Tek Değişkenli Zaman Serilerinde Model Seçim Ölçütleri Üzerine Bir İnceleme

Abstract

Bu çalışmada, Akaike Bilgi (AIC), Son Kestirim Hatası (FPE), Hannan-Quinn Bilgi (HQ), Düzeltilmiş Akaike Bilgi (AICC) ve Schwarz Bilgi (SIC) Ölçütleri dikkate alınarak, tek değişkenli zaman dizileri modellerinde uygun model derecesinin seçilmesi incelenmiştir. Ölçütlerin birbirleri ile karşılaştırılması, Monte Carlo simülasyon yöntemi kullanılarak hangi ölçütün hangi gecikme sayısını kaç kez seçtiği çalışmaları yapılmıştır.

Keywords

• Model seçim ölçütleri
• Simülasyon
• Zaman serileri

Examining Model Selection Criteria for Single Variable Time Series

Abstract

In this study, by using Akaike Information Criteria (AIC), Final Prediction Error (FPE), Hannan-Quinn Information Criteria (HQ), Adjusted Akaike Information Criteria (AICC) and Schwarz Information Critera (SIC), in selecting appropriate model degree in single variable time series are examined. In order to compare these criteria, Monte Carlo simulation method is employed to compute the lag lengths selected by each criteria.

Keywords

• Model selection criteria
• Simulation
• Time series

References

1. Akaike, H., 1969. Fitting autoregressive model for prediction. Annals of the Institute of Statistical Mathematics, 21: 243-247.
2. Akaike, H., 1974. A new look at the statistical model identification. I.E.E.E Transactions on Automatic Control, AC-19: 716-722.
3. Baran, T., Bacanlı, Ü. G., 2006. Uygun stokastik model seçim ölçütlerinin değerlendirilmesi. IMO Teknik Dergi, 264: 3987-4002.
4. Bedrick, E. J. and Tsai, C. L. , 1994. Model selection for multivariate regression in small saınples", Biometrics, 50: 226-231.
5. Burnham, K. P., Anderson, D. R., 2004. Multimodel inference understanding AIC and BIC in model selection. Sociological Methods & Research, 33: 261-304.
6. Box, G. E. P., Jenkins, G. M., Reinsel, G. C., 1994. Time series analysis: Forecasting and a control, Prentice Hall, New Jersey, 10-100,200-202.
7. Enders, W., 2004. Applied econometric time series. Wiley, United States of America, 96-97.
8. Hannan E. J., Quinn B. G. , 1979. The determination of the order of an autoregression. Journal of the Royal Statistical Society, 41: 190-195.

9. Hannan E. J., 1980. The estimation of the order of an ARMA process. The Annals of Statistics, 8:1071-1081.
10. Hurvich, C. M., Tsai C. T., 1989. Regression and time series model selection in small samples. Biometrika, 76: 297-307.
11. Luna, X., 1995. An improvement of Akaike's FPE criterion to produce its variability. Journal of Time Series Analysis, 19: 457-471.
12. Koehler, A. B., Murphree, E. S., 1998. A comparision of the Akaike and Schwarz criteria for selecting model order. Applied Statistics, 37: 187-195.
13. Neftçi, S. N., 1982. Specification of economic time series models using Akaike's criterion. Journal of the American Statistical Association, 77: 537-540.
14. Parkhurst, A. M., 1992. Evaluation of order determination prosedures in ARMA models. Doktora Tezi, Presented to the Faculty of The Graduate Collage at The University of Nebraska, 91-93(İngilizce).
15. Quinn, B. G., 1980. Order determination for a multivariate autoregression. Journal of Time Series Analysis, 42,182-185.
16. Schwarz, G. D., 1978. Estimating the dimension of a model. The Annals of Statistics, 6: 461-464.
17. Stone, M., 1979. Model selection criteria of Akaike and Schwarz. Journal of the Royal Statistical Sociaty.Series B (Methodogical), 41: 276-278.
18. Wei, W. W. S., 1990. Time series analysis: Univariate and multivariate analysis. Addison-Wesley Publishing company, Inc., England, 32-57, 67-84.