Testing for Coefficient Constancy in Random Walk Models with Particular Reference to the Initial Value Problem
This article is concerned with Locally Best Invariant tests for coefficient stability in a univariate random walk coefficient regression model. In particular, we explore the effects that different assumptions about the initial value of the random walk process have on the form and asymptotic distribution of the resulting test statistics. When this initial value is allowed to be random, it is shown that the test statistics are either exactly the same, or possess the same asymptotic distributions, as when the initial value is fixed.
Key wordsBrownian Motion Brownian Bridge Invariance Locally Best Invariant Test Mixing Random Walk Weak Convergence
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