Tests for cointegration with structural breaks based on subsamples

Tests for cointegration with allowance for structural breaks using the extrema of residual-based tests over subsamples of the data are considered. One motivation for the approach is to formalize the practice of data snooping by practitioners, who may examine subsamples after failing to find a predicted cointegrating relationship. Valid critical values for such multiple testing situations may be useful. The methods also have the advantage of not imposing a form for the alternative hypothesis–in particular slope vs. intercept shifts and single versus multiple breaks–and being comparatively easy to compute. A range of alternative subsampling procedures, including sample splits, incremental and rolling samples are tabulated and compared experimentally. Shiller’s annual stock prices and dividends series provide an illustration.