Test Statistics for Parameter Changes in INAR(p) Models and a Simulation Study

Authors

  • Tamás T. Szabó University of Szeged, Hungary

DOI:

https://doi.org/10.17713/ajs.v40i4.216

Abstract

In the paper a change detection procedure is introduced for integervalued autoregressive processes which are inspired by the ordinary autoregressive model. The power of the test is investigated in a simulation study to determine how effectively it can detect changes in the key parameters of the process.

References

Alzaid, A. A., and Al-Osh, M. A. (1987). First order integer-valued autoregressive (INAR(1)) processes. Journal of Time Series Analysis, 8, 261-275.

Alzaid, A. A., and Al-Osh, M. A. (1990). An integer-valued pth order autoregressive structure (INAR(p)) process. Journal of Applied Probability, 27, 314-324.

Barczy, M., Ispány, M., and Pap, G. (2011). Asymptotic behavior of unstable INAR(p) processes. Stochastic Processes and Applications, 121, 583-608.

Berkes, I., Gombay, E., and Horváth, L. (2009). Testing for changes in the covariance structure of linear processes. Journal of Statistical Planning and Inference, 139, 2044-2063.

Csörgő, M., and Horváth, L. (1997). Limit Theorems in Change-point Analysis. New York: Wiley.

Kang, J., and Lee, S. (2009). Parameter change test for random coefficient integer-valued autoregressive processes with application to polio data analysis. Journal of Time Series Analysis, 30, 239-258.

Klimko, L. A., and Nelson, P. I. (1978). On conditional least squares estimation for stochastic processes. The Annals of Statistics, 6, 629-642.

Kuiper, N. H. (1960). Tests concerning random points on a circle. Nederl. Akad. Wetensch. Proc. Ser. A, 63, 38-47.

Lee, S., and Na, O. (2005). Test for parameter change in stochastic processes based on conditional least-squares estimator. Journal of Multivariate Analysis, 93, 375-393.

Steutel, F. W., and Harn, K. van. (1979). Discrete analogues of self-decomposability and stability. The Annals of Probability, 8, 893-899.

Published

2016-02-24

How to Cite

Szabó, T. T. (2016). Test Statistics for Parameter Changes in INAR(p) Models and a Simulation Study. Austrian Journal of Statistics, 40(4), 265–280. https://doi.org/10.17713/ajs.v40i4.216

Issue

Section

Articles