A quadratic ARCH(∞) model with long memory and Lévy stable behavior of squares
Keyword(s):
We introduce a modification of the linear ARCH (LARCH) model (Giraitis, Robinson, and Surgailis (2000)) - a special case of Sentana's (1995) quadratic ARCH (QARCH) model - for which the conditional variance is a sum of a positive constant and the square of an inhomogeneous linear combination of past observations. Necessary and sufficient conditions for the existence of a stationary solution with finite variance are obtained. We give conditions under which the stationary solution with infinite fourth moment can exhibit long memory, the leverage effect, and a Lévy-stable limit behavior of partial sums of squares.
2008 ◽
Vol 40
(4)
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pp. 1198-1222
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Keyword(s):
2016 ◽
Vol 15
(03)
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pp. 1650049
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2021 ◽
Vol 14
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pp. 380-395
1970 ◽
Vol 22
(2)
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pp. 297-307
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2002 ◽
Vol 39
(2)
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pp. 370-382
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