A General Regression Changepoint Test for Time Series Data

This article develops a test for a single changepoint in a general setting that allows for correlated time series regression errors, a seasonal cycle, time-varying regression factors, and covariate information. Within, a changepoint statistic is constructed from likelihood ratio principles and its asymptotic distribution is derived. The asymptotic distribution of the changepoint statistic is shown to be invariant of the seasonal cycle and the covariates should the latter obey some simple limit laws; however, the limit distribution depends on any time-varying factors. A new test based on ARMA residuals is developed and is shown to have favorable properties with finite samples. Driving our work is a changepoint analysis of the Mauna Loa record of monthly carbon dioxide concentrations. This series has a pronounced seasonal cycle, a nonlinear trend, heavily correlated regression errors, and covariate information in the form of climate oscillations. In the end, we find a prominent changepoint in the early 1990s, often attributed to the eruption of Mount Pinatubo, which cannot be explained by covariates. Supplementary materials for this article are available online.