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Comments on the presence of serial correlation in the random coefficients of an autoregressive process

by   Frédéric Proïa, et al.

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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