NATIONAL BUREAU OF ECONOMIC RESEARCH
NATIONAL BUREAU OF ECONOMIC RESEARCH

Continuous Record Asymptotics for Rolling Sample Variance Estimators

Dean P. Foster, Daniel B. Nelson

NBER Technical Working Paper No. 163
Issued in August 1994
NBER Program(s):   AP

It is widely known that conditional covariances of asset returns change over time. Researchers adopt many strategies to accommodate conditional heteroskedasticity. Among the most popular are: (a) chopping the data into short blocks of time and assuming homoskedasticity within the blocks, (b) performing one-sided rolling regressions, in which only data from, say, the preceding five year period is used to estimate the conditional covariance of returns at a given date, and (c) two-sided rolling regressions which use, say, five years of leads and five years of lags. GARCH amounts to a one-sided rolling regression with exponentially declining weights. We derive asymptotically optimal window lengths for standard rolling regressions and optimal weights for weighted rolling regressions. An empirical model of the S&P 500 stock index provides an example.

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Document Object Identifier (DOI): 10.3386/t0163

Published: Foster, Dean P. and Dan B. Nelson. "Continuous Record Asymptotics For Rolling Sample Variance Estimators," Econometrica, 1996, v64(1), 139-174.

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