# zbMATH — the first resource for mathematics

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

##### MSC:
 62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH) 60J05 Discrete-time Markov processes on general state spaces
Full Text:
##### References:
 [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 [3] Quinn B. G., J. Time Series Anal. 3 pp 249– (1982) [4] Revuz D., Markov Chains (1975) [5] Tong H., J. Time Series Anal. 2 pp 279– (1981) [6] Tweedie R. L., Probability, Statistics and Analysis (1983) [7] DOI: 10.2307/3213735 · Zbl 0513.60067 · doi:10.2307/3213735
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.