Note on AR(1)-characterisation of stationary processes and model fitting

被引：4

作者：

Voutilainen, Marko ^{[1
]}

Viitasaari, Lauri ^{[2
]}

Ilmonen, Pauliina ^{[1
]}

机构：

[1] Aalto Univ, Sch Sci, Dept Math & Syst Anal, POB 11100, FI-00076 Aalto, Finland

[2] Univ Helsinki, Dept Math & Stat, POB 68, FI-00014 Helsinki, Finland

来源：

MODERN STOCHASTICS-THEORY AND APPLICATIONS | 2019年 / 6卷 / 02期

关键词：

AR(1)-characterisation; stationary processes; covariance functions;

D O I：

10.15559/19-VMSTA132

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

It was recently proved that any strictly stationary stochastic process can be viewed as an autoregressive process of order one with coloured noise. Furthermore, it was proved that, using this characterisation, one can define closed form estimators for the model parameter based on autocovariance estimators for several different lags. However, this estimation procedure may fail in some special cases. In this article, a detailed analysis of these special cases is provided. In particular, it is proved that these cases correspond to degenerate processes.

引用

页码：195 / 207

页数：13

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