IDEAS home Printed from https://ideas.repec.org/a/wly/jforec/v34y2015i3p220-229.html
   My bibliography  Save this article

Forecasting Multivariate Time Series with the Theta Method

Author

Listed:
  • Dimitrios D. Thomakos
  • Konstantinos Nikolopoulos

Abstract

In this study building on earlier work on the properties and performance of the univariate Theta method for a unit root data‐generating process we: (a) derive new theoretical formulations for the application of the method on multivariate time series; (b) investigate the conditions for which the multivariate Theta method is expected to forecast better than the univariate one; (c) evaluate through simulations the bivariate form of the method; and (d) evaluate this latter model in real macroeconomic and financial time series. The study provides sufficient empirical evidence to illustrate the suitability of the method for vector forecasting; furthermore it provides the motivation for further investigation of the multivariate Theta method for higher dimensions. Copyright © 2015 John Wiley & Sons, Ltd.

Suggested Citation

  • Dimitrios D. Thomakos & Konstantinos Nikolopoulos, 2015. "Forecasting Multivariate Time Series with the Theta Method," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 34(3), pages 220-229, April.
    • Handle: RePEc:wly:jforec:v:34:y:2015:i:3:p:220-229
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    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. Hyndman, Rob J. & Billah, Baki, 2003. "Unmasking the Theta method," International Journal of Forecasting, Elsevier, vol. 19(2), pages 287-290.
    3. Athanasopoulos, George & Vahid, Farshid, 2008. "VARMA versus VAR for Macroeconomic Forecasting," Journal of Business & Economic Statistics, American Statistical Association, vol. 26, pages 237-252, April.
    4. A. C. Harvey, 1986. "Analysis and Generalisation of a Multivariate Exponential Smoothing Model," Management Science, INFORMS, vol. 32(3), pages 374-380, March.
    5. George Athanasopoulos & Ashton de Silva, 2010. "Multivariate exponential smoothing for forecasting tourist arrivals to Australia and New Zealand," Monash Econometrics and Business Statistics Working Papers 11/09, Monash University, Department of Econometrics and Business Statistics.
    6. Assimakopoulos, V. & Nikolopoulos, K., 2000. "The theta model: a decomposition approach to forecasting," International Journal of Forecasting, Elsevier, vol. 16(4), pages 521-530.
    7. Ashton de Silva & Rob J. Hyndman & Ralph D. Snyder, 2007. "The vector innovation structural time series framework: a simple approach to multivariate forecasting," Monash Econometrics and Business Statistics Working Papers 3/07, Monash University, Department of Econometrics and Business Statistics.
    8. Makridakis, Spyros & Hibon, Michele, 2000. "The M3-Competition: results, conclusions and implications," International Journal of Forecasting, Elsevier, vol. 16(4), pages 451-476.
    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. Spiliotis, Evangelos & Assimakopoulos, Vassilios & Nikolopoulos, Konstantinos, 2019. "Forecasting with a hybrid method utilizing data smoothing, a variation of the Theta method and shrinkage of seasonal factors," International Journal of Production Economics, Elsevier, vol. 209(C), pages 92-102.
    2. Fotios Petropoulos & Evangelos Spiliotis, 2021. "The Wisdom of the Data: Getting the Most Out of Univariate Time Series Forecasting," Forecasting, MDPI, vol. 3(3), pages 1-20, June.
    3. Fiorucci, Jose A. & Pellegrini, Tiago R. & Louzada, Francisco & Petropoulos, Fotios & Koehler, Anne B., 2016. "Models for optimising the theta method and their relationship to state space models," International Journal of Forecasting, Elsevier, vol. 32(4), pages 1151-1161.
    4. Petropoulos, Fotios & Apiletti, Daniele & Assimakopoulos, Vassilios & Babai, Mohamed Zied & Barrow, Devon K. & Ben Taieb, Souhaib & Bergmeir, Christoph & Bessa, Ricardo J. & Bijak, Jakub & Boylan, Joh, 2022. "Forecasting: theory and practice," International Journal of Forecasting, Elsevier, vol. 38(3), pages 705-871.
      • Fotios Petropoulos & Daniele Apiletti & Vassilios Assimakopoulos & Mohamed Zied Babai & Devon K. Barrow & Souhaib Ben Taieb & Christoph Bergmeir & Ricardo J. Bessa & Jakub Bijak & John E. Boylan & Jet, 2020. "Forecasting: theory and practice," Papers 2012.03854, arXiv.org, revised Jan 2022.
    5. Sbrana, Giacomo & Silvestrini, Andrea, 2023. "The RWDAR model: A novel state-space approach to forecasting," International Journal of Forecasting, Elsevier, vol. 39(2), pages 922-937.
    6. Kyriazi, Foteini & Thomakos, Dimitrios D. & Guerard, John B., 2019. "Adaptive learning forecasting, with applications in forecasting agricultural prices," International Journal of Forecasting, Elsevier, vol. 35(4), pages 1356-1369.

