techniques that allow improving their efficiency. This type of model is particularly appealing as it can be applied to large data sets as by Angelini et al. (2011), Barhoumi et al. (2010), Schumacher and Breitung (2008). The DFMs are based on static and dynamic principal components. The static principal components are obtained as in Stock and Watson (2002a), (2002b). The dynamic principal components are based on either time domain methods, as in Doz, Giannone and Reichlin (2011, 2012), or frequency domain methods, as in Forni et al. (2003). DFMs have so far never been used for forecasting Greek GDP growth rates. Unlike DFMs, Time Series Factor Analysis (TSFA) Gilbert and Meijer (2005) obviates the need for explicitly modeling the process dynamics of the underlying phenomena. It also differs from standard factor models (FM) in important respects: the factor model has a non-trivial mean structure, the observations are allowed to be dependent over time, and the data does not need to be covariance stationary as long as differenced data satisfies a weak boundedness condition. TSFA is suitable for a relatively small number of series and therefore relies on somewhat stronger model assumptions. TSFA is useful when measurement and modeling are being used simultaneously, because specific assumptions about factor dynamics are usually much more fragile than the assumption that factors exist. What is important to note is that TSFA is very well suited for the data used in this paper. The rest of the paper is organized as follows. In Section 2, we give a summary of the data set used in our paper, in Section 3, a brief presentation of the bridge and TSFA models. In Section 4, we discuss the results of our forecasting analysis and Section 5 offers some concluding remarks for future research.
2. Data set Our dependent variable is obtained from the, seasonally adjusted, quarterly real GDP series expressed as annual growth rate. As explanatory variables we consider the quarterly Gross Capital Formation (GCF), the Gross Fixed Capital Formation (GFCF) and the Exports (EXP) and the monthly economic activity indicators, namely the index of industrial production (IPI), the total turnover of retail sales (RSTOT) and the volume of retail sales (RSVOL). All variables are from seasonally adjusted indices and expressed in real terms as annual growth rates. Additionally, we used aggregation of the variables (A-IPI, A-RSTOT, A-RSVOL) using the average of the three months of the quarter. All variables are obtained from the Greek Statistical Authority website (www.statistics.gr) and we consider two vintage series, a first and second revision from 2013 data, and the latest release as of the time of writing of this paper from 2015.
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The industrial production index is a well-known business cycle indicator which measures monthly changes in the priceadjusted output of industry. The industrial production index is one of the most important short-term statistics indicators. It is used to identify turning points in the economic development at an early stage and to assess the future development of GDP. It is available on a monthly basis in a detailed activity breakdown and with a rather short delay little more than one month. Total turnover of retail sales (RSTOT) is the objective of the turnover index to show the development of the market for goods and services. Comprises the totals invoiced by the observation unit during the reference period, and this corresponds to market sales of goods or services supplied to third parties. Turnover also includes all other charges (transport, packaging, etc.) passed on to the customer, even if these charges are listed separately in the invoice. It excludes VAT and other similar deductible taxes directly linked to turnover as well as all duties and taxes on the goods or services invoiced by the unit. The volume of sales (RSVOL) represents the value of turnover in constant prices and as such is a quantity index. It is normally calculated as turnover at current prices, deflated by the deflator of sales. While turnover shows sales in current prices, the volume of sales indicates the situation once price changes have been removed. The index of the volume of retail trade is a business indicator which measures the monthly changes of the deflated turnover of retail trade. Trade volume data are available on a monthly basis, in working-day adjusted and seasonally adjusted form, in our example we used the second one. Gross capital formation (GCF) is measured by the total value of the gross fixed capital formation, changes in inventories and acquisitions less disposals of valuables for a unit or sector. Gross fixed capital formation (GFCF) consists of resident producers’ acquisitions, less disposals, of