Statistics Papers

Document Type

Journal Article

Date of this Version

1-1996

Publication Source

Econometrica

Volume

64

Issue

1

Start Page

139

Last Page

174

DOI

10.2307/2171927

Abstract

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.

Copyright/Permission Statement

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.

Keywords

stochastic volatility, ARCH, continuous record

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Date Posted: 27 November 2017

This document has been peer reviewed.