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On stationarity of a multiple doubly stochastic model. (English) Zbl 0729.60025
Summary: A multiple linear process with random coefficients is investigated in the paper. Conditions for the existence of such a process are derived and its covariance function as well as the matrix of spectral densities are calculated. The results are applied to multiple AR(1) process with random coefficients, where the matrices of coefficients can be described by a stationary process. In this case conditions for existence and stationarity of the AR(1) process are given.

60G10 Stationary stochastic processes
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
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[1] J. Aněl: Autoregressive series with random parameters. Math. Operationsforsch. Statist., Ser. Statistics 7 (1976), 735-741. · Zbl 0346.62066
[2] J. Anděl: On autoregressive models with random parameters. Proc. 3rd Prague Symp. on Asymptotic Statistics (P. Mandl, M. Hušková, Elsevier, Amsterdam 1984, pp. 17-30.
[3] D. R. Brillinger: Time Series: Data Analysis and Theory. Holt, Rinehart and Winston, Inc., New York 1975. · Zbl 0321.62004
[4] A. Koubková: First-order autoregressive processes with time-dependent random parameters. Kybernetika 18 (1982), 408-414. · Zbl 0517.62092
[5] D. E. Nicholls, B. G. Quinn: The estimation of random coefficient autoregressive models. J. Time Ser. Anal. 1 (1980), 37-46. · Zbl 0495.62083
[6] D. E. Nicholls, B. G. Quinn: Multiple autoregressive models with random coefficients. J. Multivariate Anal. 11 (1981), 185-198. · Zbl 0512.62084
[7] D. E. Nicholls, B. G. Quinn: Random Coefficient Autoregressive Models: An Introduction. (Lecture Notes in Statistics 11.) Springer-Verlag, Berlin-Heidelberg-New York 1982. · Zbl 0497.62081
[8] M. Pourahmadi: On stationarity of the solution of a doubly stochastic model. J. Time Ser. Anal. 7 (1986), 123-131. · Zbl 0595.60041
[9] D. Tjøstheim: Some doubly stochastic time series models. J. Time Ser. Anal. 7 (1986), 51-72. · Zbl 0588.62169
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