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.

中文翻译：

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自回归过程随机系数中存在序列相关性的评论

通过这篇笔记，我们打算表明自回归过程的随机系数中存在序列相关性，尽管可能在时间顺序的背景下，可能会导致不恰当的结论。为此，我们考虑了 RCAR$(p)$ 过程，一旦系数中存在非零序列相关，我们就确定标准估计缺乏一致性。我们给出了统计的正确渐近行为，一些模拟来加强我们的观点。