IDEAS home Printed from https://ideas.repec.org/p/fip/fedlwp/2012-060.html
   My bibliography  Save this paper

Multi-step ahead forecasting of vector time series

Author

Abstract

This paper develops the theory of multi-step ahead forecasting for vector time series that exhibit temporal nonstationarity and co-integration. We treat the case of a semi-infinite past, developing the forecast filters and the forecast error filters explicitly, and also provide formulas for forecasting from a finite-sample of data. This latter application can be accomplished by the use of large matrices, which remains practicable when the total sample size is moderate. Expressions for Mean Square Error of forecasts are also derived, and can be implemented readily. Three diverse data applications illustrate the flexibility and generality of these formulas: forecasting Euro Area macroeconomic aggregates; backcasting fertility rates by racial category; and forecasting regional housing starts using a seasonally co-integrated model.

Suggested Citation

  • Michael W. McCracken & Tucker S. McElroy, 2012. "Multi-step ahead forecasting of vector time series," Working Papers 2012-060, Federal Reserve Bank of St. Louis.
    • Handle: RePEc:fip:fedlwp:2012-060
    as

    Download full text from publisher

    File URL: http://research.stlouisfed.org/wp/2012/2012-060.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Nyblom, Jukka & Harvey, Andrew, 2000. "Tests Of Common Stochastic Trends," Econometric Theory, Cambridge University Press, vol. 16(2), pages 176-199, April.
    2. Boubacar Mainassara, Y. & Francq, C., 2011. "Estimating structural VARMA models with uncorrelated but non-independent error terms," Journal of Multivariate Analysis, Elsevier, vol. 102(3), pages 496-505, March.
    3. Tucker McElroy & Thomas Trimbur, 2015. "Signal Extraction for Non-Stationary Multivariate Time Series with Illustrations for Trend Inflation," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(2), pages 209-227, March.
    4. Granger, C. W. J., 1981. "Some properties of time series data and their use in econometric model specification," Journal of Econometrics, Elsevier, vol. 16(1), pages 121-130, May.
    5. Engle, Robert & Granger, Clive, 2015. "Co-integration and error correction: Representation, estimation, and testing," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 39(3), pages 106-135.
    6. Tucker McElroy & Brian Monsell, 2015. "Model Estimation, Prediction, and Signal Extraction for Nonstationary Stock and Flow Time Series Observed at Mixed Frequencies," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(511), pages 1284-1303, September.
    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. & Wildi, Marc, 2020. "The Multivariate Linear Prediction Problem: Model-Based and Direct Filtering Solutions," Econometrics and Statistics, Elsevier, vol. 14(C), pages 112-130.
    2. Chevillon, Guillaume, 2016. "Multistep forecasting in the presence of location shifts," International Journal of Forecasting, Elsevier, vol. 32(1), pages 121-137.
    3. Chevillon, Guillaume, 2017. "Robustness of Multistep Forecasts and Predictive Regressions at Intermediate and Long Horizons," ESSEC Working Papers WP1710, ESSEC Research Center, ESSEC Business School.

