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Asymptotic Bias in Parameter Estimation of AR‐Processes Using Recursive Least Squares with Exponential Forgetting

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  • L. Arvastson
  • H. Olsson
  • J. Holst

Abstract

The recursive least squares technique is often extended with exponential forgetting as a tool for parameter estimation in time‐varying systems. The distribution of the resulting parameter estimates is, however, unknown when the forgetting factor is less than one. In this paper an approximative expression for bias of the recursively obtained parameter estimates in a time‐invariant AR(na) process with arbitrary noise is given, showing that the bias is non‐zero and giving bounds on the approximation errors. Simulations confirm the approximation expressions.

Suggested Citation

  • L. Arvastson & H. Olsson & J. Holst, 2000. "Asymptotic Bias in Parameter Estimation of AR‐Processes Using Recursive Least Squares with Exponential Forgetting," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 27(1), pages 177-192, March.
    • Handle: RePEc:bla:scjsta:v:27:y:2000:i:1:p:177-192
    DOI: 10.1111/1467-9469.00185
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    1. Roger Buckland & Julian Williams & Janice Beecher, 2015. "Risk and regulation in water utilities: a cross-country comparison of evidence from the CAPM," Journal of Regulatory Economics, Springer, vol. 47(2), pages 117-145, April.
    2. Calice, Giovanni & Chen, Jing & Williams, Julian, 2013. "Liquidity spillovers in sovereign bond and CDS markets: An analysis of the Eurozone sovereign debt crisis," Journal of Economic Behavior & Organization, Elsevier, vol. 85(C), pages 122-143.

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