Simple, Robust and Powerful Tests of the Breaking TrendHypothesis

In this paper we develop a simple procedure which delivers tests for the pres-ence of a broken trend in a univariate time series which do not require knowledgeof the form of serial correlation in the data and are robust as to whether theshocks are generated by an I(0) or an I(1) process. Two trend break modelsare considered: the …rst holds the level …xed while allowing the trend to break,while the latter allows for a simultaneous break in level and trend. For theknown break date case our proposed tests are formed as a weighted average ofthe optimal tests appropriate for I(0) and I(1) shocks. The weighted statisticsare shown to have standard normal limiting null distributions and to attain theGaussian asymptotic local power envelope, in each case regardless of whether theshocks are I(0) or I(1). In the unknown break date case we adopt the methodof Andrews (1993) and take a weighted average of the statistics formed as thesupremum over all possible break dates, subject to a trimming parameter, inboth the I(0) and I(1) environments. Monte Carlo evidence suggests that ourtests are in most cases more powerful, often substantially so, than the robustbroken trend tests of Sayginsoy and Vogelsang (2004)...