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On the Asymptotic Power of Tests of Fit under Local Alternatives in Autoregression

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We consider a stationary AR(p) model. The autoregression parameters are unknown as well as the distribution of innovations. Based on the residuals from the parameter estimates, an analog of empirical… Click to show full abstract

We consider a stationary AR(p) model. The autoregression parameters are unknown as well as the distribution of innovations. Based on the residuals from the parameter estimates, an analog of empirical distribution function is defined and the tests of Kolmogorov’s and ω2 type are constructed for testing hypotheses on the distribution of innovations. We obtain the asymptotic power of these tests under local alternatives.

Keywords: asymptotic power; local alternatives; power tests; tests fit; fit local

Journal Title: Mathematical Methods of Statistics
Year Published: 2019

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