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The purpose of this paper is to provide a sharp analysis on the asymptotic behavior of the Durbin–Watson statistic. We focus our attention on the first-order autoregressive process where the driven noise is also given by a first-order autoregressive process. We establish the almost sure convergence and the asymptotic normality for both the least squares estimator of the unknown parameter of the autoregressive process as well as for the serial correlation estimator associated with the driven noise....
Under regularity assumptions, we establish a sharp large
deviation principle for Hermitian quadratic forms of
stationary Gaussian processes. Our result is similar to
the well-known Bahadur-Rao theorem [2] on the sample
mean. We also provide several examples of application
such as the sharp large deviation properties of
the Neyman-Pearson likelihood ratio test, of the sum of squares,
of the Yule-Walker
estimator of the parameter of a stable autoregressive Gaussian process,
and finally of the empirical...
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