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.
Similar content being viewed by others
References
Anderson, A.D.O., Moore, J.B., 1979. Optimal Filtering. Prentice Hall, Englewood Cliffs, NJ.
Bittanti, S., Campi, M., 1994. Bounded error identification of time-varying parameters by RLS techniques. IEEE Trans. Automat. Contr., 39, 1106–1110.
Campi, M., 1994. Exponentially weighted least squares identification of time-varying systems with white disturbances. IEEE Trans. Signal Processing, 42, 2906–2914.
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.
Eweda, E., 1994. Comparison of RLS, LMS, and sign algorithms for tracking randomly time-varying channels. IEEE Trans. Signal Processing, 42, 2937–2944.
Eweda, E., Macchi, O., 1985. Tracking error bounds of adaptive nonstationary filtering. Automatica, 21, 293–302.
Guo, L., Ljung, L., Priouret, P., 1993. Performance analysis of forgetting factor RLS algorithm. Int. J. Adaptive Contr., Signal Processing, 7, 525–537.
Hsia, T.C., 1977. System Identification. Lexington Books, Lexington, MA.
Harvey, A.C., 1989. Forecasting, Structural Time Series Models and the Kalman Filter. Cambridge University Press, Cambridge, UK.
Haykin, S., 1996. Adaptive Filter Theory, 3rd Edn., Prentice Hall, Upper Saddle River, NJ.
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.
Jazwinski, A.H., 1970. Stochastic Processes and Filtering Theory. Academic Press, San Diego, CA.
Li, T.H., 2005. A hierarchical framework for modeling and forecasting web server workload. J. Amer. Statist. Assoc., 100, 748–763.
Li, T.H., Hinich, M.J., 2002. A filter bank approach for modeling and forecasting seasonal patterns. Technometrics, 44, 1–14.
Pollock, D.S.G., 2003. Recursive estimation in econometrics. Computational Statistics & Data Analysis, 44, 37–75.
Rao, C.R., 1973. Linear statistical inference and its applications, 2nd Edn. Wiley & Sons, New York.
Sayed, A.H., Kailath, T., 1994. A state-space approach to adaptive RLS filtering. IEEE Signal Processing Mag., 11, 11–60.
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.
Young, P., 1984. Recursive Estimation and Time Series Analysis. Springer-Verlag, Berlin.
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.
Zhu, Y., 1999. Efficient recursive state estimator for dynamic systems without knowledge of noise covariances. IEEE Trans. Aerospace and Electronic Systems, 35, 102–114.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Li, TH. On Exponentially Weighted Recursive Least Squares for Estimating Time-Varying Parameters and its Application to Computer Workload Forecasting. J Stat Theory Pract 2, 339–354 (2008). https://doi.org/10.1080/15598608.2008.10411879
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1080/15598608.2008.10411879