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Estimation Of Coefficients Of Time Series Regression With A Nonstationary Error Process

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  • Yoshihiro Usami
  • Mituaki Huzii

Abstract

. We treat a problem of estimating unknown coefficients of a time series regression when the variance of the error changes with time, i.e. when a process which the error term obeys is nonstationary. First, we show the weak consistency of the ordinary least squares estimator for the coefficients of a polynomial regression under some assumptions on the covariance structure of the error process. Next, we propose a nonparametric method for estimating the variance of the error process and a weighted least squares estimator of the regression coefficients, which is constructed by using the estimator of the variance. We investigate statistical properties of our proposed estimator in the following way. We consider the prediction of a future value of a linear trend by using our proposed estimator and evaluate its prediction error. By simulation studies, we compare the prediction error of the predictor constructed by using our proposed estimator with the prediction errors obtained for other estimators including the ordinary least squares estimator when the variance of the error process increases with time and the sample sizes are small. As a result, our proposed estimator seems to be reasonable.

Suggested Citation

  • Yoshihiro Usami & Mituaki Huzii, 1995. "Estimation Of Coefficients Of Time Series Regression With A Nonstationary Error Process," Journal of Time Series Analysis, Wiley Blackwell, vol. 16(1), pages 105-118, January.
  • Handle: RePEc:bla:jtsera:v:16:y:1995:i:1:p:105-118
    DOI: 10.1111/j.1467-9892.1995.tb00224.x
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    References listed on IDEAS

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    1. Harvey, A C, 1976. "Estimating Regression Models with Multiplicative Heteroscedasticity," Econometrica, Econometric Society, vol. 44(3), pages 461-465, May.
    2. White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, vol. 48(4), pages 817-838, May.
    3. Breusch, T S & Pagan, A R, 1979. "A Simple Test for Heteroscedasticity and Random Coefficient Variation," Econometrica, Econometric Society, vol. 47(5), pages 1287-1294, September.
    4. Robinson, P M, 1987. "Asymptotically Efficient Estimation in the Presence of Heteroskedasticity of Unknown Form," Econometrica, Econometric Society, vol. 55(4), pages 875-891, July.
    5. A. C. Harvey & P. M. Robinson, 1988. "Efficient Estimation Of Nonstationary Time Series Regression," Journal of Time Series Analysis, Wiley Blackwell, vol. 9(3), pages 201-214, May.
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