Journal
SCIENCE IN CHINA SERIES A-MATHEMATICS
Volume 48, Issue 9, Pages 1169-1181Publisher
SCIENCE PRESS
DOI: 10.1360/02ys0246
Keywords
tail probability; stationary distribution; nonlinear AR model; nonlinear autoregressive functional; conditional heteroscedastic model; heavy-tailed distribution
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We study the tail probability of the stationary distribution of nonparametric nonlinear autoregressive functional conditional heteroscedastic (NARFCH) model with heavy-tailed innovations. Our result shows that the tail of the stationary marginal distribution of an NARFCH series is heavily dependent on its conditional variance. When the innovations are heavy-tailed, the tail of the stationary marginal distribution of the series will become heavier or thinner than that of its innovations. We give some specific formulas to show how the increment or decrement of tail heaviness depends on the assumption on the conditional variance function. Some examples are given.
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