Publication: A new class of distribution-free tests for time series models specification
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2009-02
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Abstract
The construction of asymptotically distribution free time series model specification tests using
as statistics the estimated residual autocorrelations is considered from a general view point. We
focus our attention on Box-Pierce type tests based on the sum of squares of a few estimated
residual autocorrelations. This type of tests belong to the class defined by quadratic forms of
weighted residual autocorrelations, where weights are suitably transformed resulting in
asymptotically distribution free tests. The weights can be optimally chosen to maximize the
power function when testing in the direction of local alternatives. The optimal test in this class
against MA, AR or Bloomfield alternatives is a Box-Pierce type test based on the sum of
squares of a few transformed residual autocorrelations. Such transformations are, in fact, the
recursive residuals in the projection of the residual autocorrelations on a certain score function.
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Dynamic regression model, Optimal tests, Recursive residuals, Residual autocorrelation function, Specification tests, Time series models