NONLINEAR TIME SERIES MODELS PREDICTING AUTOREGRESSIVE

Year 2012, Issue: 28, 205 - 218, 01.12.2012

Öznur İşçi

Abstract

It is known that parametric and nonparametric methods are used for nonlinear time series. Of the parametric methods, autoregressive (AR) model and self-threshold value (SETAR) model and, of the nonparametric methods, additive regression model (ARM) have been used in this study. Nonparametric regression techniques are often sensitive to presence of otocorrelation in errors. Practical results of this sensitivity is explanied by appropriate selection of smoothing parameter. In this context, backfittting algorithm based on smoothing spline method in the existing literature is discussed. As an application, an appropriate model for the export unit value index data for Turkey is try to be determined by fitting each of AR, SETAR and, ARM models to the data.

Keywords

Time series, AR model, SETAR model, ARM model

DOĞRUSAL OLMAYAN OTOREGRESİF ZAMAN SERİLERİ MODELLERİNİN KESTİRİMİ

Abstract

Doğrusal olmayan zaman serileri için parametrik ve parametrik olmayan yöntemlerin kullanıldığı bilinmektedir. Bu çalışmada, parametrik yöntemlerden otoregresif (AR) ve kendinden eşik değerli (SETAR) modelleri, parametrik olmayan yöntemlerden ise toplamsal regresyon modeli (ARM) kullanılmıştır. Parametrik olmayan regresyon teknikleri hatalardaki otokorelasyonun varlığına genellikle duyarlıdırlar. Bu duyarlılığın pratik sonuçları düzeltme parametresinin uygun seçimiyle açıklanır. Bu bağlamda mevcut literatürdeki splayn düzeltme yöntemini esas alan backfitting algoritması incelenmiştir. Bu amaçla, Türkiye’deki ihracat birim değer endeks verisi, AR, SETAR ve ARM modelleri ile tahmin edilerek uygun model belirlenmeye çalışılmıştır.

Keywords

Zaman serisi, AR modeli, SETAR modeli, ARM modeli

References

• Altman, N. S. (1990). Kernel Smoothing of Data with Correlated Errors. Journal of the American Statistical Association, 85: 749-759.
• Box, G. E. P., Jenkins, G. M. ve Reinsel, G. C. (1994). Time Series Analysis. New Jersey: Prentice Hall.
• Chan, K. S. ve Tong, H. (2001). Chaos: A Statistical Perspective. Springer Verlag.
• Dagum, E. B. ve Giannerini, S. (2006). A Critical İnvestigation On Detrending Procedures For Non Linear Processes. Journal of Macroeconomics, Elsevier, Vol. 28(1), 175-191.
• Engle, R., Granger, W., Rice, J. ve Weiss, A. (1986). Semi Parametric Esitmates of The Relation Between Weather and Electricity Sales. J. Am. Statist. Ass., 81, 310-320.
• Eilers, P. H. C. ve Marx, B. D. (1996). Flexible Smoothing with B-Splines And Penalties (with discussion). Statist. Sci., 89, 89–121.
• Fan, J. ve Gijbels, I. (1996). Local Polynomial Modelling and its Applications. Chapman and Hall: London.
• Franses, P. H. ve Dijk, V. D. (2000). Nonlinear Time Series Models in Empirical Finance. Cambridge University Press, Cambridge.
• Granger, C. W. J. ve Terasvirta, T. (1993). Modelling Nonlinear Economic Relationships. Oxford University Press, Oxford.
• Green, P. J. ve Silverman, B. W. (1994) . Nonparametric Regression and Generalized Linear Models: A Roughness Penalty Approach. Chapman and Hall, London.
• Hart, J. D. (1991). Kernel Regression Estimation with Time Series Errors. Journal of the Royal Statistical Society, B 53: 173-187.
• Hart, J. D. (1994). Automated Kernel Smoothing of Dependent Data By Using Time Series Cross-Validation. Journal of the Royal Statistical Society, B 56: 529-542.
• Harvey, A. C. ve S. J. Koopman (1993) . Short Term Forecasting of Periodic Time Series Using Time-Varying Splines. J. Amer. Statist. Assoc., to appear.
• Hastie, T. J. ve Tibshirani, R. J. (1990). Generalized Additive Models. New York: Chapman and Hall.
• Henry, Ó., Olekalns, N. ve Summers, P. (2001). Exchange Rate İnstability, A Threshold Autoregressive Approach. Economic Record, 237, 160-166.
• Hurvich, C. M. ve Zeger, S. L. (1990). A Frequency Domain Selection Criterion for Regression with Autocorrelated Errors. Journal of the American Statistical Association, 85: 705-714.
• Pfann, G. A., Schotman, P. C. ve Tschernig, R. (1996). Nonlinear Interest Rate Dynamics and Implications for The Term Structure. Journal of Econometrics, 74, 149–176.
• Smith, M., Wong, C. M. ve Kohn, R. (1998) “Additive Nonparametric Regression with Autocorrelated Errors” Journal of the Royal Statistical Society: Series B: Statistical Methodology, Vol. 60, 2, 311-331.
• Tong, H. (1978). On a Thresold Model. In Pattern Reconition and Signal Processing. (Edited by C. H. Chen), Sijthoff and Noordhoff, Amsterdam, 101-41.
• Tong, H. ve Lim, K. S. (1980). Threshold Autoregression, Limit Cycles and Cyclical Data (with discussion). Journal of the Royal Statistical Society, Ser. B, 42, 245-292.
• Tong, H. (1983). Threshold Models in Nonlinear Time Series Analysis. Lecture Notes in Statistics, Springer-Verlag.
• Tong, H. (1990). Nonlinear Time Series: A Dynamical System Approach. Oxford University Press, Oxford.
• Tong, H. (2007). Birth of The Threshold Time Series Model. Statist. Sinica, 17, 8–14.
• TUİK (2012). Türkiye İstatistik Kurumu. Erişim Tarihi: 04.12.2012, http://www.tuik.gov.tr/VeriBilgi.do?alt_id=13
• Wood, S. N. (2000). Modelling and Smoothing Parameter Estimation with Multiple Quadratic Penalties. J.R. Statist. Soc. B 62, 413-428.
• Zivot, E. (2005). Nonlinear Time Series Models. Erişim Tarihi: 04.12.2012, http://faculty.washington.edu/ezivot/econ584/notes/nonlinear.pdf