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1 results

  • A quadratic ARCH(∞) model with long memory and Lévy stable behavior of squares

  • Part of
  • Donatas Surgailis
  • Journal:
    Advances in Applied Probability / Volume 40 / Issue 4 / December 2008
    Published online by Cambridge University Press:
    01 July 2016, pp. 1198-1222
    Print publication:
    December 2008
    • Article
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  • 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.