Linear and nonlinear dynamic systems in financial time series prediction

Abstract: Autoregressive moving average (ARMA) process and dynamic neural networks namely the nonlinear autoregressive moving average with exogenous inputs (NARX) are compared by evaluating their ability to predict financial time series; for instance the S & P500 returns. Two classes of ARMA are considered. The first one is the standard ARMA model which is a linear static system. The second one uses Kalman filter (KF) to estimate and predict ARMA coefficients. This model is a linear dynamic system. The forecasting ability of each system is evaluated by means of mean absolute error (MAE) and mean absolute deviation (MAD) statistics. Simulation results indicate that the ARMA-KF system performs better than the standard ARMA alone. Thus, introducing dynamics into the ARMA process improves the forecasting accuracy. In addition, the ARMA-KF outperformed the NARX. This result may suggest that the linear component found in the S & P500 return series is more dominant than the nonlinear part. In sum, we conclude that introducing dynamics into the ARMA process provides an effective system for S & P500 time series prediction.

How to cite this paper

 Lahmiri, S. (2012). Linear and nonlinear dynamic systems in financial time series prediction.Management Science Letters , 2(7), 2551-2556.

Refrences

Arash, A., & Atry, F. (2009). Multi-step ahead forecasts for electricity prices using NARX: a new approach, a critical analysis of one-step ahead forecasts. Energy Conversion and Management, 50 (3), 739–747.

Awan, M.S.K., & Awais, M.M. (2011). Predicting weather events using fuzzy rule based system. Applied Soft Computing, 11, 56–63.

Box, G. E. P., & Jenkins, G. (1976). Time series analysis, forecasting and control. San Francisco: Holden-Day.

Castro-Neto, M., Jeong, Y.-S., Jeong, M.-K., & Han, L.D. (2009). Online-SVR for short-term traf?c ?ow prediction under typical and atypical traf?c conditions. Expert Systems with Applications, 36, 6164–6173.

Chen, K.Y., & Wang, C.H. (2007). A hybrid SARIMA and support vector machines in forecasting the production values of the machinery industry in Taiwan. Expert Systems with Applications, 32, 254–264.

Denton, J.W. (1995). How good are neural networks for causal forecasting? The Journal of Business Forecasting, 14 (2), 17–20.

Hagan, M.T., Demuth, H.B., & Beale, M.H. (1996). Neural Network Design. Boston: PWS Publishing.

Hann, T.H., & Steurer, E. (1996). Much ado about nothing? Exchange rate forecasting: neural networks vs. linear models using monthly and weekly data. Neurocomputing, 10, 323–339.

Harvey, A.C. (1993). Time Series Models. 2nd ed., Harvester Wheatsheaf, Hemel Hempstead.

Jin, M., Zhou, X., Zhang, Z.M., & Tentzeris, M.M. (2012). Short-term power load forecasting using grey correlation contest modeling. Expert Systems with Applications, 39, 773–779.

Kalman, R.E. (1960). A new approach to linear filtering and prediction problems. Trans ASME, Series D, Journal of Basic Engineering, 82, 35–45.

Khashei, M., & Bijari, M. (2011). A novel hybridization of artificial neural networks and ARIMA models for time series forecasting. Applied Soft Computing, 11, 2664–2675.

Khashei, M., & Bijari, M. (2012). A new class of hybrid models for time series forecasting. Expert Systems with Applications, 39, 4344–4357.

Khashei, M., Bijari, M. (2010). An artificial neural network (p,d,q) model for time series forecasting. Expert Systems with Applications, 37, 479–489.

Leontaritis, I.J., & Billings, S.A. (1985). Input–output parametric models for non-linear systems. Part I: Deterministic non-linear systems. International Journal of Control, 41 (2), 303–328.

Liu, C.-F., Yeh, C.-Y., & Lee, S.-J. (2012). Application of type-2 neuro-fuzzy modeling in stock price prediction. Applied Soft Computing, 12, 1348–1358.

Menezes, J.M.P., & Barreto, G.A, (2008). Long-term time series prediction with the NARX network: An empirical evaluation. Neurocomputing, 71, 3335–3343.

Mirmomeni, M., Lucas, C., Moshiri, B., & Araabi, B.N. (2010). Introducing adaptive neurofuzzy modeling with online learning method for prediction of time-varying solar and geomagnetic activity indices. Expert Systems with Applications, 37, 8267–8277.

Nasseri, M., Moeini, A., & Tabesh, M. (2011). Forecasting monthly urban water demand using Extended Kalman Filter and Genetic Programming. Expert Systems with Applications, 38, 7387–7395.

Niu, D., Liu, D., & Wu, D.D. (2010). A soft computing system for day-ahead electricity price forecasting. Applied Soft Computing, 10, 868–875.

Pai, P.F., & Lin, C.S. (2005). A hybrid ARIMA and support vector machines model in stock price forecasting. Omega, 33, 497–505.

Pham, H.T., Tran. V.T., & Yang, B.-S. (2010). A hybrid of nonlinear autoregressive model with exogenous input and autoregressive moving average model for long- term machine state forecasting. Expert Systems with Applications, 37 (4), 3310-3317.

Pisoni, E., Farina, M., Carnevale, C., & Piroddi, L. (2009). Forcasting peak air pollution levels using NARX models. Engineering Applications of Artificial Intelligence, 22, 593–602.

Taskaya, T., & Casey, M.C. (2005). A comparative study of autoregressive neural network hybrids, Neural Networks, 18, 781–789.

Tseng, F.M., Tzeng, G., Yu, H.C., & Yuana, B.J.C. (2001). Fuzzy ARIMA model for forecasting the foreign exchange market. Fuzzy Sets and Systems, 118, 9–19.

Zhang, G., Patuwo, B.E., & Hu, M.Y. (1998). Forecasting with artificial neural networks: the state of the art. International Journal of Forecasting, 14 (1), 35–62.

Zhang, G.P. (2003). Time series forecasting using a hybrid ARIMA and neural network model.
Neurocomputing, 50, 159–175.

Zhou, Z.J., & Hu, C.H. (2008). An effective hybrid approach based on grey and ARMA for forecasting gyro drift. Chaos. Solitons and Fractals, 35, 525–529.

Journals

MSL Volumes

Keywords

Authors

Countries

Management Science Letters

Linear and nonlinear dynamic systems in financial time series prediction Pages 2551-2556 Download PDF

Add Reviews