IDEAS home Printed from https://ideas.repec.org/a/eee/intfor/v39y2023i2p922-937.html
   My bibliography  Save this article

The RWDAR model: A novel state-space approach to forecasting

Author

Listed:
  • Sbrana, Giacomo
  • Silvestrini, Andrea

Abstract

This paper introduces the Random Walk with Drift plus AutoRegressive model (RWDAR) for time-series forecasting. Owing to the presence of a random walk plus drift term, this model shares some similarities with the Theta model of Assimakopoulos and Nikolopoulos (2000). However, the addition of a first-order autoregressive term in the state equation provides additional adaptability and flexibility. Indeed, it is shown that RWDAR tends to outperform the Theta model when forecasting both stationary and nearly non-stationary time series. This paper also proposes a simple estimation method for the RWDAR model based on the solution of the algebraic Riccati equation for the prediction error covariance of the state vector. Simulation results show that this estimator performs as well as the standard Kalman filter approach. Finally, using yearly data from the M3 and M4 competition datasets, it is found that RWDAR outperforms traditional forecasting methods.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:intfor:v:39:y:2023:i:2:p:922-937
    DOI: 10.1016/j.ijforecast.2022.03.003
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0169207022000437
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ijforecast.2022.03.003?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
    ---><---

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

    References listed on IDEAS

    as
    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. Sbrana, Giacomo & Silvestrini, Andrea, 2020. "Forecasting with the damped trend model using the structural approach," International Journal of Production Economics, Elsevier, vol. 226(C).
    3. Canova, Fabio, 1998. "Detrending and business cycle facts: A user's guide," Journal of Monetary Economics, Elsevier, vol. 41(3), pages 533-540, May.
    4. Canova, Fabio, 1998. "Detrending and business cycle facts," Journal of Monetary Economics, Elsevier, vol. 41(3), pages 475-512, May.
    5. 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.
    6. Hodrick, Robert J & Prescott, Edward C, 1997. "Postwar U.S. Business Cycles: An Empirical Investigation," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 29(1), pages 1-16, February.
    7. 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.
    8. Fotios Petropoulos & Konstantinos Nikolopoulos, 2017. "The Theta Method," Foresight: The International Journal of Applied Forecasting, International Institute of Forecasters, issue 46, pages 11-17, Summer.
    9. Tommaso Proietti, 2021. "Predictability, real time estimation, and the formulation of unobserved components models," Econometric Reviews, Taylor & Francis Journals, vol. 40(5), pages 433-454, April.
    10. Sbrana, Giacomo & Silvestrini, Andrea, 2019. "Random switching exponential smoothing: A new estimation approach," International Journal of Production Economics, Elsevier, vol. 211(C), pages 211-220.
    11. Beveridge, Stephen & Nelson, Charles R., 1981. "A new approach to decomposition of economic time series into permanent and transitory components with particular attention to measurement of the `business cycle'," Journal of Monetary Economics, Elsevier, vol. 7(2), pages 151-174.
    12. Watson, Mark W., 1986. "Univariate detrending methods with stochastic trends," Journal of Monetary Economics, Elsevier, vol. 18(1), pages 49-75, July.
    13. 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.
    14. Hyndman, Rob J. & Billah, Baki, 2003. "Unmasking the Theta method," International Journal of Forecasting, Elsevier, vol. 19(2), pages 287-290.
    15. Nelson, Charles R. & Plosser, Charles I., 1982. "Trends and random walks in macroeconmic time series : Some evidence and implications," Journal of Monetary Economics, Elsevier, vol. 10(2), pages 139-162.
    16. Makridakis, Spyros, 1993. "Accuracy measures: theoretical and practical concerns," International Journal of Forecasting, Elsevier, vol. 9(4), pages 527-529, December.
    17. Durbin, James & Koopman, Siem Jan, 2012. "Time Series Analysis by State Space Methods," OUP Catalogue, Oxford University Press, edition 2, number 9780199641178.
    18. A. C. Harvey, 1986. "Analysis and Generalisation of a Multivariate Exponential Smoothing Model," Management Science, INFORMS, vol. 32(3), pages 374-380, March.
    19. 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).
    20. 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.
    21. Assimakopoulos, V. & Nikolopoulos, K., 2000. "The theta model: a decomposition approach to forecasting," International Journal of Forecasting, Elsevier, vol. 16(4), pages 521-530.
    22. 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.
    23. Makridakis, Spyros & Spiliotis, Evangelos & Assimakopoulos, Vassilios, 2020. "The M4 Competition: 100,000 time series and 61 forecasting methods," International Journal of Forecasting, Elsevier, vol. 36(1), pages 54-74.
    24. Makridakis, Spyros & Hibon, Michele, 2000. "The M3-Competition: results, conclusions and implications," International Journal of Forecasting, Elsevier, vol. 16(4), pages 451-476.
    25. Oh, Kum Hwa & Zivot, Eric & Creal, Drew, 2008. "The relationship between the Beveridge-Nelson decomposition and other permanent-transitory decompositions that are popular in economics," Journal of Econometrics, Elsevier, vol. 146(2), pages 207-219, October.
    26. Harvey, A C, 1985. "Trends and Cycles in Macroeconomic Time Series," Journal of Business & Economic Statistics, American Statistical Association, vol. 3(3), pages 216-227, June.
    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. Giacomo Sbrana & Andrea Silvestrini, 2024. "The structural Theta method and its predictive performance in the M4-Competition," Temi di discussione (Economic working papers) 1457, Bank of Italy, Economic Research and International Relations Area.

