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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.

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