Stationarity and memory of \(\text{ARCH}(\infty)\) models. (English) Zbl 1046.62096
Summary: Necessary and sufficient conditions for covariance stationarity of \(\text{ARCH}(\infty)\) models, for both the levels and the squares, are established. The result applies to any form of the conditional variance coefficients. This includes \(\text{GARCH}(p,q)\) and also specifications with hyperbolically decaying coefficients, such as the autoregressive coefficients of the autoregressive fractionally integrated moving average model. The covariance stationarity condition for the levels rules out long memory in the squares.
MSC:
| 62M10 | Time series, auto-correlation, regression, etc. in statistics (GARCH) |
Keywords:
nonlinear time series modelsReferences:
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