fixed assets during a given period plus certain additions to the value of nonproduced assets realised by the productive activity of producer or institutional units. GFCF includes acquisition less disposals of, e.g. buildings, structures, machinery and equipment, mineral exploration, computer software, literary or artistic originals and major improvements to land such as the clearance of forests. Exports (EXP) consist of transactions in goods and services (sales, barter, gifts or grants) from residents to non-residents. An export of a good occurs when there is a change of ownership from a resident to a non-resident. Change of ownership does not necessarily imply that the good in question physically crosses the frontier. If goods cross the border due to financial leasing, as deliveries between affiliates of the same enterprise or for significant processing to order or repair national accounts impute a change of ownership even though in legal terms no change of ownership takes place. Export of services consists of all services rendered by residents to non-residents. Any direct purchases by non-residents in the economic territory of a country are recorded as exports of services; therefore all expenditure by foreign tourists in the economic territory of a country is considered as part of the exports of services of that country. Real GDP Gross Capital formation, Gross Fixed Capital formation and exports are available in quarterly basis and released three to six weeks after the end of the quarter of examination. 2.1. Analysis of data used in our models To make things specific, we used three different data sets. The first two are from January 2000 until December 2013 (Table 1) this is due to a data revision made by the Greek Statistical Authority one month after the original publication of the data in September 2014. These datasets include the quarterly variable of Real GDP the index of industrial production (IPI), the total turnover of retail sales (RSTOT) and the volume of retail sales (RSVOL). The data set 3 contains data from January 2000 until Jun 2015 (Table 2) gathered in November 2015. In this data set we obtained three more variables than the previous data sets the Gross Capital Formation (GCF), the Gross Fixed Capital Formation (GFCF) and the Exports (EXP). We present some descriptive statistics for Data Set 3 in Table 3, for the full sample we have. The Real GDP Growth rate varies from 0.046 at the first quarter of 2009, which is the trough, to the peak 0.033 at the first quarter of 2006. Note that, because of the crisis, the growth rate is negatively skewed but has kurtosis close to 3. It also has medium first order autocorrelation. The IPI in every lag has a negative autocorrelation and on the contrast the RSTOT has a positive one. The volume of retail sales on March 2008 presents the highest price and April 2013 the lowest and has kurtosis over than 3 and negative skewness.
Table 1 Data series used in our analysis—Data Set 1 and 2.Source: ELSTAT Data series
Full-sample period
Data collection period/ reporting frequency
Number of observations with reporting lag of 1 month or quarter
RGDP IPI RSVOL RSTOT
1Q 2000 4Q 2013 Jan 2000 - Dec 2013 Jan 2000- Dec 2013 Jan 2000 - Dec 2013
Quarterly Monthly Monthly Monthly
56 168
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Number of observations with reporting lag of 2 months
168 168
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Table 2 Data series used in our analysis—Data Set 3.Source: ELSTAT Data series
Full-sample period
Data collection period/ reporting frequency
Number of observations with reporting lag of 1 month or quarter
RGDP GCF GFCF EXP IPI RSVOL RSTOT
1Q 2000 2Q 2015 1Q 2000 2Q 2015 1Q 2000 2Q 2015 1Q 2000 2Q 2015 Jan 2000-Jun 2015 Jan 2000-Jun 2015 Jan 2000-Jun 2015
Quarterly Quarterly Quarterly Quarterly Monthly Monthly Monthly
62 62 62 62 186
Number of observations with reporting lag of 2 months
186 186
We split the data into a training period up to 2007 and use the post-crisis data as our evaluation period. To examine robustness, we then proceed to move the training period up to 2008 and 2009, particularly for seeing whether the post crisis period provides us with different models than when including in our evaluation period the 2008 observations. An important point we should make is that we use our data aligned correctly and taking account of release lags. This is important for making the exercise realistic. For example, we always use a two-month lag on the aligned monthly data: if we are at the end of the 4th quarter we use monthly data for October. So, if the real GDP for the 4th quarter is released, for example, in mid-February and the monthly variable is released in November or December we always use past data correctly in producing the forecasts.
.
