On the existence of some ARCH($\infty$) processes

Abstract

A new sufficient condition for the existence of a stationary causal solution of an ARCH($\infty$) equation is provided. This condition allows to consider polynomially decaying coefficients, so that it can be applied to the so-called FIGARCH processes, whose existence is thus proved.

Cited by in corpus (4)

• Propagation of Memory Parameter from Durations to Counts
• Limit theorems for long memory stochastic volatility models with infinite variance: Partial Sums and Sample Covariances
• Quantile autoregressive conditional heteroscedasticity
• Moment conditions for random coefficient AR($\infty$) under non-negativity assumptions