Generating stochastic processes from distributions of random variables

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A stochastic process is a sequence of random variables $\{Y_t : t=0,\pm 1,\pm 2,\pm 3,\pm 4,\dots \}$. How is this determined by the set of distributions of all finite collections of $Y$'s? I do not quite understand what this means, it is just stated as fact in Time Series Analysis - With Applications in R by J Cryer.