Covariance changes detection in multivariate time series

Journal of Statistical Planning and Inference

Volumn 137, Issue 1, 2007, Pages 194-211

  Galeano, Pedro ^a   Peña, Daniel ^a  

^a UNIVERSIDAD CARLOS III DE MADRID   (Spain)

Author keywords

Cusum statistic; Heteroskedasticity; Likelihood ratio test statistic; Step changes; VARMA models

Indexed keywords

EID: 33748431335     PISSN: 03783758     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jspi.2005.09.003     Document Type: Article

References (27)

1. Abraham B., and Wei W.W.S. Inferences about the parameters of a time series model with changing variance. Metrika 31 (1984) 183-194
2. Andrews D.W.K. Tests for parameter instability and structural change with unknown change point. Econometrica 61 (1993) 821-856
3. Bai J. On the partial sums of residuals in autoregressive and moving average models. J. Time Ser. Anal. 14 (1993) 247-260
4. Bai J. Least squares estimation of a shift in linear processes. J. Time Ser. Anal. 15 (1994) 453-472
5. Bai J. Weak-convergence of the sequential empirical processes of residuals in ARMA models. Ann. Statist. 22 (1994) 2051-2061
6. Bai J., and Perron P. Estimating and testing linear models with multiple structural changes. Econometrica 66 (1998) 47-78
7. Bai J., Lumsdaine R.L., and Stock J.H. Testing for and dating common breaks in multivariate time series. Rev. Econom. Stud. 65 (1998) 395-432
8. Baufays, P., Rasson, J.P., 1985. Variance changes in autoregressive models. In: Time Series. Theory and Methods, second ed. Springer, New York, pp. 119-127.
9. Billingsley P. Convergence of Probability Measures (1968), Wiley, New York
10. Chen J., and Gupta A.K. Testing and locating variance changepoints with application to stock prices. J. Amer. Statist. Assoc. 92 (1997) 739-747
11. Gombay E., and Horvath L. Asymptotic distributions of maximum likelihood tests for change in mean. Biometrika 77 (1990) 411-414
12. Grubb H. A multivariate time series analysis of some flour price data. Appl. Statist. 26 (1992) 279-284
13. Inclán C. Detection of multiple tests of variances using posterior odds. J. Business Econom. Statist. 11 (1993) 189-200
14. Inclán C., and Tiao G.C. Use of cumulative sums of squares for retrospective detection of changes of variance. J. Amer. Statist. Assoc. 89 (1994) 913-923
15. Johansen S. Estimation and hypothesis testing of cointegration vectors in Gaussian vector autoregressive models. Econometrica 59 (1991) 1551-1580
16. Lee S., and Park S. The cusum of squares test for scale changes in infinite order moving average models. Scand. J. Statist. 28 (2001) 625-644
17. Ling S.Q. Weak convergence of the sequential empirical processes of residuals in nonstationary autoregressive models. Ann. Statist. 26 (1998) 741-754
18. Lütkepohl H., and Poskitt D.S. Specification of echelon-form VARMA models. J. Business Econom. Statist. 14 (1996) 69-79
19. McCulloch R.E., and Tsay R.S. Bayesian inference and prediction for mean and variance shifts in autoregressive time series. J. Amer. Statist. Assoc. 88 (1993) 968-978
20. Park S., Lee S., and Jeon J. The cusum of squares test for variance changes in infinite order autoregressive models. J. Korean Statist. Soc. 29 (2000) 351-361
21. Peña D., and Box G.E.P. Identifying a simplifying structure in time series. J. Amer. Statist. Assoc. 82 (1987) 836-843
22. Phillips P.C.B., and Solo V. Asymptotics for linear processes. Ann. Statist. 20 (1992) 971-1001
23. Tiao G.C., and Tsay R.S. Model specification in multivariate time series (with discussion). J. Roy. Statist. Soc. Ser. B 51 (1989) 157-213
24. Tsay R.S. Outliers, level shifts and variance changes in time series. J. Forecasting 7 (1988) 1-20
25. Tsay R.S., Peña D., and Pankratz A.E. Outliers in multivariate time series. Biometrika 87 (2000) 789-804
26. Wang J., and Zivot E. A Bayesian time series model of multiple structural changes in level, trend, and variance. J. Business Econom. Statist. 18 (2001) 374-386
27. Wichern D.W., Miller R.B., and Hsu D.A. Changes of variance in first order autoregressive time series models-with an application. Appl. Statist. 25 (1976) 248-256