IDEAS home Printed from https://ideas.repec.org/a/bla/jtsera/v25y2004i4p603-623.html
   My bibliography  Save this article

Computation of asymmetric signal extraction filters and mean squared error for ARIMA component models

Author

Listed:
  • William R. Bell
  • Donald E. K. Martin

Abstract

. Standard signal extraction results for both stationary and nonstationary time series are expressed as linear filters applied to the observed series. Computation of the filter weights, and of the corresponding frequency response function, is relevant for studying properties of the filter and of the resulting signal extraction estimates. Methods for doing such computations for symmetric, doubly infinite filters are well established. This study develops an algorithm for computing filter weights for asymmetric, semi‐infinite signal extraction filters, including the important case of the concurrent filter (for signal extraction at the current time point). The setting is where the time series components being estimated follow autoregressive integrated moving‐average (ARIMA) models. The algorithm provides expressions for the asymmetric signal extraction filters as rational polynomial functions of the backshift operator. The filter weights are then readily generated by simple expansion of these expressions, and the corresponding frequency response function is directly evaluated. Recursive expressions are also developed that relate the weights for filters that use successively increasing amounts of data. The results for the filter weights are then used to develop methods for computing mean squared error results for the asymmetric signal extraction estimates.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:jtsera:v:25:y:2004:i:4:p:603-623
    DOI: 10.1111/j.1467-9892.2004.01920.x
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/j.1467-9892.2004.01920.x
    Download Restriction: no
    File URL: https://libkey.io/10.1111/j.1467-9892.2004.01920.x?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Ian McLeod, 1975. "Derivation of the Theoretical Autocovariance Function of Autoregressive–Moving Average Time Series," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 24(2), pages 255-256, June.
    2. Ian McLeod, 1977. "Derivation of the Theoretical Autocovariance Function of Autoregressive‐Moving Average Time Series," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 26(2), pages 194-194, June.
    3. Gersch, Will & Kitagawa, Genshiro, 1983. "The Prediction of Time Series with Trends and Seasonalities," Journal of Business & Economic Statistics, American Statistical Association, vol. 1(3), pages 253-264, July.
    4. Pierce, David A., 1980. "Data revisions with moving average seasonal adjustment procedures," Journal of Econometrics, Elsevier, vol. 14(1), pages 95-114, September.
    5. Koopman, Siem Jan & Harvey, Andrew, 2003. "Computing observation weights for signal extraction and filtering," Journal of Economic Dynamics and Control, Elsevier, vol. 27(7), pages 1317-1333, May.
    Full references (including those not matched with items on IDEAS)

    Citations

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


    Cited by:

