We discuss the relationship between the marginal tail risk probability and the innovation'stail risk probability for some stationary financial time series models.We first give the main results on the tail behavior of a class of infinite weighted sums of random variableswith heavy-tailed probabilities. And then, the main results are applied tothree important types of time series models:infinite order moving averages, the simple bilinear time series and the solutions of stochasticdifference equations. The explicit formulas are given to describe how the marginaltail probabilities come from the innovation's tail probabilities for these time series.Our results can be applied to the tail estimation of time series and are useful for risk analysis in finance.
