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Signal Extraction in Nonstationary Series

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  • Burridge, Peter
  • Wallis, Kenneth F

Abstract

The state-space method is applied to the problem of separating an autoregressive (AR) signal from composite AR and white normal noise. In the stationary case, for which the Wiener filter exists, we show explicitly its equavalence to the steady-state Kalman filter. Existing results for difference-stationary processes are generalised to the explosive AR case, with careful attention paid to initial conditions, the limiting filter is shown to be stable. Conditions are given for convergence of the signal extraction erroe variance, and these are seen to exclude the existence of an unstable common factor in signal and noise autoregressions, but not nonstationarity. The general argument is illustrated with simple examples and the role of controllability and detectability is explored in an appendix.

Suggested Citation

  • Burridge, Peter & Wallis, Kenneth F, 1983. "Signal Extraction in Nonstationary Series," The Warwick Economics Research Paper Series (TWERPS) 234, University of Warwick, Department of Economics.
  • Handle: RePEc:wrk:warwec:234
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    File URL: https://www2.warwick.ac.uk/fac/soc/economics/research/workingpapers/1978-1988/twerp234.pdf
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    References listed on IDEAS

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    3. Krugman, Paul, 1979. "A Model of Balance-of-Payments Crises," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 11(3), pages 311-325, August.
    4. Blanchard, Olivier Jean & Kahn, Charles M, 1980. "The Solution of Linear Difference Models under Rational Expectations," Econometrica, Econometric Society, vol. 48(5), pages 1305-1311, July.
    5. Dornbusch, Rudiger & Fischer, Stanley, 1980. "Exchange Rates and the Current Account," American Economic Review, American Economic Association, vol. 70(5), pages 960-971, December.
    6. Dornbusch, Rudiger, 1976. "Expectations and Exchange Rate Dynamics," Journal of Political Economy, University of Chicago Press, vol. 84(6), pages 1161-1176, December.
    7. Flood, Robert P & Garber, Peter M, 1980. "Market Fundamentals versus Price-Level Bubbles: The First Tests," Journal of Political Economy, University of Chicago Press, vol. 88(4), pages 745-770, August.
    8. Olivier Jean Blanchard, 1980. "The Monetary Mechanism in the Light of Rational Expectations," NBER Chapters,in: Rational Expectations and Economic Policy, pages 75-116 National Bureau of Economic Research, Inc.
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