3. Bridge and TSFA models 3.1. Bridge models The general specification of a bridge model is that of an autoregressive-distributed-lag (ARDL) for q explanatory variables and is given as follows: m
Yt = a +
q
k
∑ βiYt − i + ∑ ∑ δj, iXj, t −1 + εt i=1
j=1 i=1
where m is the number of autoregressive parameters, q is the number of explanatory variables, and k is the number of lags for the explanatory variables. Note that under the restriction that now monthly variables appear above, we see that the equation collapses to a standard autoregression – which thus becomes the natural benchmark to compare forecasting performance. In our analysis we consider models that use each monthly variable, a pair of monthly variables and all three monthly variables together, all the previous combinations aggregated and factor analysis. These models are benchmarked against an AR(1) model and an AR(AIC) model. 3.2. TSFA models The factors k for a sample of T time periods will be indicated by ξit, t ¼1,…, T, i¼1,…, k. The indicators M will be denoted by yit, t¼1,…, T, i¼1,…, M. The factors and indicators for period t are collected in the vectors ξt and yt , respectively. It is assumed there is a measurement model relating the indicators to the factors given by:
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Table 3 Summary of statistics — Data Set 3.
RGDP GCF GFCF EXP RSTOT (0) RSTOT ( 1) RSTOT ( 2) RSVOL (0) RSVOL ( 1) RSVOL ( 2) IPI (0) IPI ( 1) IPI ( 2)
Average
Std. Dev.
Min
Max
Skewness
Kurtosis
ACF, lag 1
0,0001 0,0083 0,0099 0,0047 0,0036 0,0038 0,0040 0,0022 0,0021 0,0018 0,0053 0,0050 0,0049
0,0162 0,1122 0,0728 0,0463 0,0371 0,0345 0,0315 0,0385 0,0330 0,0323 0,0298 0,0339 0,0280
0,0329 0,3275 0,1634 0,1096 0,0924 0,1052 0,0456 0,1011 0,0884 0,0402 0,0532 0,0819 0,0729
0,3592 0,0219 0,1236 0,2569 0,8136 0,2344 1,2559 0,4576 0,8386 1,1688 0,1872 0,2246 0,2026
3,0717 3,7839 2,8013 3,7781 5,0531 3,9694 4,1758 4,6890 5,7582 3,5453 2,6257 3,1759 3,0030
0,3798 0,2117 0,0597 0,0705 0,0225 0,1640 0,0538 0,1333 0,2944 0,0648 0,4088 0,4812 0,3647
0,0465 0,2952 0,1814 0,1430 0,1249 0,1012 0,0995 0,1102 0,1261 0,0870 0,0777 0,0870 0,0738
The variables (0),( 1)( 2) refer to the growth rates of the current month, the previous and two months back, respectively.
where α is an M-vector of intercept parameters, B is an M k matrix parameter of factor loadings or simply loadings, and εt is a random M-vector of measurement errors, disturbances, and unique or idiosyncratic factors. This is a standard FA model except that indicators are indexed by time and intercepts are explicitly included, whereas in FA means are usually subtracted. A slightly more general variant of the previous equation is:
yt = at + Bξt + εt where at is a possibly time-varying intercept vector, but loadings are assumed time-invariant. Many time series integrate of order 1 so the variances of the indicators increase with time. This violates assumptions for standard estimators where parameters are constant and moments converge in probability to finite limits (Wansbeek and Meijer, 2000). In order to find the most suitable models we run for every one of the three data sets 24 models making all possible combinations changing the frequency from year-on-year, Y-o-Y, to quarter-on-quarter, Q-o-Q (F), the back month (M) to use for two months and five months, the maximum autoregressive lag (L) and three different choices of principal components (C) used by the TSFA. We narrowed down the best 5 models for each data set for the purposes of presentation and further understanding.
