Forecasting Economic Time Series with Artificial Neural Networks

Transcription

1 Forecasting Economic Time Series with Artificial Neural Networks Özgür Polat * Abstract Economic policy makers are responsible for making decisions about economic variables without knowing future values of these economic variables. Uncertainty of future values of economic values causes crucial risks on decisions concerning future of whole nation given by economic policy makers. This study focuses on the use of ANNs in forecasting macroeconomic variables. For that purpose, CPI and PPI of Turkey for the period of 2000: :12 are used to forecast monthly data of year Forecasted values are compared with 2009 monthly actual values of CPI and PPI. APE for all months and MAPE for the year 2009 are calculated to evaluate ex post forecast performance of ANNs for macroeconomic variables. Results clearly indicate that ANNs provide an efficient and effective tool to forecast macroeconomic variables. APE of all months and MAPE of year 2009 of CPI and PPI are all far below 10% indicating high accuracy of ANN forecasts in macroeconomic time series. Keywords: Artificial Neural Networks, Economic Time Series, Forecasting Yapay Sinir Ağlari İle Ekonomik Zaman Serilerinin Tahmini Özet Ekonomi politikalarına karar vericiler, ekonomik değişkenlerin gelecekteki değerlerine ait bilgiler olmaksızın karar vermekten sorumludurlar. Bu değişkenlerin gelecekteki değerlerinin belirsizliği, karar vericilerin tüm ülkenin geleceğini ilgilendiren kararlarında önemli risklere neden olmaktadır. Bu çalışma, Yapay Sinir Ağlarının makroekonomik değişkenlerin tahmininde kullanılmasını araştırmaktadır. Bu amaçla, Türkiye nin 2000: :12 dönemine ait TÜFE ve ÜFE değerleri kullanılarak 2009 yılına ait aylık tahminler yapılmıştır. Tahmin edilen değerler, Yapay Sinir Ağlarının makroekonomik değişkenlerin tahmin edilmesindeki performansının değerlendirilmesi amacıyla 2009 yılında gerçekleşen aylık TÜFE ve ÜFE değerleri ile karşılaştırılmıştır. Sonuçlar, Yapay Sinir Ağlarının makroekonomik değişkenlerin tahmin edilmesinde etkili ve yeterli bir performansa sahip olduğuna işaret etmektedir. Tüm aylara ait mutlak yüzde sapma ve 2009 yılına ait ortalama mutlak yüzde sapma %10 un altında çıkarak, Yapay Sinir Ağlarının * Dicle University, Department of Economics, Diyarbakır, Turkey.

2 makroekonomik zaman serilerinin tahmininde başarılı tahmin sonuçlarını ortaya koyabileceğini göstermektedir. Anahtar Kelimeler: Yapay Sinir Ağları, Ekonomik Zaman Serisi, Öngörü Introduction Economic policy makers are responsible for making decisions about economic variables without knowing future values of these economic variables. Uncertainty of future values of economic values causes crucial risks on decisions concerning future of whole nation given by economic policy makers. The more future values of macroeconomic variables are forecasted precisely, the less macroeconomic decisions will include risks and the more policies will be successful. In this sense, economic forecasting is very important for economic planning and policy analysis. Economic forecasting has been focus of many researches in different perspectives, since forecasting of economic variables has a crucial and a prominent role in business decision-making, government policy analysis, and economic research (Ericsson, 2004). Linear estimation techniques like regression models are insufficient to analyze economic data, often nonlinear, thus an ANN based approach with superior ability to analyze nonlinearity in the data is very preferable to research economics and finance problems with nonlinear structure, noisy data and models with insufficient knowledge (Aminian et al., 2006). In the recent years, Artificial Neural Networks (ANNs) have gained rapid and vast popularity in the economic forecasting literature. Because of their flexibility, simplicity and demonstrated successes in many empirical applications, ANNs have been the focus of substantial attention as a possible technique for forecasting economic variables (Swanson and White, 1997). A short list of macroeconomic forecasting problems solved by ANNs includes commodity prices (Kohzadi et al., 1996), macroeconomic indices (Maasoumi et al., 1994), total industrial production (Chumacero, 2004), inflation (McNelis and McAdam 2004), Gross Domestic Product (Aminian et al., 2006; Swanson and White, 1997). The objective of this study is to investigate the forecast performance of ANNs in macroeconomic time series. For this purpose, 2009 monthly values of Consumer Price Index (CPI) and Producer Price Index (PPI) of Turkey are forecasted using ANN technique

3 by using data for the period of 2003: :12. The rest of the paper is organized as follows. In section 2 ANN modeling approach in forecasting time series is briefly discussed. Results of forecasting analysis are presented in section 3. Concluding remarks are gathered in section 4. Artificial Neural Networks A neural network is a massively parallel distributed processor made up of simple processing units, which has a natural propensity for storing experiential knowledge and making it available for use. It resembles brain in two respects: (1) knowledge is acquired by network from its environment through a learning process, (2) interneuron connection strengths, known as synaptic weights, are used to store the acquired knowledge. (Haykin, 2005). As a simulation of biological neurons, ANN systems are composed of a number of neurons (Zhang et al., 1998), which are interconnected data process unit (Haykin, 2005). An ANN analyzes and models the data through learning process in which every neuron receives an input from environment or from other neurons, processes it through a summing or/and activation function and sends a transformed output to other neurons or external outputs. This information processing capability enables ANNs a strength computational device and capable to learn from examples and then generalize to examples never seen before (Zhang et al., 1998). Output of a neuron can be formulated as below: n f ( wij xi j ) o (1) i where x i, w, β j and o represent inputs (or output of another neuron), weights, bias and output, respectively. Interconnection of neurons is defined by architecture of ANNs. There are three layers in a multi-layer network: an input layer, hidden layer(s), and an output layer. Data is processed throughout this network only in one direction, beginning from the input layer towards the output layer (Coakley and Brown, 2000). Learning process in ANN can be viewed as problem of updating weights so that a network can efficiently perform its task (Jain et al, 1996). ANNs conduct a dynamic programming approach using learning algorithm to iteratively adjust the weights until the error between target and output of the network is minimized (Coakley and Brown, 2000). Weights chosen at randomly at the beginning of the learning process are adjusted using learning algorithm in order to minimize network error. During the learning process, smaller learning rates tend to slow down learning process, while larger ones tend to cause network oscillation in the weight space (Zhang et al., 1998).

