Statistical inference in Lombard's smooth-change model
Abstract
The sample properties of various inference procedures in Lombard's smooth-change model are studied in this work. In particular, the power of six test statistics for the detection of change-points in the mean and the variance of a series of independent observations is investigated under several alternatives. The robustness of the procedures under heterogeneity and serial dependence is considered as well. An investigation of the efficiency of an estimator of the change-points is also presented. Conditional on these estimated change-points, least squares estimators of the means in Lombard's model are derived and their efficiency is carefully studied. The procedures are illustrated on two environmental data sets, namely the annual volume of discharge from the Nile River and the annual temperature anomalies for the northern hemisphere. It will be seen that Lombard's model is flexible, that the test statistics of Lombard (1987) are powerful, and that the proposed estimators have nice properties; hence Lombard's model has a high potential for applications in the environmental sciences.