engleski

Functional limit theorem for moving average processes

Functional limit theorems have been first obtained for independent and identically distributed random variables with finite second moments. We consider a strictly stationary sequence of random variables with infinite second moments and show that under the properties of weak dependence and regular variation with index bwtween 0 and 2, the corresponding partial sum stochastic process converges in distribution to a stable Levy process in the space D[0, 1] endowed with Skorohod's M1 topology. Here, D[0, 1] is the space of real-valued right continuous functions on [0, 1] with left limits. The limiting process is characterized in terms of its characteristic triple. This result is then applied to moving average processes.

functional limit theorem ; moving average ; regular variation ; mixing ; stable processes

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