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Continuous Record Asymptotics for Rolling Sample Variance Estimators


  • Dean P. Foster
  • Daniel B. Nelson


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.

Suggested Citation

  • Dean P. Foster & Daniel B. Nelson, 1994. "Continuous Record Asymptotics for Rolling Sample Variance Estimators," NBER Technical Working Papers 0163, National Bureau of Economic Research, Inc.
  • Handle: RePEc:nbr:nberte:0163
    Note: AP

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    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models


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