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Forecasting of Time Series Data Using Multiple Break Points and Mixture Distributions

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New Frontiers of Multidisciplinary Research in STEAM-H (Science, Technology, Engineering, Agriculture, Mathematics, and Health)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 90))

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Abstract

Stochastic processes have applications in many areas such as oceanography and engineering. Special classes of such processes deal with time series of sparse data. Studies in such cases focus in the analysis, construction and prediction in parametric models. Here, we assume several non-linear time series with additive noise components, and the model fitting is proposed in two stages. The first stage identifies the density using all the clusters information, without specifying any prior knowledge of the underlying distribution function of the time series. In the second stage, we partition the time series into consecutive non-overlapping intervals of quasi stationary increments where the coefficients shift from one stable regression relationship to a different one using breakpoint detection algorithm. These breakpoints are estimated by minimizing the likelihood from the residuals. We approach time series prediction through the mixture distribution of combined error components. Parameter estimation of mixture distribution is done by using the EM algorithm. We apply the method to a simulated data.

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Notes

  1. 1.

    A small subset of the many papers that have reported evidence of breaks in economic and financial time series includes Garcia and Perron [21], Koop and Potter [24], and Pastor and Stambaugh [25].

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Acknowledgements

The authors would like to express sincere thanks to the late Professor Dayanand Naik for his insightful comments and suggestions during the research which resulted in an improvement in the presentation of this work. We dedicate this work to him.

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Authors and Affiliations

  1. Department of Mathematics, Texas A&M University-Kingsville, Kingsville, TX, 78363, USA

    Rajan Lamichhane

  2. Department of Mathematics and Statistics, Old Dominion University, Norfolk, VA, 23529, USA

    Norou Diawara

  3. Department of Ocean, Earth and Atmospheric Sciences, Old Dominion University, Norfolk, VA, 23523, USA

    Cynthia M. Jones

Authors
  1. Rajan Lamichhane
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  2. Norou Diawara
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  3. Cynthia M. Jones
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Corresponding author

Correspondence to Rajan Lamichhane .

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Editors and Affiliations

  1. Dept of Mathematics & Computer Sciences, Virginia State University, Petersburg, Virginia, USA

    Bourama Toni

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Lamichhane, R., Diawara, N., Jones, C.M. (2014). Forecasting of Time Series Data Using Multiple Break Points and Mixture Distributions. In: Toni, B. (eds) New Frontiers of Multidisciplinary Research in STEAM-H (Science, Technology, Engineering, Agriculture, Mathematics, and Health). Springer Proceedings in Mathematics & Statistics, vol 90. Springer, Cham. https://doi.org/10.1007/978-3-319-07755-0_11

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