A FULLY FLEXIBLE CHANGEPOINT TEST FOR REGRESSION MODELS WITH STATIONARY ERRORS

摘要

Temporal discontinuities in time series represent one of the classic problems of time series. Such discontinuities are often analyzed by detecting changes at specific times in the parameters governing a regression model fit to the series. The regression framework examined here contains three classes of predictors: functional form, seasonal, and stochastic. Regression errors are allowed to observe a general stationary structure. Methods are proposed that provide the analyst with full flexibility in selecting which set of regression parameters are allowed to change under the alternative hypothesis. Here, we also examine several mathematical complications that arise in the development of such procedures. A simulation study illustrates the efficacy of the proposed methodology, where a test statistic based on the residuals from an ARMA model is shown to perform most favorably. The methods are applied to a carbon dioxide time series measured at Mauna Loa Observatory, where a shift in the seasonal variations is detected (in addition to a known shift in trend), and to a series of monthly temperatures at Barrow, Alaska, where only a shift in trend is found.