Change point detection in vector autoregression

Prášková, Zuzana

Kybernetika, Tome 54 (2018) no. 6, pp. 1122-1137

Abstract (VO)

In the paper a sequential monitoring scheme is proposed to detect instability of parameters in a multivariate autoregressive process. The proposed monitoring procedure is based on the quasi-likelihood scores and the quasi-maximum likelihood estimators of the respective parameters computed from a training sample, and it is designed so that the sequential test has a small probability of a false alarm and asymptotic power one as the size of the training sample is sufficiently large. The asymptotic distribution of the detector statistic is established under both the null hypothesis of no change as well as under the alternative that a change occurs.

Détail

DOI : 10.14736/kyb-2018-6-1122

Classification : 62E20, 62M10
Keywords: vector autoregression; change point; quasi-maximum likelihood

Bibliographie

[1] Bai, J., Perron, P.: Estimating and testing linear models with multiple structural changes. Econometrica 66 (1998), 47-78. | DOI | MR

[2] Berkes, I., Gombay, E., Horváth, L., Kokoszka, P.: Sequential change-point detection in GARCH(p,q) models. Econometr. Theory 20 (2004), 1140-1167. | DOI | MR

[3] Mainassara, Y. Boubacar, Francq, C.: Estimating structural VARMA models with uncorrelated but non-independent error terms. J. Multivariate Anal. 102 (2011), 496-505. | DOI | MR

[4] Carsoule, F., Franses, P. H.: A note on monitoring time-varying parameters in an autoregression. | DOI

[5] Chu, C.-S. J., Stinchcombe, M., White, H.: Monitoring structural change. | DOI

[6] Davidson, J.: Stochastic Limit Theory. Oxford University Press, Oxford 1994. | DOI | MR

[7] Dvořák, M.: Stability in Autoregressive Time Series Models. Ph.D. Dissertation, Charles University, Prague 2015.

[8] Gombay, E., Serban, D.: Monitoring parameter change in AR(p) time series models. | DOI

[9] Hamilton, J. D.: Time Series Analysis. Princeton University Press, Princeton 1994. | DOI | MR

[10] Horváth, L., Hušková, M., Kokoszka, P., Steinebach, J.: Monitoring changes in linear models. | DOI

[11] Hlávka, Z., Hušková, M., Kirch, C., Meintanis, S. G.: Monitoring changes in the error distribution of autoregressive models based on Fourier methods. Test 21 (2012), 605-634. | DOI | MR

[12] Hušková, M., Koubková, A.: Sequential procedures for detection of changes in autoregressive sequences.

[13] Kuelbs, J., Philipp, W.: Almost sure invariance principles for partial sums of mixing $B-$valued random variables. | DOI

[14] Li, F., Tian, Z., Qi, P.: Structural change monitoring for random coefficient autoregressive time series. Comm. Statist. Simulation Comput. 44 (2015), 996-1009. | DOI | MR

[15] Lee, S., Lee, Y., Na, O.: Monitoring distributional changes in autoregressive models. | DOI

[16] Lütkepohl, H.: New Introduction to Multiple Time Series Analysis. Springer-Verlag, Berlin 2005. | DOI | MR

[17] Na, O., Lee, J., Lee, S.: Monitoring parameter changes for random coefficient autoregressive models. | DOI

[18] Prášková, Z.: Monitoring changes in RCA models. In: Stochastic Models, Statistics and Their Applications, Springer Proceedings in Mathematics and Statistics 122 (A. Steland, E. Rafajlowicz and K. Szajowski, eds.), Springer, Berlin 2015, pp. 129-137. | DOI | MR

[19] Straumann, D.: Estimation in Conditionally Heteroscedastic Time Series Models. Lecture Notes in Statistics 181, Springer, Berlin 2005. | DOI | MR