Exact Tests for Univariate Random Walk Coefficients
In the previous chapter the linear state space model was discussed and some estimation methods were proposed. The topic of this and the following chapters is to test whether a state space model, i.e. a regression model with time varying coefficients, is the appropriate model for the data generating process or whether a regression model with constant coefficients is sufficient. More precisely, we want to test the null hypothesis that the coefficients of a regression model are constant over time against the alternative that some coefficients follow a possibly multivariate random walk. Different tests exist for this testing problem, depending on the assumptions regarding the regressors and on which alternative one has in mind.
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