4. Discussion of results To evaluate our forecasting results, and considering the relatively short evaluation we have, we use the standard measures of mean squared error and mean absolute error of each variable or combination of them, expressed in ratios over the benchmark models AR(1) and AR(AIC). Additional results on tests of predictive ability (Diebold & Mariano, 1995) tests and predictive (Mincer-Zarnowitz type) regressions are also available on request. 4.1. Forecasting results for Data Set 1 The Data Sets 1 and 2, as mentioned before, include the first and second revision of the data from Q1 2000 to Q4 2013 for the three monthly variables of IPI, RSTOT, RSVOL. After applying all the 24 different combination of models in data set 1 we concluded that most models perform better with Q-o-Q frequency. The factor analysis performs better than the rest of the variables when the number of the principal components is 2 and 2 lags. As it can be seen in Table 4 the impact on changing the frequency and the components from 2 to 6 the best Table 4 Forecasting results Data Set 1 for the Top 5 Models. Training Period Ends 31/12/2007
A-IPI ALL 3 FA A-RSVOL A-RSVOL
AR (1)-bench-greece-2013-rev1
AR (AIC)-bench-greece-2013-rev1
Top 5 Performing Combinations
RMSE
MAE
RMSE
MAE
F
M
L
C
1,0429 11.544 1,1366 1,1546 1,1493
1,0859 1,1235 1,1821 1,1526 1,1021
1,0505 1,1628 1,0762 1,0474 1,0882
1,1055 1,1438 1,1386 1,0378 1,0616
Y-o-Y Y-o-Y Q-o-Q Q-o-Q Q-o-Q
2 5 5 2 2
2 4 2 4 2
2 6 2 2 6
Frequency (F), the back month (M), the maximum autoregressive lag (L) and principal components (C)
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performing model is changing from A-IPI to A-RSVOL. A-RSVOL is the best performing model when the back month set to 2 both in the combinations of 4 lags and 2 components and 2 lags and 6 components. Finally, the model performing better in Y-o-Y frequency with back month set to 5 and the principal components are set to 6 is that of the combination of the three variables together followed by the A-IPI. 4.2. Forecasting results for Data Set 2 While examining the results of the second data set, we came up with the following Table 5. The use of 5 back months, on Y-o-Y frequency shows the combination of the three variables perform better with the combination RSVOL&IPI following. The A-RSVOL performs better in Q-o-Q frequency and two principal components in FA. In contrast with results of the first data set the FA underperforms in all cases. In both data sets 1 & 2 on Y-o-Y frequency, back month 5, 4 lags and 6 components the combination of the IPI, RSVOL and RSTOT perform better than the rest.
Table 5 Forecasting results Data Set 2 for the Top 5 Models. Training Period Ends 31/12/2007
ALL 3 ALL 3 A-RSVOL A-RSVOL A-RSVOL
AR (1)–bench-greece-2013-rev2
AR (AIC)–bench-greece-2013-rev2
Top 5 Performing Combinations
RMSE
MAE
RMSE
MAE
F
M
L
C
1,1508 1,1518 1,1433 1,1468 1,1433
1,1372 1,1308 1,1786 1,1400 1,1786
1,1508 1,1602 1,0826 1,0404 1,0826
1,1372 1,1512 1,1353 1,0264 1,1353
Y-o-Y Y-o-Y Q-o-Q Q-o-Q Q-o-Q
5 5 5 5 5
2 4 2 4 2
6 6 2 2 6
Frequency (F), the back month (M), the maximum autoregressive lag (L) and principal components (C)
4.3. Forecasting results for Data Set 3 The third data set includes data from Q1 2000 to Q2 2015. The best performance is that of the FA while the frequency is Q-o-Q and the principal components are set to 6. As it can be seen in Table 6 the values of the forecasting results on Q-o-Q frequency, 2 lags and 2 components is better for the RSVOL. On Q-o-Q frequency with back month 5 and 4 lags we can see that by changing the number of the principal components from 6 to 8 we can see that the best performing model changes from the FA to the combination of the three variables. Moreover, in change of frequency to Y-o-Y with 2 components the IPI model distinguishes. We have to mention than when the number of the components are set to 8, on Q-o-Q frequency with back month 5 and 2 lags the combination of RSVOL with the IPI is performing better than the other variables.
