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[en] We develop a class of tests for the structural stability of infinite order regression models, when the time of a structural change is unknown. Examples include the infinite order autoregressive model, the nonparametric sieve regression and many others whose dimensions grow to infinity. When the number of parameters diverges, the traditional tests such as the supremum of Wald, LM or LR statistic or their exponentially weighted averages diverge 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 grow to infinity simultaneously. In general, this limit distribution is different from the sequential limit, which can be obtained by increasing the order p of the standardized tied-down Bessel process in Andrews (1993). More interestingly, our joint asymptotic analysis discovers that the joint asymptotic distribution depends on a higher order serial correlation. We also establish a weighted power optimality property of our tests under certain regularity conditions. A new result on partial sums of random matrices is established. We examine finite-sample performance in a Monte Carlo study and illustrate the test with a number of empirical examples.