    1. 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.
    2. Wildi, Marc & McElroy, Tucker S., 2019. "The trilemma between accuracy, timeliness and smoothness in real-time signal extraction," International Journal of Forecasting, Elsevier, vol. 35(3), pages 1072-1084.
    3. Maravall, Agustin, 2006. "An application of the TRAMO-SEATS automatic procedure; direct versus indirect adjustment," Computational Statistics & Data Analysis, Elsevier, vol. 50(9), pages 2167-2190, May.
    4. Balakrishna, N. & Hareesh, G., 2009. "Statistical signal extraction using stable processes," Statistics & Probability Letters, Elsevier, vol. 79(7), pages 851-856, April.
    5. Suhasini Subba Rao & Junho Yang, 2023. "A prediction perspective on the Wiener–Hopf equations for time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 44(1), pages 23-42, January.
    6. David F. Findley & Demetra P. Lytras & Agustin Maravall, 2016. "Illuminating ARIMA model-based seasonal adjustment with three fundamental seasonal models," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 7(1), pages 11-52, March.
    7. Wildi Marc & McElroy Tucker, 2016. "Optimal Real-Time Filters for Linear Prediction Problems," Journal of Time Series Econometrics, De Gruyter, vol. 8(2), pages 155-192, July.
    8. Agustín Maravall Herrero & Domingo Pérez Cañete, 2011. "Applying and interpreting model-based seasonal adjustment. The euro-area industrial production series," Working Papers 1116, Banco de España.
    9. Terence Mills, 2007. "A Note on Trend Decomposition: The 'Classical' Approach Revisited with an Application to Surface Temperature Trends," Journal of Applied Statistics, Taylor & Francis Journals, vol. 34(8), pages 963-972.
    10. Tommaso Proietti, 2012. "Seasonality, Forecast Extensions And Business Cycle Uncertainty," Journal of Economic Surveys, Wiley Blackwell, vol. 26(4), pages 555-569, September.
    11. Proietti, Tommaso, 2007. "Signal extraction and filtering by linear semiparametric methods," Computational Statistics & Data Analysis, Elsevier, vol. 52(2), pages 935-958, October.
    12. McElroy, Tucker S. & Wildi, Marc, 2020. "The Multivariate Linear Prediction Problem: Model-Based and Direct Filtering Solutions," Econometrics and Statistics, Elsevier, vol. 14(C), pages 112-130.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Andrle, Michal, 2012. "Understanding DSGE Filters in Forecasting and Policy Analysis," Dynare Working Papers 16, CEPREMAP.
    2. Drew Creal & Siem Jan Koopman & Eric Zivot, 2008. "The Effect of the Great Moderation on the U.S. Business Cycle in a Time-varying Multivariate Trend-cycle Model," Tinbergen Institute Discussion Papers 08-069/4, Tinbergen Institute.
    3. Regina Kaiser & Agustín Maravall, 2002. "A Complete Model-Based Interpretation of the Hodrick-Prescott Filter: Spuriousness Reconsidered," Working Papers 0208, Banco de España.
    4. Ismael Sanchez & Daniel Pena, 2001. "Properties of Predictors in Overdifferenced Nearly Nonstationary Autoregression," Journal of Time Series Analysis, Wiley Blackwell, vol. 22(1), pages 45-66, January.
    5. Fukuda, Kosei, 2012. "Illustrating extraordinary shocks causing trend breaks," Economic Modelling, Elsevier, vol. 29(4), pages 1045-1052.
    6. Siem Jan Koopman & Marius Ooms & Irma Hindrayanto, 2009. "Periodic Unobserved Cycles in Seasonal Time Series with an Application to US Unemployment," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 71(5), pages 683-713, October.
    7. Proietti, Tommaso, 2007. "Signal extraction and filtering by linear semiparametric methods," Computational Statistics & Data Analysis, Elsevier, vol. 52(2), pages 935-958, October.
    8. Dennis Kant & Andreas Pick & Jasper de Winter, 2022. "Nowcasting GDP using machine learning methods," Working Papers 754, DNB.
    9. Scotti, Chiara, 2016. "Surprise and uncertainty indexes: Real-time aggregation of real-activity macro-surprises," Journal of Monetary Economics, Elsevier, vol. 82(C), pages 1-19.
    10. Danilo Leiva-Leon & Lorenzo Ductor, 2019. "Fluctuations in Global Macro Volatility," Working Papers 1925, Banco de España.
    11. Elena Angelini & Gonzalo Camba‐Mendez & Domenico Giannone & Lucrezia Reichlin & Gerhard Rünstler, 2011. "Short‐term forecasts of euro area GDP growth," Econometrics Journal, Royal Economic Society, vol. 14(1), pages 25-44, February.
    12. Saligari, Grant R. & Snyder, Ralph D., 1997. "Trends, lead times and forecasting," International Journal of Forecasting, Elsevier, vol. 13(4), pages 477-488, December.
    13. Irma Hindrayanto & Siem Jan Koopman & Jasper de Winter, 2014. "Nowcasting and Forecasting Economic Growth in the Euro Area using Principal Components," Tinbergen Institute Discussion Papers 14-113/III, Tinbergen Institute.
    14. Hindrayanto, Irma & Koopman, Siem Jan & de Winter, Jasper, 2016. "Forecasting and nowcasting economic growth in the euro area using factor models," International Journal of Forecasting, Elsevier, vol. 32(4), pages 1284-1305.
    15. Kaiser, Regina & Maravall, Agustin, 2005. "Combining filter design with model-based filtering (with an application to business-cycle estimation)," International Journal of Forecasting, Elsevier, vol. 21(4), pages 691-710.
    16. Harvey,Andrew C., 2013. "Dynamic Models for Volatility and Heavy Tails," Cambridge Books, Cambridge University Press, number 9781107034723, November.
    17. Koopman, Siem Jan & Ooms, Marius, 2006. "Forecasting daily time series using periodic unobserved components time series models," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 885-903, November.
    18. S. Boragan Aruoba & Frank Schorfheide, 2011. "Sticky Prices versus Monetary Frictions: An Estimation of Policy Trade-Offs," American Economic Journal: Macroeconomics, American Economic Association, vol. 3(1), pages 60-90, January.
    19. Itkonen, Juha & Juvonen, Petteri, 2017. "Nowcasting the Finnish economy with a large Bayesian vector autoregressive model," BoF Economics Review 6/2017, Bank of Finland.
    20. Kirchner, Robert, 1999. "Auswirkungen des neuen Saisonbereinigungsverfahrens Census X-12-ARIMA auf die aktuelle Wirtschaftsanalyse in Deutschland," Discussion Paper Series 1: Economic Studies 1999,07, Deutsche Bundesbank.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    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:bla:jtsera:v:25:y:2004:i:4:p:603-623. See general information about how to correct material in RePEc.

    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 bibliographic 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.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0143-9782 .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.