Comments on the presence of serial correlation in the random coefficients of an autoregressive process
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Through this note, we intend to show that the presence of serial correlation in the random coefficients of an autoregressive process, although likely in a chronological context, may lead to inappropriate conclusions. To this aim, we consider an RCAR(p) process and we establish that the standard estimation lacks consistency as soon as there exists a nonzero serial correlation in the coefficients. We give the correct asymptotic behavior of the statistic and some simulations come to strengthen our point.
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