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On Residual Variance Estimation in Autoregressive Models

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  • Raul P. Mentz
  • Pedro A. Morettin
  • Clélia Toloi

Abstract

In this paper we consider time series models belonging to the autoregressive (AR) family and deal with the estimation of the residual variance. This is important because estimates of the variance are involved in, for example, confidence sets for the parameters of the model, estimation of the spectrum, expressions for the estimated error of prediction and sample quantities used to make inferences about the order of the model. We consider the asymptotic biases for moment and least squares estimators of the residual variance, and compare them with known results when available and with those for maximum likelihood estimators under normality. Simulation results are presented for finite samples

Suggested Citation

  • Raul P. Mentz & Pedro A. Morettin & Clélia Toloi, 1998. "On Residual Variance Estimation in Autoregressive Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 19(2), pages 187-208, March.
    • Handle: RePEc:bla:jtsera:v:19:y:1998:i:2:p:187-208
    DOI: 10.1111/1467-9892.00085
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    Cited by:

    1. Mentz, R. P. & Morettin, P. A. & Toloi, C. M. C., 1999. "On least-squares estimation of the residual variance in the first-order moving average model," Computational Statistics & Data Analysis, Elsevier, vol. 29(4), pages 485-499, February.
    2. Niels Joachim Gormsen, 2021. "Time Variation of the Equity Term Structure," Journal of Finance, American Finance Association, vol. 76(4), pages 1959-1999, August.

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