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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: (a) chopping the data into short blacks 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 and example.
This is the peer reviewed version of the following article: Econometrica, which has been published in final form at http://www.jstor.org/stable/2171927. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving link to http://olabout.wiley.com/WileyCDA/Section/id-820227.html#terms.
stochastic volatility, ARCH, continuous record
Foster, D. P., & Nelson, D. B. (1996). Continuous Record Asymptotics for Rolling Sample Variance Estimators. Econometrica, 64 (1), 139-174. http://dx.doi.org/10.2307/2171927
Date Posted: 27 November 2017
This document has been peer reviewed.