Table 6 Forecasting results Data Set 3 for the Top 5 Models. Training Period Ends 31/12/2007
IPI RSVOL FA ALL 3 RSVOL&IPI
AR (1)–bench-greece-2015
AR (AIC)–bench-greece-2015
Top 5 Performing Combinations
RMSE
MAE
RMSE
MAE
F
M
L
C
0,9205 1,0911 1,0189 0,7814 1,0964
0,9605 1,128 0,991 0,7586 1,1162
1,0346 1,0087 1,3445 1,0311 1,0136
1,0148 0,9928 1,4121 1,0810 0,9824
Y-o-Y Q-o-Q Q-o-Q Q-o-Q Q-o-Q
5 5 5 5 5
4 2 4 4 2
2 2 6 8 8
Frequency (F), the back month (M), the maximum autoregressive lag (L) and principal components (C)
We have to highlight that on the one hand the FA performs better in the third data set but on the other hand applying the models on the second revision data the FA underperforms in most combinations. As mentioned before we have split the data into a training period up to 2007 and use the post-crisis data as our evaluation period. By changing the training period and splitting the data firstly up to 2008 and secondly up to 2009.
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7
In order to examine robustness we then proceed to move the training period up to 2008 and 2009, particularly for seeing whether the post crisis period provides us with different models than when including in our evaluation period the 2008 observations. In Table 7 we can see that the same combinations perform better. After 2009 there is a trending growth which makes it natural that the models regain their predicting ability. It probably means that in periods of trending growth and lower volatility we need to use more information in terms of back month, lags and numbers of components. The IPI and RSVOL are directly infected by the crisis.
Table 7 Forecasting result by changing the training period. Training Period Ends 31/12/2008
AR (1)-bench-greece-2015
AR (AIC)-bench-greece-2015
Top 5 Performing Combinations
RMSE
MAE
RMSE
MAE
F
M
N
C
IPI RSVOL FA ALL 3 RSVOL&IPI
0,9012 1,1203 1,2086 0,8809 1,1257
0,9563 1,1786 1,1945 1,0163 1,1596
1,0241 1,027 1,2486 0,9101 1,0319
0,9932 1,0164 1,1486 0,9773 1,0001
Y-o-Y Q-o-Q Q-o-Q Q-o-Q Q-o-Q
5 5 5 5 5
4 2 4 4 2
2 2 6 8 8
Training Period Ends31/12/2009
AR(1)-bench-greece-2015 RMSE MAE 0,7954 0,9289 1,1661 1,2604 1,4897 1,4181 0,8735 1,1374 1,2518 1,2525
IPI RSVOL FA ALL 3 RSVOL&IPI
AR(AIC)-bench-greece-2015 RMSE MAE 1,0536 1,0664 1,0098 1,0290 1,4148 1,1466 0,8296 0,9195 1,0840 1,0226
Top 5 Performing Combinations F M N C Y-o-Y 5 4 2 Q-o-Q 5 2 2 Q-o-Q 5 4 6 Q-o-Q 5 4 8 Q-o-Q 5 2 8
5. Concluding remarks In the preceding analysis we have presented the use of Bridge Models and Time Series Factor Analysis in order to nowcast the GDP growth rate of Greece. Obviously, revisions must be therefore considered an important issue. We highlighted the importance of them and the changes in information content of predictive variables in nowcasting the Greek real growth rate, by exploiting the particular structure of data on the Greek economy. Exercises to evaluate the performance of factor models in the presence of data revisions are still relatively scarce, with the exceptions of Schumacher and Breitung (2008) for Germany, Camacho and Perez-Quiros (2010) for the euro area, and Bańbura et al. (2013) and Lahiri and Monokroussos (2013) for the US. Moreover, we found that it is possible to get reasonably good estimates of current quarterly GDP growth in anticipation of the official release. We considered three data sets, two vintage series, a first and second revision from 2013 data, and the latest release as of the time of writing of this paper from 2015. Comparing 24 different models for every data set varying by frequency, back month, lags and components for each data set gave us a multitude of results. Our results suggest that not only do we observed large changes in the informational content due to data revisions but the models with highest predictive ability are varying based on both the predictive variables being used and the point in time of the forecast origin. We concluded that it is important to consider an array of models when nowcasting, especially under periods of higher volatility and data revisions, as in the case of Greece.
Appendix A See Fig. A1.
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Fig. A1. Graphs of each time series in comparison with the Real GDP Growth.
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Fig. A1. (continued)
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