We develop a class of tests for the structural stability of infinite-order models such as the infinite-order autoregressive model and the nonparametric sieve regression . When the number p of restrictions diverges, the traditional testsbased on the suprema of Wald, LM and LR statistics or their exponentially weighted averages diverge as well. We introduce a suitable transformation of these tests and obtain proper weak limits under the condition that p grows to infinity as the sample size n goes to infinity. In general, this limit distribution is different from the sequential limit, which can be obtained by increasing the order of the standardized tied-down Bessel process in Andrews (1993). In particular, our joint asymptotic analysis discovers a nonlinear high order serial correlation, for which we provide a consistent estimator. Our Monte Carlo simulation illustrates the importance of robustifying the structural break test against the nonlinear serial correlation even when p is moderate. Furthermore, we also establish a weighted power optimality property of our tests under some regularity conditions. We examine finite-sample performance in a Monte Carlo study and illustrate the test with a number of empirical examples .
We develop a class of tests for a growing number of restrictions in infinite and increasing order time series models such as infinite-order autoregression, nonparametric sieve regression and multiple regression with growing dimension. Examples include the Chow test, Andrews and Ploberger (1994) type exponential tests, and testing of general linear restrictions of growing rank p. Notably, our tests introduce a new scale correction to the conventional quadratic forms that are recentered and normalized to account for diverging p. This correction accounts for a high-order long-run variance that emerges as p grows with sample size in time series regression. Furthermore, we propose a bias correction via a null-imposed bootstrap to control finite sample bias without sacrificing power unduly. A simulation study stresses the importance of robustifying testing procedures against the high-order long-run variance even when p is moderate. The tests are illustrated with an application to the oil regression in Hamilton (2003) .
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the structural stability of infinite-order
a growing number of restrictions in infinite and increasing order time series
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the
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autoregressive model and the
autoregression,
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. When the number p of restrictions diverges, the traditional testsbased on the suprema of Wald, LM and LR statistics or their exponentially weighted averages diverge as well. We introduce a suitable transformation of these tests and obtain proper weak limits under the condition that p grows to infinity as the sample size n goes to infinity. In general, this limit distribution is different from the sequential limit, which can be obtained by increasing the order of the standardized tied-down Bessel process in Andrews (1993). In particular, our joint asymptotic analysis discovers a nonlinear high order serial correlation, for which we provide a consistent estimator. Our Monte Carlo simulation illustrates
and multiple regression with growing dimension. Examples include the Chow test, Andrews and Ploberger (1994) type exponential tests, and testing of general linear restrictions of growing rank p. Notably, our tests introduce a new scale correction to the conventional quadratic forms that are recentered and normalized to account for diverging p. This correction accounts for a high-order long-run variance that emerges as p grows with sample size in time series regression. Furthermore, we propose a bias correction via a null-imposed bootstrap to control finite sample bias without sacrificing power unduly. A simulation study stresses
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the structural break test against the nonlinear serial correlation
testing procedures against the high-order long-run variance
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Furthermore, we also establish a weighted power optimality property of our tests under some regularity conditions. We examine finite-sample performance in a Monte Carlo study and illustrate the test with a number of empirical examples
The tests are illustrated with an application to the oil regression in Hamilton (2003)