A LARCH($\infty$) Vector Valued Process
Résumé
We introduce a vector version of the ARCH($\infty$) equation yielding a simple approach to various models like bilinear or GARCH models. To this aim we provide an explicit chaotic expansion of a solution for this LARCH equation, and show the uniqueness of this solution under reasonable conditions. Independent or $N$-Markov approximations of this process allow to simulate their trajectory or to derive bounds for their weak dependence coefficients as defined by Doukhan and Louhichi (1999). We finally consider a long range dependent version of this model; in this case we provide an existence and uniqueness result.
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