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Econometrics Paper
Alternative Forms of Fractional Brownian Motion - (Now published in 'Journal of Statistical Planning and Inference', 80 (1999), pp.111-122.)
D Marinucci and Peter M Robinson July 1998
Paper No' EM/1998/354:
Full Paper (pdf)

Tags: frational brownian motion; nonstationary time series; long-range dependence

It is pointed out that two contradictory definitions of fractional Brownian motion are well established, one prevailing in the probabilistic literature, the other in the econometric literature. Each is associated with a different definition of nonstationary fractional time series. These various definitions have occasionally led to some confusion. The paper discusses the definitions and attempts a clarification.