    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. Sbrana, Giacomo & Silvestrini, Andrea, 2022. "Random coefficient state-space model: Estimation and performance in M3–M4 competitions," International Journal of Forecasting, Elsevier, vol. 38(1), pages 352-366.
    2. Athanasopoulos, George & Hyndman, Rob J. & Song, Haiyan & Wu, Doris C., 2011. "The tourism forecasting competition," International Journal of Forecasting, Elsevier, vol. 27(3), pages 822-844.
    3. Sbrana, Giacomo & Silvestrini, Andrea, 2023. "The RWDAR model: A novel state-space approach to forecasting," International Journal of Forecasting, Elsevier, vol. 39(2), pages 922-937.
    4. Gardner, Everette Jr., 2006. "Exponential smoothing: The state of the art--Part II," International Journal of Forecasting, Elsevier, vol. 22(4), pages 637-666.
    5. Hyndman, Rob J. & Koehler, Anne B., 2006. "Another look at measures of forecast accuracy," International Journal of Forecasting, Elsevier, vol. 22(4), pages 679-688.
    6. Petropoulos, Fotios & Makridakis, Spyros & Assimakopoulos, Vassilios & Nikolopoulos, Konstantinos, 2014. "‘Horses for Courses’ in demand forecasting," European Journal of Operational Research, Elsevier, vol. 237(1), pages 152-163.
    7. Jan G. De Gooijer & Rob J. Hyndman, 2005. "25 Years of IIF Time Series Forecasting: A Selective Review," Monash Econometrics and Business Statistics Working Papers 12/05, Monash University, Department of Econometrics and Business Statistics.
    8. Fiorucci, Jose A. & Pellegrini, Tiago R. & Louzada, Francisco & Petropoulos, Fotios & Koehler, Anne B., 2016. "Models for optimising the theta method and their relationship to state space models," International Journal of Forecasting, Elsevier, vol. 32(4), pages 1151-1161.
    9. Petropoulos, Fotios & Apiletti, Daniele & Assimakopoulos, Vassilios & Babai, Mohamed Zied & Barrow, Devon K. & Ben Taieb, Souhaib & Bergmeir, Christoph & Bessa, Ricardo J. & Bijak, Jakub & Boylan, Joh, 2022. "Forecasting: theory and practice," International Journal of Forecasting, Elsevier, vol. 38(3), pages 705-871.
      • Fotios Petropoulos & Daniele Apiletti & Vassilios Assimakopoulos & Mohamed Zied Babai & Devon K. Barrow & Souhaib Ben Taieb & Christoph Bergmeir & Ricardo J. Bessa & Jakub Bijak & John E. Boylan & Jet, 2020. "Forecasting: theory and practice," Papers 2012.03854, arXiv.org, revised Jan 2022.
    10. Hyndman, Rob J. & Khandakar, Yeasmin, 2008. "Automatic Time Series Forecasting: The forecast Package for R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 27(i03).
    11. Fildes, Robert & Petropoulos, Fotios, 2015. "Simple versus complex selection rules for forecasting many time series," Journal of Business Research, Elsevier, vol. 68(8), pages 1692-1701.
    12. Theodosiou, Marina, 2011. "Forecasting monthly and quarterly time series using STL decomposition," International Journal of Forecasting, Elsevier, vol. 27(4), pages 1178-1195, October.
    13. Pritularga, Kandrika F. & Svetunkov, Ivan & Kourentzes, Nikolaos, 2023. "Shrinkage estimator for exponential smoothing models," International Journal of Forecasting, Elsevier, vol. 39(3), pages 1351-1365.
    14. Fotios Petropoulos & Evangelos Spiliotis, 2021. "The Wisdom of the Data: Getting the Most Out of Univariate Time Series Forecasting," Forecasting, MDPI, vol. 3(3), pages 1-20, June.
    15. Spiliotis, Evangelos & Assimakopoulos, Vassilios & Makridakis, Spyros, 2020. "Generalizing the Theta method for automatic forecasting," European Journal of Operational Research, Elsevier, vol. 284(2), pages 550-558.
    16. De Gooijer, Jan G. & Hyndman, Rob J., 2006. "25 years of time series forecasting," International Journal of Forecasting, Elsevier, vol. 22(3), pages 443-473.
    17. Kourentzes, Nikolaos & Petropoulos, Fotios & Trapero, Juan R., 2014. "Improving forecasting by estimating time series structural components across multiple frequencies," International Journal of Forecasting, Elsevier, vol. 30(2), pages 291-302.
    18. Meira, Erick & Cyrino Oliveira, Fernando Luiz & de Menezes, Lilian M., 2022. "Forecasting natural gas consumption using Bagging and modified regularization techniques," Energy Economics, Elsevier, vol. 106(C).
    19. Dean W. Wichern & Benito E. Flores, 2005. "Evaluating forecasts: a look at aggregate bias and accuracy measures," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 24(6), pages 433-451.
    20. João A. Bastos, 2019. "Forecasting the capacity of mobile networks," Telecommunication Systems: Modelling, Analysis, Design and Management, Springer, vol. 72(2), pages 231-242, October.

    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:wly:jforec:v:34:y:2015:i:3:p:220-229. 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://www3.interscience.wiley.com/cgi-bin/jhome/2966 .

    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.