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Forecasting continuous-time processes with applications to signal extraction

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  • Tucker McElroy

Abstract

The paper derives forecasting and signal extraction estimates for continuous time processes. We present explicit formulas for filters and filter kernels that yield minimum mean square error estimates of future values of the process or an unobserved component, based on a continuum of values in the semi-infinite past. The class of processes considered are cumulations of moving average processes, which includes the CARIMA class. Explicit examples are calculated, and some discussion of applications to signal extraction is provided. We also provide an explicit algorithm for spectral factorization of continuous-time moving averages. Copyright The Institute of Statistical Mathematics, Tokyo (outside the USA) 2013

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  • Tucker McElroy, 2013. "Forecasting continuous-time processes with applications to signal extraction," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(3), pages 439-456, June.
    • Handle: RePEc:spr:aistmt:v:65:y:2013:i:3:p:439-456
    DOI: 10.1007/s10463-012-0373-x
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    References listed on IDEAS

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    1. P. Brockwell, 2001. "Lévy-Driven Carma Processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 53(1), pages 113-124, March.
    2. Bergstrom, A. R., 1988. "The History of Continuous-Time Econometric Models," Econometric Theory, Cambridge University Press, vol. 4(3), pages 365-383, December.
    3. Tucker McElroy & Thomas M. Trimbur, 2011. "On the Discretization of Continuous-Time Filters for Nonstationary Stock and Flow Time Series," Econometric Reviews, Taylor & Francis Journals, vol. 30(5), pages 475-513, October.
    4. Peter J. Brockwell & Vincenzo Ferrazzano & Claudia Klüppelberg, 2012. "High‐frequency sampling of a continuous‐time ARMA process," Journal of Time Series Analysis, Wiley Blackwell, vol. 33(1), pages 152-160, January.
    5. Tucker S. McElroy & Thomas M. Trimbur, 2007. "Continuous time extraction of a nonstationary signal with illustrations in continuous low-pass and band-pass filtering," Finance and Economics Discussion Series 2007-68, Board of Governors of the Federal Reserve System (U.S.).
    6. McElroy, Tucker, 2008. "Matrix Formulas For Nonstationary Arima Signal Extraction," Econometric Theory, Cambridge University Press, vol. 24(4), pages 988-1009, August.
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    Cited by:

    1. Brockwell, Peter J. & Lindner, Alexander, 2015. "CARMA processes as solutions of integral equations," Statistics & Probability Letters, Elsevier, vol. 107(C), pages 221-227.
    2. P. Brockwell, 2014. "Recent results in the theory and applications of CARMA processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(4), pages 647-685, August.
    3. Trimbur Thomas & McElroy Tucker, 2017. "Signal Extraction for Nonstationary Time Series with Diverse Sampling Rules," Journal of Time Series Econometrics, De Gruyter, vol. 9(1), pages 1-37, January.

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