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.
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Acknowledgments
The author is sincerely grateful to Prof. D. M. Chibisov for useful discussions.
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Boldin, M.V. On the Asymptotic Power of Tests of Fit under Local Alternatives in Autoregression. Math. Meth. Stat. 28, 144–154 (2019). https://doi.org/10.3103/S1066530719020042
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DOI: https://doi.org/10.3103/S1066530719020042
Keywords
- autoregression
- residuals
- empirical distribution function
- Kolmogorov’s and omegasquare tests
- local alternatives