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Marginal distributions of autoregressive processes. (English) Zbl 0537.60027
Information theory, statistical decision functions, random processes, Trans. 9th Prague Conf., Prague 1982, Vol. A, 127-135 (1983).
Summary: [For the entire collection see Zbl 0531.00015.]
Consider a stationary autoregressive process \(\{X_ s\}\) defined by the relation \(X_ s=\rho X_{s-1}+Y_ s\), where \(\{Y_ s\}\) is a white noise. Assume that \(Y_ s\) are independent and have the same distribution (normal, rectangular, Laplace or Cauchy). For these cases the distribution of \(X_ s\) is calculated. Conversely, if a distribution of \(X_ s\) is given (normal, exponential, gamma, Laplace, rectangular or Cauchy), the corresponding distribution of \(Y_ s\) is derived. The results are applicable in Monte Carlo methods for constructing dependent random variables with a given univariate marginal distribution.

60G10 Stationary stochastic processes
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)