TY  - JOUR
AU  - Foster,Dean P.
AU  - Nelson,Daniel B.
TI  - Continuous Record Asymptotics for Rolling Sample Variance Estimators
JF  - National Bureau of Economic Research Technical Working Paper Series
VL  - No. 163
PY  - 1994
Y2  - August 1994
UR  - http://www.nber.org/papers/t0163
L1  - http://www.nber.org/papers/t0163.pdf
AB  - 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.
ER  -