Econometric Theory

Table of Contents - 2000 - Volume 16, Issue 05  


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

(Fractionally Integrated Processes)

James  Davidson a1c1 and Robert M.  de Jong a2
a1 Cardiff University
a2 Michigan State University

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 [greater-than-or-equal] 1.


Correspondence:
c1 Address correspondence to: James Davidson, Cardiff Business School, Cardiff University, Colum Drive, Cardiff CF1 3EU, UK.

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