4 Quick propagation algorithm used in this study is a modified back-propagation algorithm developed to speed up the learning process of ANN. Quick propagation algorithm adjust all weights computing the change in the connections (weights) between neurons i and j at iteration k in the network as (Soltane et al., 2004): w where and ( k 1) E ( k) w ( k 1) (2) w ( k) w represent the learning coefficient and the weight change in the immediately preceding iteration respectively. is the momentum coefficient and can be formulate as: ( E / w E / w ( k) (3) ( k 1)) ( E / w ( k) where E is the sum of squared differences between desired and actual values of the output neurons and can be define as: 1 E 2 ( y dj y j ) (4) 2 j where y dj is the desired value of output neuron j and y j is the actual output of neuron j (Soltane et al., 2004). Forecasting Results In this study, CPI and PPI with base year 2003 of Turkey are forecasted and compared with actual values by using 2000: :12 monthly data compiled from web site of TURKSTAT. Since 2003 based values of CPI and PPI start from 2003:01, a standardized CPI and PPI are used in this study extending data back to 2000:01 using 1994 based indices. Standardized CPI and PPI series are presented in Figure 1. Forecasting computations are done using NeuralPower 2.5 program.

5 Jan-00 Jun-00 Nov-00 Apr-01 Sep-01 Feb-02 Jul-02 Dec-02 May-03 Oct-03 Mar-04 Aug-04 Jan-05 Jun-05 Nov-05 Apr-06 Sep-06 Feb-07 Jul-07 Dec-07 May-08 Oct-08 Figure 1: CPI and PPI of Turkey CPI PPI In this study, Feed Forward Network model with four inputs of lagged values of CPI and PPI (t-12, t-24, t-36, t-48), two hidden layers and Quick Propagation algorithm are used. Data between 2000:01 and 2008:12 are used as training and data between 2009:01 and 2009:12 are used to test performance of forecasted data to evaluate ex-post forecasting. Data are normalized between [-1 1] in input and output layers, and hyperbolic tangent activation function is used in both input and output layers. Since more satisfactory results are obtained, logarithmic and first difference transformation applied to data. Architecture or ANN used for forecasting CPI and PPI can be written as [ ] and [ ] respectively. Number of hidden layers and number of nodes in the hidden layers are determined heuristically according to speed of the networks in minimizing network error. Networks are trained until they reached a RMSE of 0,00001.

6 Absolute percentage error (APE) and Mean Absolute Percentage Error (MAPE) are calculated for assessment of forecasting results of ANNs, given by the equations: APE Y P Y t t (5) t n 1 Yt Pt MAPE.100 (6) n Y t 1 t where Y is the observed value, P is forecasted value, n is number of observation and t is time. Table 1 MAPE Criteria for the Assessment of a Model MAPE (%) Classification of the Forecasts <10 High Accuracy Good Accuracy Reasonable Accuracy >50 Unreliable Assessments of ANNs forecasts are based on MAPE classification proposed by Lewis (1982) cited from Fernandes et al. (2008) presented in the Table 1. Values of real CPI and PPI, forecasted values of CPI and PPI using ANNs for the year 2009, APE and MAPE values are presented in Table 2. According to criteria presented in Table 1, APE and MAPE of all months are quite lower than 10% for two series indicating high accuracy of forecasts. Table 2: Forecasting accuracy of series Months CPI Real Value ANN APE Real Value ANN APE January February March April May June July August September October November December PPI

7 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec MAPE In Figure 2, real values of CPI and PPI and forecasted values for two series using ANN are presented respectively. As can be seen in figures, graphs of CPI and PPI are very close to their forecasted values, especially almost same in some months. Figure 2: Comparison of real and forecasted values CPI ANN Conclusion This study focus on the use of ANNs in forecasting macroeconomic variables. For that purpose, CPI and PPI of Turkey for the period of 2000: :12 are used to forecast monthly data of year Forecasted values are compared with 2009 monthly actual values of CPI and PPI. APE for all months and MAPE for the year 2009 are calculated to evaluate ex post forecast performance of ANNs for macroeconomic variables. Results clearly indicate that ANNs provide an efficient and effective tool to forecast macroeconomic variables. APE of all months and MAPE of year 2009 of CPI and PPI are all far below 10 indicating high accuracy of ANN forecasts in macroeconomic time series. References AMINIAN, Farzan, SUAREZ, E.Dante, AMINIAN, Mehran and WALZ, Daniel T. (2006) Forecasting Economic Data with Neural Networks, Computational Economics, 28,

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