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Linear Time Series and Optimal Linear Prediction

  • Dimitris N. Politis
Part of the Frontiers in Probability and the Statistical Sciences book series (FROPROSTAS)

Abstract

Optimal linear prediction has been well-studied since the 1940s with the work of A. Kolmogorov and N. Wiener. However, estimating the coefficients of the optimal predictor based on data had—until now—been done using a truncated predictor via a fitted AR(p) model. Here we show how the Model-Free Prediction Principle can be applied to yield a new approximation to the optimal predictor that is not truncated, i.e., uses the complete data history.

Keywords

Discrete Fourier Transform Positive Definiteness Toeplitz Matrix Shrinkage Estimator Optimal Predictor 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

Chapter  6 is based on the paper: T. McMurry and D.N. Politis (2015). ‘High-dimensional autocovariance matrices and optimal linear prediction’ (with Discussion), Electronic Journal of Statistics, vol. 9, pp. 753–822. Many thanks are due to the Editor, George Michailidis, for hosting this discussion paper, and to the discussants: Xiaohui Chen, Yulia Gel, Rob Hyndman, Wilfredo Palma, and Wei-Biao Wu for their insightful comments.

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© The Author 2015

Authors and Affiliations

  • Dimitris N. Politis
    • 1
  1. 1.Department of MathematicsUniversity of California, San DiegoLa JollaUSA

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