Kendinden Uyarımlı Eşik Otoregresif Modellerin Belirlenmesi İçin Genetik Algoritma Yaklaşımı

Günümüzde doğrusal olmayan zaman serisi analizinde yaygın olarak kullanılan kendinden uyarımlı eşik otoregresif SETAR modeller; anlaşılması ve yorumlanması kolay, basit bir model biçimine sahip olsalar da söz konusu modeller belirlenirken tahmin edilmesi gereken birçok serbest parametre bulunmaktadır. Bu nedenle bu çalışmada SETAR modellerini belirleme süreci bir optimizasyon problemi olarak düşünülmüş ve ilgili probleme genetik algoritmalar ile çözüm aranmıştır. Bu bağlamda ele alınan probleme ilişkin genetik algoritma bileşenleri tanımlanmış ve algoritma için uygun parametreler belirlenmiştir. Önerilen yaklaşım simülasyon verileri ile değerlendirilerek, kullanılabilirliği gösterilmiştir.

Anahtar Kelimeler:

Kendinden Uyarımlı Eşik Otoregresif, SETAR, Genetik Algoritma, Model Belirleme

A Genetic Algorithm Approach for the Specification of Self-Exciting Threshold Autoregressive Models

Even though, self-exciting threshold autoregressive SETAR models commonly used in nonlinear time series analysis nowadays have a simple, easy to understand and interpret model form, there are many free parameters to estimate, when building the models in question. Therefore in this paper the process of specification of SETAR models were considered as an optimization problem and the related problem was solved with genetic algorithms. In this context genetic algorithm components were defined for the discussed problem and appropriate parameters were determined for the algorithm. The usability of the proposed approach is shown by evaluating it with simulation data.

Keywords:

Self-Exciting Threshold Autoregressive, SETAR, Genetic Algorithms, Model Specification,

