Forecasting Using Functional Coefficients Autoregressive Models

Bruno, Giancarlo (2008): Forecasting Using Functional Coefficients Autoregressive Models.

Abstract

The use of linear parametric models for forecasting economic time series is widespread among practitioners, in spite of the fact that there is a large evidence of the presence of non-linearities in many of such time series. However, the empirical results stemming from the use of non-linear models are not always as good as expected. This has been sometimes associated to the difficulty in correctly specifying a non-linear parametric model. I this paper I cope with this issue by using a more general non-parametric approach, which can be used both as a preliminary tool for aiding in specifying a suitable parametric model and as an autonomous modelling strategy. The results are promising, in that the non-parametric approach achieve a good forecasting record for a considerable number of series.

• Item Type: MPRA Paper
• Language: English
• Keywords: Non-linear time-series models; non-parametric models
• Subjects: C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C53 - Forecasting and Prediction Methods ; Simulation Methods; C - Mathematical and Quantitative Methods > C2 - Single Equation Models ; Single Variables > C22 - Time-Series Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes

References

Brock, W., Dechert, W., Scheinkman, J., and LeBaron, B. (1996). A test for independence based on the correlation dimension. Econometric Reviews, 15:197–235.

Brockwell, P. J. and Davis, R. A. (1991). Time Series: Theory and Methods. Springer, New York.

Cai, Z., Fan, J., and Li, R. (2000a). Efficient estimation and inferences for varying-coefficient models. Journal of the American Statistical Association, 95(451):888–902.

Cai, Z., Fan, J., and Yao, Q. (2000b). Functional-coefficient regression models for nonlinear time series. Journal of the American Statistical Association, 5(451):941– 956.

Chen, R. and Liu, L.-M. (2001). Functional coefficient autoregressive models: Estimation and tests of hypotheses. Journal of Time Series Analysis, 22(2):151–173.

Chen, R. and Tsay, R. S. (1993). Functional-coefficient autoregressive models. Journal of the American Statistical Association, 88(421):298–308.

Fan, J. and Gijbels, I. (1996). Local Polynomial Modeling and Its Applications. Chapman and Hall, London.

Fan, J. and Yao, Q. (2003). Nonlinear Time Series: Nonparametric and Parametric Methods. Springer, New York.

Fan, J., Yao, Q., and Cai, Z. (2003). Adaptive varying-coefficient linear models. Journal of the Royal Statistical Society. Series B (Statistical Methodology), 65(1):57–80.

Harvey, D. I., Leybourne, S. J., and Newbold, P. (1997). Tests the equality of prediction mean squared error. Internation Journal of Forecasting, 13:281–291.

Harvill, J. L. and Ray, B. K. (2005). A note on multi-step forecasting with functional coefficient autoregressive models. International Journal of Forecasting, 21:717–727.

Hyndman, R. J. (2009). fma: Data sets from "Forecasting: methods and applications" by Makridakis, Wheelwright & Hyndman (1998). R package version 2.00.

Lee, T., White, H., and Granger, C. (1993). Testing for neglected nonlinearity in time series models. Journal of Econometrics, 56:269–290.

Stock, J. H. and Watson, M. W. (1998). A comparison of linear and nonlinear univariate models for forecasting macroeconomic time series. NBER Working Pa- pers 6607, National Bureau of Economic Research, Inc.

Teräsvirta, T. (2006). Forecasting economic variables with nonlinear models. In Elliot, G., Granger, C. W., and Timmermann, A., editors, Handbook of Economic Forecasting, volume I, chapter 8, pages 413–57. Elsevier.

Teräsvirta, T., Lin, C., and Granger, C. (1993). Power of the neural network linearity test. Journal of Time Series Analysis, 14:209–220.

Teräsvirta, T., van Dijk, D., and Medeiros, M. C. (2005). Linear models, smooth transition autoregressions, and neural networks for forecasting macroeconomic time series: A re-examination. International Journal of Forecasting, 21(4):755–774.

Tsay, R. S. (1986). Nonlinearity tests for time series. Biometrika, 73(2):461–466.

Tschernig, R. and Yang, L. (2000). Nonparametric lag selection for time series. Journal of Time Series Analysis, 21(4):457–487.

Xia, Y. and Li, W. K. (1999a). On single-index coefficient regression models. Journal of the American Statistical Association, 94(448):1275–1285.

Xia, Y. and Li, W. K. (1999b). On the estimation and testing of functional-coefficient linear models. Statistica Sinica, 9:735–757.

Xia, Y., Li, W.-K., and Tong, H. (2007). Threshold variable selection using nonparametric methods. Statistica Sinica, 17.