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We deal with real weakly stationary processes with non-positive autocorrelations , i. e. it is assumed that for all . We show that such processes have some special interesting properties. In particular, it is shown that each such a process can be represented as a linear process. Sufficient conditions under which the resulting process satisfies for all are provided as well.
In the paper, a heteroskedastic autoregressive process of the first order is considered where the autoregressive parameter is random and errors are allowed to be non-identically distributed. Wild bootstrap procedure to approximate the distribution of the least-squares estimator of the mean of the random parameter is proposed as an alternative to the approximation based on asymptotic normality, and consistency of this procedure is established.
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