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Stationary integrated ARCH(\(\infty\)) and AR(\(\infty\)) processes with finite variance. (English) Zbl 1406.62095

Summary: We prove the long standing conjecture of Z. Ding and C. W. J. Granger [J. Econom. 73, No. 1, 185–215 (1996; Zbl 1075.91626)] about the existence of a stationary Long Memory ARCH model with finite fourth moment. This result follows from the necessary and sufficient conditions for the existence of covariance stationary integrated AR(\(\infty\)), ARCH(\(\infty\)), and FIGARCH models obtained in the present article. We also prove that such processes always have long memory.

MSC:

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
60G10 Stationary stochastic processes
60F05 Central limit and other weak theorems

Citations:

Zbl 1075.91626
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References:

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