Fractionally Integrated Models With ARCH Errors

Hauser, Michael A. and Kunst, Robert M. (May 1993) Fractionally Integrated Models With ARCH Errors. Forschungsberichte / Research Memoranda 322

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Abstract: We introduce ARFIMA-ARCH models which simultaneously incorporate fractional differencing and conditional heteroskedasticity. We develop the likelihood function and a numerical estimation procedure for this model class. Two ARCH models - Engle- and Weiss-type - are explicitly treated and stationarity conditions are derived. Finite-sample properties of the estimation procedure are explored by Monte Carlo simulation. An application to the Standard & Poor 500 Index indicates existence of intermediate memory (d<0) for the 1980's and no fractional differencing (d=0) but strong conditional heteroskedastic effects for the 1960's. For the latter time period, contrary to the suggestion of long memory by Mandelbrot, we only found evidence for a positive first-order autoregressive parameter.;

Item Type: IHS Series
Status: Published
Date Deposited: 26 Sep 2014 10:35
Last Modified: 01 Apr 2016 14:09
URI: http://irihs.ihs.ac.at/id/eprint/677

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