On the growth rate of superadditive processes and the stability of functional GARCH models

Baye Matar Kandji ()
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Baye Matar Kandji: CREST, ENSAE, Institut Polytechnique de Paris

No 2023-07, Working Papers from Center for Research in Economics and Statistics

Abstract: We extend the result of Kesten (Proc. Am. Math. Soc., 49:205- 211, 1975) on the growth rate of random walks with stationary increments to superadditive processes. We show that superadditive processes which remain positive after a certain time diverge at least linearly to infinity. Our proof relies on new techniques based on concepts from ergodic theory. Different versions of this result are also given, generalizing Lemma 3.4 of Bougerol and Picard (Ann. Probab., 20:1714-1730, 1992) on the contraction property of products of random matrices. We use our results to provide necessary and sufficient conditions for the stability of a class of Stochastic Recurrent Equations (SRE) with positive coefficients in the space of continuous functions with compact support, including continuous functional GARCH models.

Keywords: Ergodic theorem Contraction property; functional Garch; Lyapunov exponent; Stochastic Recurrence Equation; Strict stationarity; Subadditive sequence. (search for similar items in EconPapers)
Pages: 32 pages
Date: 2023-05-06
New Economics Papers: this item is included in nep-des and nep-ets
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