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Testing for Differences Between Conditional Means in a Time Series Context

In this article we study tests for equality of two regression curves when the inputs are driven by a time series. The basic process underlying the test statistics is the empirical process of the time series marked by the difference in the pertaining dependent variables. The main results hold under strict stationarity of the input variables, but no mixing condition or special modeling of the time series will be necessary. A simulation study is reported on, which illustrates the quality of the distributional approximation and the power of the tests for small to moderate sample sizes. An application to a real dataset is also included.