THE FUNCTIONAL CENTRAL LIMIT THEOREM AND WEAK CONVERGENCE TO STOCHASTIC INTEGRALS II

James Davidson () and Robert M. de Jong

Econometric Theory, 2000, vol. 16, issue 05, pages 643-666

Abstract: This paper derives a functional central limit theorem for the partial sums of fractionally integrated processes, otherwise known as I(d) processes for d 1/2. Such processes have long memory, and the limit distribution is the so-called fractional Brownian motion, having correlated increments even asymptotically. The underlying shock variables may themselves exhibit quite general weak dependence by being near-epoch-dependent functions of mixing processes. Several weak convergence results for stochastic integrals having fractional integrands and weakly dependent integrators are also obtained. Taken together, these results permit I(p + d) integrands for any integer p 1.

Date: 2000
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Journal Article: THE FUNCTIONAL CENTRAL LIMIT THEOREM AND WEAK CONVERGENCE TO STOCHASTIC INTEGRALS I (2000)
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Persistent link: http://EconPapers.repec.org/RePEc:cup:etheor:v:16:y:2000:i:05:p:643-666_16

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