Functional convergence of stochastic integrals with application to statistical inference

Richard A. Davis and Li Song

Stochastic Processes and their Applications, 2012, vol. 122, issue 3, 725-757

Abstract: Assuming that {(Un,Vn)} is a sequence of càdlàg processes converging in distribution to (U,V) in the Skorohod topology, conditions are given under which {∬fn(β,u,v)dUndVn} converges weakly to ∬f(β,x,y)dUdV in the space C(R), where fn(β,u,v) is a sequence of “smooth” functions converging to f(β,u,v). Integrals of this form arise as the objective function for inference about a parameter β in a stochastic model. Convergence of these integrals play a key role in describing the asymptotics of the estimator of β which optimizes the objective function. We illustrate this with a moving average process.

Keywords: Weak convergence; Stochastic processes; Unit root problem (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.spa.2011.10.007

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