Advertisement

Journal of Statistical Theory and Practice

, Volume 2, Issue 3, pp 339–354 | Cite as

On Exponentially Weighted Recursive Least Squares for Estimating Time-Varying Parameters and its Application to Computer Workload Forecasting

  • Ta-Hsin Li
Article

Abstract

Motivated by a relationship between the exponentially weighted recursive least squares (RLS) and the Kalman filter (KF) under a special state-space model (SSM), several simple generalizations of RLS are discussed. These generalized RLS algorithms preserve the key feature of exponential weighting but provide additional flexibility for better tracking performance. They can even outperform KF in some situations when the SSM assumption does not hold. The algorithms are applied to a problem of computer workload forecasting with real data.

AMS Subject Classification

62M10 

Keywords

Adaptive filter computer workload Kalman filter recursive least squares seasonal time series state-space model 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Anderson, A.D.O., Moore, J.B., 1979. Optimal Filtering. Prentice Hall, Englewood Cliffs, NJ.zbMATHGoogle Scholar
  2. Bittanti, S., Campi, M., 1994. Bounded error identification of time-varying parameters by RLS techniques. IEEE Trans. Automat. Contr., 39, 1106–1110.MathSciNetCrossRefGoogle Scholar
  3. Campi, M., 1994. Exponentially weighted least squares identification of time-varying systems with white disturbances. IEEE Trans. Signal Processing, 42, 2906–2914.CrossRefGoogle Scholar
  4. Eleftheriou, E., Falconer, D., 1986. Tracking properties and steady-state performance of RLS adaptive filter algorithms. IEEE Trans. Acoust., Speech, Signal Processing, 34, 1097–1110.CrossRefGoogle Scholar
  5. Eweda, E., 1994. Comparison of RLS, LMS, and sign algorithms for tracking randomly time-varying channels. IEEE Trans. Signal Processing, 42, 2937–2944.CrossRefGoogle Scholar
  6. Eweda, E., Macchi, O., 1985. Tracking error bounds of adaptive nonstationary filtering. Automatica, 21, 293–302.MathSciNetCrossRefGoogle Scholar
  7. Guo, L., Ljung, L., Priouret, P., 1993. Performance analysis of forgetting factor RLS algorithm. Int. J. Adaptive Contr., Signal Processing, 7, 525–537.MathSciNetCrossRefGoogle Scholar
  8. Hsia, T.C., 1977. System Identification. Lexington Books, Lexington, MA.Google Scholar
  9. Harvey, A.C., 1989. Forecasting, Structural Time Series Models and the Kalman Filter. Cambridge University Press, Cambridge, UK.Google Scholar
  10. Haykin, S., 1996. Adaptive Filter Theory, 3rd Edn., Prentice Hall, Upper Saddle River, NJ.zbMATHGoogle Scholar
  11. Haykin, S., Sayed, A.H., Zeidler, J.R., Yee, P., Wei, P.C., 1997. Adaptive tracking of linear time-variant systems by extended RLS algorithm. IEEE Trans. Signal Processing, 45, 1118–1128.CrossRefGoogle Scholar
  12. Jazwinski, A.H., 1970. Stochastic Processes and Filtering Theory. Academic Press, San Diego, CA.zbMATHGoogle Scholar
  13. Li, T.H., 2005. A hierarchical framework for modeling and forecasting web server workload. J. Amer. Statist. Assoc., 100, 748–763.MathSciNetCrossRefGoogle Scholar
  14. Li, T.H., Hinich, M.J., 2002. A filter bank approach for modeling and forecasting seasonal patterns. Technometrics, 44, 1–14.MathSciNetCrossRefGoogle Scholar
  15. Pollock, D.S.G., 2003. Recursive estimation in econometrics. Computational Statistics & Data Analysis, 44, 37–75.MathSciNetCrossRefGoogle Scholar
  16. Rao, C.R., 1973. Linear statistical inference and its applications, 2nd Edn. Wiley & Sons, New York.CrossRefGoogle Scholar
  17. Sayed, A.H., Kailath, T., 1994. A state-space approach to adaptive RLS filtering. IEEE Signal Processing Mag., 11, 11–60.CrossRefGoogle Scholar
  18. Wei, P.C., Zeidler, J.R., Ku, W.H., 1997. Adaptive recovery of a chirped signal using the RLS algorithm. IEEE Trans. Signal Processing, 45, 363–376.CrossRefGoogle Scholar
  19. Young, P., 1984. Recursive Estimation and Time Series Analysis. Springer-Verlag, Berlin.CrossRefGoogle Scholar
  20. Young, P., 2000. Stochastic, dynamic modelling and signal processing: time variable and state dependent parameter estimation. Nonstationary and Nonlinear Signal Processing, pp. 74–114, W.J. Fitzgerald, A. Walden, R. Smith and P. Young, Eds., Cambridge University Press, Cambridge, UK.Google Scholar
  21. Zhu, Y., 1999. Efficient recursive state estimator for dynamic systems without knowledge of noise covariances. IEEE Trans. Aerospace and Electronic Systems, 35, 102–114.CrossRefGoogle Scholar

Copyright information

© Grace Scientific Publishing 2008

Authors and Affiliations

  1. 1.Department of Mathematical SciencesIBM T. J. Watson Research CenterYorktown HeightsUSA

Personalised recommendations