TESTING CHANGE‐POINTS IN THE EXPLOSIVE GAUSSIAN AUTOREGRESSIVE PROCESSES

M. Raimondo

Journal of Time Series Analysis, 1996, vol. 17, issue 5, 461-480

Abstract: Abstract. A functional limit theorem with a particular function class and topology is derived for non‐ergodic type time series. This limit theorem allows us to study the asymptotic law of the associated likelihood ratio test (LRT) statistic for testing the presence of a change in the covariance parameter in the explosive Gaussian autoregressive model. We show that the level of the LRT cannot be approximated without introducing appropriate normalization. The limit law of a particular weighted likelihood ratio test is examined through a simulation study and is compared with the well‐known Kolmogorov distribution obtained in the stationary case; we conclude that for practical applications when the root is really close to unity one can use the same thresholds as in the stationary case. This procedure is applied to the study of three real time series known to be non‐stationary.

Date: 1996
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