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Weighted least squares approximate restricted likelihood estimation for vector autoregressive processes

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  • Willa W. Chen
  • Rohit S. Deo

Abstract

We derive a weighted least squares approximate restricted likelihood estimator for a k-dimensional pth-order autoregressive model with intercept. Exact likelihood optimization of this model is generally infeasible due to the parameter space, which is complicated and high-dimensional, involving pk-super-2 parameters. The weighted least squares estimator has significantly reduced bias and mean squared error than the ordinary least squares estimator for both stationary and nonstationary processes. Furthermore, at the unit root, the limiting distribution of the weighted least squares approximate restricted likelihood estimator is shown to be the zero-intercept Dickey--Fuller distribution, unlike the ordinary least squares with intercept estimator that has a different distribution with significantly higher bias. Copyright 2010, Oxford University Press.

Suggested Citation

  • Willa W. Chen & Rohit S. Deo, 2010. "Weighted least squares approximate restricted likelihood estimation for vector autoregressive processes," Biometrika, Biometrika Trust, vol. 97(1), pages 231-237.
  • Handle: RePEc:oup:biomet:v:97:y:2010:i:1:p:231-237
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    File URL: http://hdl.handle.net/10.1093/biomet/asp071
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    Cited by:

    1. Peter C.B. Phillips & Ye Chen, "undated". "Restricted Likelihood Ratio Tests in Predictive Regression," Cowles Foundation Discussion Papers 1968, Cowles Foundation for Research in Economics, Yale University.
    2. Deo, Rohit S., 2012. "Improved forecasting of autoregressive series by weighted least squares approximate REML estimation," International Journal of Forecasting, Elsevier, vol. 28(1), pages 39-43.

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