    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. 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.
    2. 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.
    3. 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.
    4. 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.
    5. Kang, Yanfei & Spiliotis, Evangelos & Petropoulos, Fotios & Athiniotis, Nikolaos & Li, Feng & Assimakopoulos, Vassilios, 2021. "Déjà vu: A data-centric forecasting approach through time series cross-similarity," Journal of Business Research, Elsevier, vol. 132(C), pages 719-731.
    6. 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).
    7. Makridakis, Spyros & Spiliotis, Evangelos & Assimakopoulos, Vassilios, 2020. "The M4 Competition: 100,000 time series and 61 forecasting methods," International Journal of Forecasting, Elsevier, vol. 36(1), pages 54-74.
    8. Semenoglou, Artemios-Anargyros & Spiliotis, Evangelos & Makridakis, Spyros & Assimakopoulos, Vassilios, 2021. "Investigating the accuracy of cross-learning time series forecasting methods," International Journal of Forecasting, Elsevier, vol. 37(3), pages 1072-1084.
    9. Theodosiou, Marina, 2011. "Forecasting monthly and quarterly time series using STL decomposition," International Journal of Forecasting, Elsevier, vol. 27(4), pages 1178-1195, October.
    10. Sbrana, Giacomo & Silvestrini, Andrea, 2020. "Forecasting with the damped trend model using the structural approach," International Journal of Production Economics, Elsevier, vol. 226(C).
    11. 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.
    12. Hall, Viv B & Thomson, Peter, 2022. "A boosted HP filter for business cycle analysis: evidence from New Zealand’s small open economy," Working Paper Series 9473, Victoria University of Wellington, School of Economics and Finance.
    13. Nghia Chu & Binh Dao & Nga Pham & Huy Nguyen & Hien Tran, 2022. "Predicting Mutual Funds' Performance using Deep Learning and Ensemble Techniques," Papers 2209.09649, arXiv.org, revised Jul 2023.
    14. 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.
    15. 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.
    16. Perron, Pierre & Wada, Tatsuma, 2009. "Let's take a break: Trends and cycles in US real GDP," Journal of Monetary Economics, Elsevier, vol. 56(6), pages 749-765, September.
    17. Makridakis, Spyros & Hyndman, Rob J. & Petropoulos, Fotios, 2020. "Forecasting in social settings: The state of the art," International Journal of Forecasting, Elsevier, vol. 36(1), pages 15-28.
    18. Han, Yang & Liu, Zehao & Ma, Jun, 2020. "Growth cycles and business cycles of the Chinese economy through the lens of the unobserved components model," China Economic Review, Elsevier, vol. 63(C).
    19. Kang, Yanfei & Cao, Wei & Petropoulos, Fotios & Li, Feng, 2022. "Forecast with forecasts: Diversity matters," European Journal of Operational Research, Elsevier, vol. 301(1), pages 180-190.
    20. T. Berger, 2008. "Estimating Europe’s Natural Rates from a forward-looking Phillips curve," Working Papers of Faculty of Economics and Business Administration, Ghent University, Belgium 08/498, Ghent University, Faculty of Economics and Business Administration.

    More about this item

    Keywords

    Theta method; Kalman gain; Forecasting; M3 and M4 competitions; Approximate maximum likelihood estimation;
    All these keywords.

    JEL classification:

    • M3 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Marketing and Advertising
    • M4 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Accounting

    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:eee:intfor:v:39:y:2023:i:2:p:922-937. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/ijforecast .

    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.