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Recursive Estimation in Armax Models

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New Directions in Time Series Analysis

Part of the book series: The IMA Volumes in Mathematics and its Applications ((IMA,volume 46))

Abstract

Herein we first review some important algorithms and their statistical properties in the literature on recursive estimation of the parameters of an ARMAX model. We then describe some recent developments of efficient procedures for recursive estimation and their statistical theory. These developments not only extend important statistical properties such as consistency, asymptotic normality, asymptotic efficiency, that have been established for certain classes of offline estimators to their recursive counterparts, but are also applicable to on-line adaptive prediction and adaptive control of ARMAX systems.

This research was supported by the National Science Foundation, the National Security Agency and the Air Force Office of Scientific Research. The paper was prepared while the author was in residence at the Institute for Mathematics and Its Applications, whose hospitality and support are gratefully acknowledged.

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Author information

Authors and Affiliations

  1. Department of Statistics, Stanford University, Stanford, CA, 94305, USA

    Tze Leung Lai

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  1. Tze Leung Lai
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Editor information

Editors and Affiliations

  1. Department of Statistics, University of California, Berkeley, CA, 94720, USA

    David Brillinger

  2. Department of Electrical Engineering, McGill University, Montreal, Quebec, H3A 2A7, Canada

    Peter Caines

  3. Department of Economics, University of Minnesota, Minneapolis, MN, 55455, USA

    John Geweke

  4. Department of Statistics, Texas A&M University, College Station, TX, 77843-3143, USA

    Emanuel Parzen

  5. Mathematics Department, University of California, San Diego, La Jolla, CA, 92093, USA

    Murray Rosenblatt

  6. Department of Mathematics, Boston University, Boston, MA, 02215, USA

    Murad S. Taqqu

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© 1993 Springer-Verlag New York, Inc.

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Lai, T.L. (1993). Recursive Estimation in Armax Models. In: Brillinger, D., Caines, P., Geweke, J., Parzen, E., Rosenblatt, M., Taqqu, M.S. (eds) New Directions in Time Series Analysis. The IMA Volumes in Mathematics and its Applications, vol 46. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-9296-5_16

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  • DOI: https://doi.org/10.1007/978-1-4613-9296-5_16

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4613-9298-9

  • Online ISBN: 978-1-4613-9296-5

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