Statistics and Data Science Seminar
Michael Levine
Purdue University
Consistent long-memory parameter estimation in a LARCH time series model and its connection to the Hurst parameter of the fractional Brownian motion
Abstract: We investigate several possible strategies for consistently estimating the
so-called Hurst parameter H responsible for the long-memory property in a
special class of nonlinear ARCH-type models popularly known as LARCH, as well as
in the continuous-time Gaussian stochastic process named fractional Brownian
motion (fBm). Several estimation methods are discussed, including a conditional
MLE method and a local Whittle-type estimation procedure. The conditional MLE is
proved to be consistent and a Portmanteau-type test for model validation is
established. By constructing the LARCH and fBm processes on a common probability
space, and showing the convergence of various partial sums of the former to the
latter in mean squared, we can propose a specially designed conditional maximum
likelihood method for estimating the fBm's Hurst parameter. In keeping with the
popular financial interpretation of ARCH-type models, all estimators are
based only on observation of the "returns" of the model and not on the
"volatilities".
Tea at 3:15 PM
Wednesday November 14, 2007 at 3:30 PM in SEO 712