=1, the linear prediction of yt+h based on yt, yt-1,... is considered using an autoregressive model of finite order k fitted to a realization of length T. Assuming that k --> [infinity] (at some rate) as T --> [infinity], the consistency and asymptotic normality of the estimated autoregressive coefficients are derived, and an asymptotic approximation to the mean square prediction error based on this autoregressive model fitting approach is obtained. The asymptotic effect of estimating autoregressive parameters is found to inflate the minimum mean square prediction error by a factor of (1 + kr/T)."> =1, the linear prediction of yt+h based on yt, yt-1,... is considered using an autoregressive model of finite order k fitted to a realization of length T. Assuming that k --> [infinity] (at some rate) as T --> [infinity], the consistency and asymptotic normality of the estimated autoregressive coefficients are derived, and an asymptotic approximation to the mean square prediction error based on this autoregressive model fitting approach is obtained. The asymptotic effect of estimating autoregressive parameters is found to inflate the minimum mean square prediction error by a factor of (1 + kr/T)."> =1, the linear prediction of yt+h based on yt, yt-1,... is considered us">
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Prediction of multivariate time series by autoregressive model fitting

Author

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  • Lewis, Richard
  • Reinsel, Gregory C.
Abstract
Suppose the stationary r-dimensional multivariate time series {yt} is generated by an infinite autoregression. For lead times h>=1, the linear prediction of yt+h based on yt, yt-1,... is considered using an autoregressive model of finite order k fitted to a realization of length T. Assuming that k --> [infinity] (at some rate) as T --> [infinity], the consistency and asymptotic normality of the estimated autoregressive coefficients are derived, and an asymptotic approximation to the mean square prediction error based on this autoregressive model fitting approach is obtained. The asymptotic effect of estimating autoregressive parameters is found to inflate the minimum mean square prediction error by a factor of (1 + kr/T).

Suggested Citation

  • Lewis, Richard & Reinsel, Gregory C., 1985. "Prediction of multivariate time series by autoregressive model fitting," Journal of Multivariate Analysis, Elsevier, vol. 16(3), pages 393-411, June.
    • Handle: RePEc:eee:jmvana:v:16:y:1985:i:3:p:393-411
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