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Recursive estimation and modelling of nonstationary and nonlinear time series

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  • David E. Runkle
  • Peter C. Young

Abstract

This paper presents a unified approach to nonlinear and nonstationary time-series analysis for a fairly wide class of linear time variable parameter (TVP) or nonlinear systems. The method theory exploits recursive filtering and fixed interval smoothing algorithms to derive TVP linear model approximations to the nonlinear or nonstationary stochastic system, on the basis of data obtained from the system during planned experiments or passive monitoring exercises. This TVP model includes the State Dependent type of Model (SDM) as a special case, and two particular SDM forms, due to Priestly and Young, are discussed in detail. The paper concludes with three practical examples: the first based on the modelling of data from a simulated nonlinear growth equation; the second concerned with the adaptive forecasting and smoothing of the Box-Jenkins Airline Passenger data; and the third providing a critical appraisal of state dependent modelling applied to the famous Sunspot time-series.

Suggested Citation

  • David E. Runkle & Peter C. Young, 1989. "Recursive estimation and modelling of nonstationary and nonlinear time series," Discussion Paper / Institute for Empirical Macroeconomics 7, Federal Reserve Bank of Minneapolis.
    • Handle: RePEc:fip:fedmem:7
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    References listed on IDEAS

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    1. Christopher A. Sims, 1986. "Are forecasting models usable for policy analysis?," Quarterly Review, Federal Reserve Bank of Minneapolis, vol. 10(Win), pages 2-16.
    2. M. B. Priestley, 1980. "State‐Dependent Models: A General Approach To Non‐Linear Time Series Analysis," Journal of Time Series Analysis, Wiley Blackwell, vol. 1(1), pages 47-71, January.
    3. Thomas Doan & Robert B. Litterman & Christopher A. Sims, 1983. "Forecasting and Conditional Projection Using Realistic Prior Distributions," NBER Working Papers 1202, National Bureau of Economic Research, Inc.
    4. Kalaba, Robert & Tesfatsion, Leigh, 1988. "The flexible least squares approach to time-varying linear regression," Journal of Economic Dynamics and Control, Elsevier, vol. 12(1), pages 43-48, March.
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    Cited by:

    1. Young, Peter C. & Pedregal, Diego J., 1999. "Macro-economic relativity: government spending, private investment and unemployment in the USA 1948-1998," Structural Change and Economic Dynamics, Elsevier, vol. 10(3-4), pages 359-380, December.

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    time series analysis;

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