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Random coefficient autoregressive processes: A Markov chain analysis of stationarity and finiteness of moments. (English) Zbl 0572.62069
J. Time Ser. Anal. 6, 1-14 (1985); correction ibid. 41, No. 6, 899-900 (2020).
This paper is concerned with a class of discrete time vector processes, the random coefficient regression (RCA), \[ X_ t=(\theta +\Gamma_ t)X_{t+1}+R_ t, \] where \(\theta\) is a non-random matrix, \(\Gamma_ t\) are random matrices, and \(R_ t\) are random vectors. The main result is that \(X_ t\) is geometrically ergodic under the conditions:
i) \(R_ t\), \(\Gamma_ t\) are i.i.d. with mean zero and independent each of other; ii) \(\theta \otimes \theta +E(\Gamma_ t\otimes \Gamma_ t)\) have moduli less than unity,
where \(\otimes\) denotes the Kronecker product of matrices. The fact comes from a property of the Markov chain \(X_ t\), which is a Feller process under a set of conditions.
Reviewer: C.J.Tian

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
60J05 Discrete-time Markov processes on general state spaces
Full Text: DOI
[1] Nicholls D. F., Random Coefficient Autoregressive Models:An Introduction 11 (1982) · doi:10.1007/978-1-4684-6273-9
[2] DOI: 10.1016/0304-4149(82)90041-2 · Zbl 0484.60056 · doi:10.1016/0304-4149(82)90041-2
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[7] DOI: 10.2307/3213735 · Zbl 0513.60067 · doi:10.2307/3213735
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