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Continuous Record Asymptotics for Rolling Sample Variance Estimators


  • Foster, Dean P
  • Nelson, Daniel B


It is widely known that conditional covariances of asset returns change over time. Researchers doing empirical work have adopted many strategies for accommodating conditional heteroskedasticity. One popular strategy is performing 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. The authors develop continuous record asymptotic approximations for the measurement error in conditional variances when using these methods. They derive asymptotically optimal window lengths for the standard rolling regressions and optimal weights for weighted rolling regressions. The S&P 500 is used as an empirical example. Copyright 1996 by The Econometric Society.

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  • Foster, Dean P & Nelson, Daniel B, 1996. "Continuous Record Asymptotics for Rolling Sample Variance Estimators," Econometrica, Econometric Society, vol. 64(1), pages 139-174, January.
  • Handle: RePEc:ecm:emetrp:v:64:y:1996:i:1:p:139-74

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    References listed on IDEAS

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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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