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Forecasting stochastic processes using singular spectrum analysis: Aspects of the theory and application

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  • Khan, M. Atikur Rahman
  • Poskitt, D.S.

Abstract

This paper presents theoretical results on the properties of forecasts obtained by using singular spectrum analysis to forecast time series that are realizations of stochastic processes. The mean squared forecast errors are derived under broad regularity conditions, and it is shown that, in practice, the forecasts obtained will converge to their population ensemble counterparts. The theoretical results are illustrated by examining the performances of singular spectrum analysis forecasts when applied to autoregressive processes and a random walk process. Simulation experiments suggest that the asymptotic properties developed are reflected in the behaviour of observed finite samples. Empirical applications using real world data sets indicate that forecasts based on singular spectrum analysis are competitive with other methods currently in vogue.

Suggested Citation

  • Khan, M. Atikur Rahman & Poskitt, D.S., 2017. "Forecasting stochastic processes using singular spectrum analysis: Aspects of the theory and application," International Journal of Forecasting, Elsevier, vol. 33(1), pages 199-213.
    • Handle: RePEc:eee:intfor:v:33:y:2017:i:1:p:199-213
    DOI: 10.1016/j.ijforecast.2016.01.003
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    References listed on IDEAS

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    1. Dimitrios D. Thomakos, 2008. "Optimal Linear Filtering, Smoothing and Trend Extraction for Processes with Unit Roots and Cointegration," Working Paper series 14_08, Rimini Centre for Economic Analysis.
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    3. 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).
    4. Hassani, Hossein & Heravi, Saeed & Zhigljavsky, Anatoly, 2009. "Forecasting European industrial production with singular spectrum analysis," International Journal of Forecasting, Elsevier, vol. 25(1), pages 103-118.
    5. Poskitt, Don S, 2000. "Strongly Consistent Determination of Cointegrating Rank via Canonical Correlations," Journal of Business & Economic Statistics, American Statistical Association, vol. 18(1), pages 77-90, January.
    6. repec:rim:rimwps:14-08 is not listed on IDEAS
    7. Thomakos, Dimitrios D. & Wang, Tao & Wille, Luc T., 2002. "Modeling daily realized futures volatility with singular spectrum analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 312(3), pages 505-519.
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    Cited by:

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    4. Josu Arteche & Javier García‐Enríquez, 2022. "Singular spectrum analysis for value at risk in stochastic volatility models," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 41(1), pages 3-16, January.
    5. Salah L. Zubaidi & Sandra Ortega-Martorell & Patryk Kot & Rafid M. Alkhaddar & Mawada Abdellatif & Sadik K. Gharghan & Maytham S. Ahmed & Khalid Hashim, 2020. "A Method for Predicting Long-Term Municipal Water Demands Under Climate Change," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 34(3), pages 1265-1279, February.
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    7. Xu, Shuojiang & Chan, Hing Kai & Zhang, Tiantian, 2019. "Forecasting the demand of the aviation industry using hybrid time series SARIMA-SVR approach," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 122(C), pages 169-180.

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