Bayesgil VAR Modelinin Gerçek Zaman Dizileri için Kestirim Amaçlı Kullanılması

Abstract

In this paper, it has been done the application of the forecasting for real time series using the Bayesian vector autoregressive (BVAR) that is improvised by Litterman [1,2]. So, for the data, the performance of forecasting for BVAR according to VAR and the univariate (Box-Jenkins) [3] model has been compared by the known measurement that is RMSE (root mean square error). Time series that are used for the analysis are the annual (1925-1999) series of the population, the export for every person, the import for every person and the ratio of GNP (gross national product) for export of Turkey. As a result of this study, it may said that the BVAR models can be used as a method to produce appropriate forecasts on time series that have different fluctuations.

Keywords

• Time series analysis,forecasting,VAR (vector autoregressive),Bayesian VAR,RMSE criterion

References

1. 1] R. B. Litterman, A Bayesian Procedure for Forecasting with Informative Prior Distribution, Manuscript, Department of Economics, MIT, Cambridge, MA 1980.
2. [2] R. B. Litterman, Forecasting with Bayesian vector autoregressions: five years of experience, Journal of Business and Economic Statistics 4 (1986), 25–38.
3. [3] G. E. P. Box and G. M. Jenkins, Time Series Analysis: Forecasting and Control, Holden-Day, Oakland, California 1976.
4. [4] G. E. P. Box and G. C. Tiao, Bayesian Inference in Statistical Analysis, Addison-Wesley, Reading, MA 1973.
5. [5] N. Gürsakal, Bayesgil İstatistik, Uludağ Üniversitesi Güçlendirme Vakfı, Bursa 1992.
6. [6] G. Ergün, Devingen Doğrusal Modeller ve Bayesci Ongörüler Üzerine Bir Çalışma, Doktora Tezi, Hacettepe Üniversitesi, Ankara 1995.
7. [7] E. Çoker and F. Sezgin, Türkiye’deki enflasyonun Bayesci vektör otoregresyon modeller ile incelenmesi, Marmara Üniversitesi Sosyal Bilimler Enstitüsü Dergisi ¨ 7 (2007), 287–300.
8. [8] D. E. Spencer, Developing a Bayesian vector otoregression forecasting model, International Journal of Forecasting 9 (1993), 407–421.

9. [9] R. Kasap, Zaman Dizileri Analizi, BasılmamışDers Notu, Gazi Üniversitesi, Fen-Edebiyat ¨ Fakültesi, İstatistik Bölümü, Ankara 2002.
10. [10] G. E. P. Box and D. A. Pierce, Distribution of residual autocorrelation in autoregressive integrated moving average time series models, Journal of American Statistical Association 65 (1970), 1509–1526.
11. [11] R. Kasap, Using CFA for the identification of the order and the estimation of the parameters of the AR(p) models, Hacettepe Bulletin of Natural Sciences and Enginering 17 (1996), 195-205.
12. [12] A. Özmen, ¨ Zaman Serisi Analizinde Box-Jenkins Y¨ontemi ve Banka Mevduat Tahmininde Uygulama Denemesi, Doktora Tezi, Anadolu Üniversitesi 1986. ¨
13. [13] W. W. S. Wei, Time Series Analysis: Univariate and Multivariate, Addison-Wesley, UK 1990.
14. [14] G. C. Reinsel, Elements of Multivariate Time Series, Springer-Verlag, London 1995.
15. [15] C. A. Sims, Macroeconomics and reality, Econometrica 48 (1980), 1–48.
16. [16] R. B. Literman, Forecasting and policy analysis with Bayesian vector autoregression models, Quarterly Review 8 (1984), 30–41.
17. [17] J. A. Bikker, Inflation forecasting for aggregates of the EU-7 and EU-14 with Bayesian VAR models, Journal of Forecasting 17 (1998), 147–165.
18. [18] G. Tiao and G. Box, Modeling multiple time series with applications, Journal of American Statistical Association, 76 (1981), 802–816.
19. [19] G. Tiao and R. Tsay, Model specification in multivariate time series, Journal of The Royal Statistical Society, Series B, 51 (1989), 157–213.
20. [20] F. F. R. Ramos. Forecasting market shares using VAR and BVAR models: A comparison of their forecasting performance. http://129.3.20.41/eps/em/papers/9601/9601003.pdf, 1996. Online; accessed 11-February-2010.
21. [21] T. A. Doan, RATS (Regression Analysis of Time Series) for Windows (V.4.31), USA 1997.
22. [22] S. Kavak, Bayesgil Vektör Otoregressif (BVAR) Kestirim Modeli ve Uygulaması, Yüksek Lisans Tezi, Gazi Üniversitesi, Ankara 2002. ¨
23. [23] Türkiye İstatistik Yıllığı 2000, DİE, Ankara.