PDF

___

Andrews, Donald W. K. (1993), “Tests for Parameter Instability and Structural Change With Unknown Change Point”, Econometrica, Volume: 61, Issue: 4, p. 821–856.
Balcombe, Kelvin G. (2005), “Model Selection Using Information Criteria and Genetic Algorithms”, Computational Economics, Volume: 25, Issue: 3, p. 207–228.
Baragona, Roberto, Francesco Battaglia ve Domenico Cucina (2004), “Fitting piecewise linear threshold autoregressive models by means of genetic algorithms”, Computational Statistics & Data Analysis, Volume: 47, Issue: 2, p. 277–295.
Baragona, Roberto ve Domenico Cucina (2008), “Double threshold autoregressive conditionally heteroscedastic model building by genetic algorithms”, Journal of Statistical Computation and Simulation, Volume: 78, Issue: 6, p. 541–558.
Baragona, Roberto ve Domenico Cucina (2009), “Genetic search for threshold parameters in time series threshold models: algorithms and computer programs”, TECHNICAL REPORT 10/2009, Department of Statistics, Probability and Applied Statistics, Sapienza University of Rome, Italy.
Battaglia, Francesco ve Mattheos K. Protopapas (2011a), “Time-varying multi-regime models fitting by genetic algorithms”, Journal of Time Series Analysis, Volume: 32, Issue: 3, p. 237–252.
Battaglia, Francesco ve Mattheos K. Protopapas (2011b), “Multi–regime models for nonlinear nonstationary time series”, Computational Statistics, Volume: 27, Issue: 2, p. 319-341.
Bingul, Z. A. S. Sekmen S. Palaniappan ve S. Zein-Sabatto (2000), “Genetic algorithms applied to real time multiobjective optimization problems”, Southeastcon 2000. Proceedings of the IEEE, p. 95–103.
Blickle, Tobias ve Lothar Thiele (1995), “A Mathematical Analysis of Tournament Selection”, Proceedings Of The Sixth International Conference On Genetic Algorithms, p. 9–16.
Cryer, Jonathan D. ve Kung-Sik Chan (2008), Time Series Analysis: With Applications in R (2nd ed.), Springer.
De Gooijer, Jan G. (2001), “Cross-validation Criteria for Setar Model Selection”, Journal of Time Series Analysis, Volume: 22, Issue: 3, p. 267–281.
Franses, Philip H. ve Dick van Dijk (2000), Nonlinear Time Series Models In Empirical Finance, Cambridge University Press.
Gilli Manfred ve Peter Winker (2009), “Heuristic Optimization Methods In Econometrics”, BELSLEY, David A. ve Erricos J. KONTOGHIORGHES (Ed.), Handbook of Computational Econometrics, p. 81-119, John Wiley and Sons.
Gonzalo, Jesus ve Jean-Yves Pitarakis (2002), “Estimation And Model Selection Based Inference In Single And Multiple Threshold Models”, Journal of Econometrics, Volume: 110, Issue: 2, p. 319–352.
Hamaker, E. L. (2009), “Using Information Criteria To Determine The Number Of Regimes In Threshold Autoregressive Models”, Journal of Mathematical Psychology, Volume: 53, Issue: 6, p. 518–529.
Hansen, Bruce (1997), “Inference in TAR Models”, Studies in Nonlinear Dynamics ve Econometrics, Volume: 2, Issue: 1, p. 1-14.
Hansen, Bruce (1999), “Testing for Linearity”, Journal of Economic Surveys, Volume: 13, Issue: 5, p. 551–576.
Hansen, Bruce (2005), “Challenges for Econometric Model Selection”, Econometric Theory, Volume: 21, Issue: 1, p. 60–68.
Jeremy, Piger (2010), “Econometrics: Models of Regime Changes”, MEYERS, Robert A. (Ed.), Complex Systems in Finance and Econometrics (1st ed.), p. 190-202, Springer.
Maringer, Dietmar G. ve Mark Meyer (2008), “Smooth Transition Autoregressive Models - New Approaches to the Model Selection Problem”, Studies in Nonlinear Dynamics & Econometrics, Volume: 12, Issue: 1, p. 1-21.
Michalewicz, Zbigniew (1996), Genetic Algorithms + Data Structures = Evolution Programs (3rd ed.), Springer.
Ong, Chorng-Shyong, Jih-Jeng Huang ve Gwo-Hshiung Tzeng (2005), “Model Identification Of ARIMA Family Using Genetic Algorithms”, Applied Mathematics and Computation, Volume: 164, Issue: 3, p. 885–912.
Peña, Daniel ve Julio Rodriguez (2005), “Detecting Nonlinearity In Time Series By Model Selection Criteria”, International Journal of Forecasting, Volume: 21, Issue: 4, p. 731–748.
Sakawa, Masatoshi; (2002), Genetic Algorithms And Fuzzy Multiobjective Optimization, Springer.
Sivanandam, S. N. ve S. N. Deepa (2007), Introduction To Genetic Algorithms, Springer.
Strikholm, Birgit ve Timo Teräsvirta (2006), “A Sequential Procedure For Determining The Number Of Regimes İn A Threshold Autoregressive Model”, The Econometrics Journal, Volume: 9, Issue: 3, p. 472–491.
Şen, Zekai (2004), GenetikAlgoritmalar Ve En İyileme Yöntemleri, İstanbul, Su Vakfı.
Tong, Howell (1978), “On A Threshold Model”, CHEN, C, (Ed.), Pattern Recognition And Signal Processing, p. 575-586, NATO ASI Series E: Applied Sc. (29), Sijthoff ve Noordhoff, Netherlands
Tong, Howell (1983), Threshold Models in Non-linear Time Series Analysis, New York, Springer.
Tong, Howell (1990), Non-Linear Time Series: A Dynamical System Approach, Oxford University Pres.
Tong, Howell ve K. S. Lim (1980), “Threshold Autoregression, Limit Cycles and Cyclical Data”, Journal of the Royal Statistical Society. Series B (Methodological), Volume: 42, Issue: 3, p. 245-292.
Tsay, Ruey S. (1989), “Testing and Modeling Threshold Autoregressive Processes”, Journal of the American Statistical Association, Volume: 84, Issue: 405, p. 231-240.
Wong, C. S. ve W. K. Li (1998), “A Note On The Corrected Akaike Information Criterion For Threshold Autoregressive Models”, Journal of Time Series Analysis, Volume: 19, Issue: 1, p. 113-124.
Wu, Berlin ve Chih-Li Chang (2002), “Using Genetic Algorithms To Parameters (d,r) Estimation For Threshold Autoregressive Models”, Computational Statistics & Data Analysis, Volume: 38, Issue: 3, p. 315-330.
Zivot, Eric ve Jiahui Wang (2006), Modeling Financial Time Series With S-PLUS, Birkhäuser.