STRUCTURAL STABILITY OF REGRESSION WITH GROWING DIMENSION

About this event

We develop a class of tests for the structural stability of a regression model, whose dimension grows to infinity, when the time of a structural change is unknown. The nonparametric series regression and the autoregressive model of infinte-order, AR(‡), fall within our framework, not to mention Bekkerfs (1994) asymptotic design. When the number of parameters diverges, the traditional tests such as the supremum of Wald statistics and exponentially weighted averages of Wald statistics diverges as well. However, we show that a suitable transformation of these tests converges to a proper weak limit as the sample size n and the dimension p grows to infinity simultaneously. In general, this limit distribution is different from the sequential limit of the traditional asymptotic distribution, which can be obtained by increasing the dimension p in Andrewsfs (1993) or Andrews and Plobergerfs (1994) asymptotic distribution to infinity. We establish an optimality property of our tests under certain regularity conditions. A new result on partial sums of random matrices is also established. We examine finite-sample performance in a Monte Carlo study and illustrate the test with a number of empirical examples.

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