Under the classical long-span asymptotic framework we develop a class of Generalized Laplace (GL) inference methods for the change-point dates in a linear time series regression model with multiple structural changes analyzed in, e.g., Bai and Perron (1998). The GL estimator is defined by an integration rather than optimization-based method and relies on the least-squares criterion function. It is interpreted as a classical (non-Bayesian) estimator and the inference methods proposed retain a frequentist interpretation. Since inference about the change-point dates is a nonstandard statistical problem, the original insight of Laplace to interpret a certain transformation of a least-squares criterion function as a statistical belief over the parameter space provides a better approximation about the uncertainty in the data about the change-points relative to existing methods. Simulations show that the GL estimator is in general more precise than the OLS estimator. On the theoretical side, depending on some input (smoothing) parameter, the class of GL estimators exhibits a dual limiting distribution; namely, the classical shrinkage asymptotic distribution of Bai and Perron (1998) , or a Bayes-type asymptotic distribution  .
Under the classical long-span asymptotic framework we develop a class of Generalized Laplace (GL) inference methods for the change-point dates in a linear time series regression model with multiple structural changes analyzed in, e.g., Bai and Perron (1998). The GL estimator is de?fined by an integration rather than optimization-based method and relies on the least-squares criterion function. It is interpreted as a classical (non-Bayesian) estimator and the inference methods proposed retain a frequentist interpretation. This approach provides a better approximation about the uncertainty in the data of the change-points relative to existing methods. On the theoretical side, depending on some input (smoothing) parameter, the class of GL estimators exhibits a dual limiting distribution; namely, the classical shrinkage asymptotic distribution , or a Bayes-type asymptotic distribution . We propose an inference method based on Highest Density Regions using the latter distribution. We show that it has attractive theoretical properties not shared by the other popular alternatives, i.e., it is bet-proof. Simulations con?rm that these theoretical properties translate to better ?nite-sample performance .
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defined
de?fined
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Since inference about the change-point dates is a nonstandard statistical problem, the original insight of Laplace to interpret a certain transformation of a least-squares criterion function as a statistical belief over the parameter space
This approach
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about
of
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Simulations show that the GL estimator is in general more precise than the OLS estimator.
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of Bai and Perron (1998)
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. We propose an inference method based on Highest Density Regions using the latter distribution. We show that it has attractive theoretical properties not shared by the other popular alternatives, i.e., it is bet-proof. Simulations con?rm that these theoretical properties translate to better ?nite-sample performance