An Exact Method for Establishing Significance in Time Series Analysis based on the Given Finite Sample

We present the first genuine test for a unit root (or of any other value of the autoregressive coeffi cient) within an autoregressive model for errors with given bounds that follow a martingale difference sequence. Without such bounds nontrivial tests are known not to exist. Our test is exact, we do not add other assumptions on the process. Competitors either do not control the type I error for a given finite sample (such as the Dickey-Fuller test) or rule out outcome variables with finite support and test a more restrictive null hypothesis by also assuming that all conditional medians are equal to 0.