# Powers of tests for constant regression coefficients under several alternative models

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It is common in time series regression work, in such fields as economics and finance, that the statistical relationship under consideration may not remain constant over time, but appears to be subject to some kinds of changes. When linear regression models with random coefficients are used in applications, a question of fundamental importance is whether the regression coefficients are constant over time. If they are then ordinary least-squares techniques can be applied. If not, then more efficient procedures are available. Several tests for constancy of regression coefficients have been developed for the random walk coefficient model. However other random models are also possible. To some extent, tests designed to detect random walk coefficients may still reject the null hypothesis of constant regression coefficients even if the coefficients actually follow some other random model. At present, not much is known about the sensitivity of these tests to alternative models. The purpose of this dissertation research is (1) to examine powers of tests designed to detect random walk coefficients when the coefficients in fact follow other regimes, and (2) to adapt existing test procedures to alternative models and to compare powers of these new tests. [...]