    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. Tucker McElroy & Thomas Trimbur, 2015. "Signal Extraction for Non-Stationary Multivariate Time Series with Illustrations for Trend Inflation," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(2), pages 209-227, March.
    2. Josep Lluís Carrion‐i‐Silvestre & Andreu Sansó, 2006. "Testing the Null of Cointegration with Structural Breaks," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 68(5), pages 623-646, October.
    3. Biqing Cai & Jiti Gao & Dag Tjøstheim, 2017. "A New Class of Bivariate Threshold Cointegration Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 35(2), pages 288-305, April.
    4. Nielsen, Morten Orregaard & Shimotsu, Katsumi, 2007. "Determining the cointegrating rank in nonstationary fractional systems by the exact local Whittle approach," Journal of Econometrics, Elsevier, vol. 141(2), pages 574-596, December.
    5. Mohamed, Hazik & Masih, Mansur, 2017. "Stock market comovement among the ASEAN-5 : a causality analysis," MPRA Paper 98781, University Library of Munich, Germany.
    6. Muhammad Shahbaz & Syed Jawad Hussain Shahzad & Mantu Kumar Mahalik & Perry Sadorsky, 2018. "How strong is the causal relationship between globalization and energy consumption in developed economies? A country-specific time-series and panel analysis," Applied Economics, Taylor & Francis Journals, vol. 50(13), pages 1479-1494, March.
    7. Erie Febrian & Aldrin Herwany, 2009. "Volatility Forecasting Models and Market Co-Integration: A Study on South-East Asian Markets," Working Papers in Economics and Development Studies (WoPEDS) 200911, Department of Economics, Padjadjaran University, revised Sep 2009.
    8. Carmen van der Merwe & Martin de Wit, 2021. "An In-Depth Investigation into the Relationship Between Municipal Solid Waste Generation and Economic Growth in the City of Cape Town," Working Papers 07/2021, Stellenbosch University, Department of Economics, revised 2021.
    9. Hassler, U. & Marmol, F. & Velasco, C., 2006. "Residual log-periodogram inference for long-run relationships," Journal of Econometrics, Elsevier, vol. 130(1), pages 165-207, January.
    10. Haldrup, Niels & Nielsen, Morten Orregaard, 2006. "A regime switching long memory model for electricity prices," Journal of Econometrics, Elsevier, vol. 135(1-2), pages 349-376.
    11. Jesus Gonzalo & Tae-Hwy Lee, 2000. "On the robustness of cointegration tests when series are fractionally intergrated," Journal of Applied Statistics, Taylor & Francis Journals, vol. 27(7), pages 821-827.
    12. Fredj Jawadi & Catherine Bruneau & Nadia Sghaier, 2009. "Nonlinear Cointegration Relationships Between Non‐Life Insurance Premiums and Financial Markets," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 76(3), pages 753-783, September.
    13. Dookie, Michele & Lugay, Beverly & Sergeant, Kelvin A., 2011. "Consumer confidence and economic growth: case studies of Jamaica and Trinidad and Tobago," Sede Subregional de la CEPAL para el Caribe (Estudios e Investigaciones) 4086, Naciones Unidas Comisión Económica para América Latina y el Caribe (CEPAL).
    14. Niccolò Battistini & Marco Pagano & Saverio Simonelli, 2014. "Systemic risk, sovereign yields and bank exposures in the euro crisis [Real effects of the sovereign debt crises in Europe: evidence from syndicated loans]," Economic Policy, CEPR, CESifo, Sciences Po;CES;MSH, vol. 29(78), pages 203-251.
    15. Chakraborty, Chandana & Nunnenkamp, Peter, 2006. "Economic reforms, foreign direct investment and its economic effects in India," Kiel Working Papers 1272, Kiel Institute for the World Economy (IfW Kiel).
    16. Asraul Hoque, 1995. "Co-integrating relationship between terms of trade and current account deficit: the Australian evidence," Applied Economics Letters, Taylor & Francis Journals, vol. 2(4), pages 130-133.
    17. David F. Hendry & Grayham E. Mizon, 2016. "Improving the teaching of econometrics," Cogent Economics & Finance, Taylor & Francis Journals, vol. 4(1), pages 1170096-117, December.
    18. Khosrow Doroodian & Chulho Jung & Roy Boyd, 1999. "Testing the law of one price under the fixed and flexible exchange rate systems," Applied Economics Letters, Taylor & Francis Journals, vol. 6(9), pages 613-616.
    19. Assogba, Noel Perceval & Zhang, Daowei, 2022. "The conservation reserve program and timber prices in the southern United States," Forest Policy and Economics, Elsevier, vol. 140(C).
    20. Yanhua Chen & Rosario N Mantegna & Athanasios A Pantelous & Konstantin M Zuev, 2018. "A dynamic analysis of S&P 500, FTSE 100 and EURO STOXX 50 indices under different exchange rates," PLOS ONE, Public Library of Science, vol. 13(3), pages 1-40, March.

    More about this item

    Keywords

    Econometric models; Economic forecasting;

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:fip:fedlwp:2012-060. 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: Scott St. Louis (email available below). General contact details of provider: https://edirc.repec.org/data/frbslus.html .

    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.