IDEAS home Printed from
   My bibliography  Save this article

Optimal Signal Extraction with Correlated Components


  • McElroy Tucker S.

    () (U.S. Census Bureau – CSRM, 4600 Silver Hill Road, Washington, DC 20233, USA)

  • Maravall Agustin

    () (Bank of Spain, Madrid, Spain)


While it is typical in the econometric signal extraction literature to assume that the unobserved signal and noise components are uncorrelated, there is nevertheless an interest among econometricians in the hypothesis of hysteresis, i.e. that major movements in the economy are fundamentally linked. While specific models involving correlated signal and noise innovation sequences have been developed and applied using state space methods, there is no systematic treatment of optimal signal extraction with correlated components. This paper provides the mean square error optimal formulas for both finite samples and bi-infinite samples and furthermore relates these filters to the more well-known Wiener–Kolmogorov (WK) and Beveridge–Nelson (BN) signal extraction formulas in the case of ARIMA component models. Then we obtain the result that the optimal filter for correlated components can be viewed as a weighted linear combination of the WK and BN filters. The gain and phase functions of the resulting filters are plotted for some standard cases. Some discussion of estimation of hysteretic models is presented, along with empirical results on an economic time series. Comparisons are made between signal extractions from traditional WK filters and those arising from the hysteretic models.

Suggested Citation

  • McElroy Tucker S. & Maravall Agustin, 2014. "Optimal Signal Extraction with Correlated Components," Journal of Time Series Econometrics, De Gruyter, vol. 6(2), pages 1-37, July.
  • Handle: RePEc:bpj:jtsmet:v:6:y:2014:i:2:p:37:n:3

    Download full text from publisher

    File URL:
    Download Restriction: For access to full text, subscription to the journal or payment for the individual article is required.

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    1. Hyndman, Rob J. & Koehler, Anne B. & Snyder, Ralph D. & Grose, Simone, 2002. "A state space framework for automatic forecasting using exponential smoothing methods," International Journal of Forecasting, Elsevier, vol. 18(3), pages 439-454.
    2. William R. Bell & Donald E. K. Martin, 2004. "Computation of asymmetric signal extraction filters and mean squared error for ARIMA component models," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(4), pages 603-623, July.
    3. McElroy, Tucker & Sutcliffe, Andrew, 2006. "An iterated parametric approach to nonstationary signal extraction," Computational Statistics & Data Analysis, Elsevier, vol. 50(9), pages 2206-2231, May.
    4. McElroy, Tucker, 2008. "Matrix Formulas For Nonstationary Arima Signal Extraction," Econometric Theory, Cambridge University Press, vol. 24(4), pages 988-1009, August.
    Full references (including those not matched with items on IDEAS)


    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.

    Cited by:

    1. Tommaso Proietti, 2019. "Predictability, Real Time Estimation, and the Formulation of Unobserved Components Models," CEIS Research Paper 455, Tor Vergata University, CEIS, revised 22 Mar 2019.

    More about this item


    Access and download statistics


    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bpj:jtsmet:v:6:y:2014:i:2:p:37:n:3. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Peter Golla). General contact details of provider: .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.