American Journal of Theoretical and Applied Statistics

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Forecast Comparison of Seasonal Autoregressive Integrated Moving Average (SARIMA) and Self Exciting Threshold Autoregressive (SETAR) Models

Received: 13 August 2017    Accepted: 31 August 2017    Published: 21 November 2017
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Abstract

Financial and Economic time series literatures have shown that financial and economic time series data exhibit non-linearity in their behavior. In order to be mindful of such behavior as applied to Nigeria inflation rates, this study therefore, applies a two stages non-linear self-exciting threshold autoregressive model (SETAR) to Nigeria inflation rates. The results obtained for both in-sample and out-of-sample forecast performances for SETAR model were compared with results of linear seasonal autoregressive integrated moving average (SARIMA). On the basis of in-sample forecast performance of linear SARIMA and non-linear SETAR, using performance measure indices like MAE and RMSE, the results obtained indicated that non-linear SETAR model performed better than linear SARIMA. So also for the out-of-sample forecast performance using multi-step ahead forecast performance, the results also indicated that non-linear SETAR out performed linear SARIMA.

DOI 10.11648/j.ajtas.20170606.13
Published in American Journal of Theoretical and Applied Statistics (Volume 6, Issue 6, November 2017)
Page(s) 278-283
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

SETAR Model, SARIMA Model, Inflation Rates, In-Sample, Out-of-Sample, Forecast Performance

References
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[2] Anderson, T. W. (1977). The Statistical Analysis of Time Series, New York and London Wiley.
[3] Bonilla, C. R. Romero, M. J., and Hinich, M. J., (2005). Episodic non-linearities in the Latin American Stock Market indices, Applied Economics Letters, vol. 13 pp 195-199.
[4] Hamilton J. D., (1989). A new approach to the economic analysis of non-stationary time series and the business cycle. Econometrica, 57(2): 357–384.
[5] Lo, M. and Piger, J., (2005). “Is the Response of Output to Monetary Policy Asymmetric? Evidence from a Regime-Switching Coefficients Model,” Journal of Money, Credit and Banking 37, 865-887.
[6] Ocal, N. and Osborn, D. R., (2000). Business cycle non-linearities in UK consumption and production, Journal of Applied Econometrics 15, 27-44.
[7] Panagiotidis, T. and Pelloni, G. (2003) Testing for nonlinearity in labour markets: the case of Germany and the UK, Journal of Policy Modeling, 25, 275–86.
[8] Preez, J. & Witt, S. F. (2003). Univariate versus Multivariate Time Series Forecasting: An Application to International Tourism Demand. International Journal of Forecasting, 19, 435-451.
[9] Pesaran, M. H. and S. M. Potter, 1997. A Floor and Ceiling Model of US Output. Journal of Economic Dynamics and Control 21: 661-695.
[10] Teräsvirta, T. and Anderson, H., (1992). Characterizing nonlinearities in business cycles using smooth transition autoregressive models. Journal of Applied Econometrics, 7: S119–S136.
[11] Tong, H. (1990) Non-Linear Time Series: A Dynamical System Approach. London: Oxford University Press.
[12] Tong, H., & Lim, K. S. (1980). Threshold autoregressive, limit cycles and cyclical data. Journal of the Royal Statistical Society Series B, 42(3), 245–292.
[13] Tong, H., (1983). Threshold Models in Non-Linear Time Series Analysis. Springer-Verlag, New York.
[14] Tsay, R. S. (1989). Testing and Modeling Threshold Autoregressive Processes. Journal of the American Statistical Association 84: 231–240.
[15] Tsay, R. S. (2005). Analysis of Financial Time Series 2ED. John Wiley & Sons, Inc., Hoboken, New Jersey.
[16] Van Dijk, Teräsvirta, T. and Franses P., (2002). Smooth transition autoregressive models – a survey of recent developments. Econometric Reviews, 21(1): 1–47.
[17] Yaser, A. S., Moody, J. and Weigend, A. (1996). Introduction to financial forecasting. Applied intelligence, 6(3), 205-213.
[18] Zhou, Z. J., & Hu, C. H. (2008). An effective hybrid approach based on grey and ARMA for forecasting gyro drift. Chaos, Solutions and Fractals, 35, 525–529.
Author Information
  • Department of Statistics, School of Applied Sciences, The Federal Polytechnic, Ede, Nigeria

  • Department of Statistics, School of Applied Sciences, The Federal Polytechnic, Ede, Nigeria

  • Department of Statistics, College of Natural Sciences, Joseph Ayo Babalola University, Ikeji-Arakeji, Nigeria

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    Akintunde Mutairu Oyewale, Olalude Gbenga Adelekan, Oseghale Osezuwa Innocient. (2017). Forecast Comparison of Seasonal Autoregressive Integrated Moving Average (SARIMA) and Self Exciting Threshold Autoregressive (SETAR) Models. American Journal of Theoretical and Applied Statistics, 6(6), 278-283. https://doi.org/10.11648/j.ajtas.20170606.13

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    Akintunde Mutairu Oyewale; Olalude Gbenga Adelekan; Oseghale Osezuwa Innocient. Forecast Comparison of Seasonal Autoregressive Integrated Moving Average (SARIMA) and Self Exciting Threshold Autoregressive (SETAR) Models. Am. J. Theor. Appl. Stat. 2017, 6(6), 278-283. doi: 10.11648/j.ajtas.20170606.13

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    Akintunde Mutairu Oyewale, Olalude Gbenga Adelekan, Oseghale Osezuwa Innocient. Forecast Comparison of Seasonal Autoregressive Integrated Moving Average (SARIMA) and Self Exciting Threshold Autoregressive (SETAR) Models. Am J Theor Appl Stat. 2017;6(6):278-283. doi: 10.11648/j.ajtas.20170606.13

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  • @article{10.11648/j.ajtas.20170606.13,
      author = {Akintunde Mutairu Oyewale and Olalude Gbenga Adelekan and Oseghale Osezuwa Innocient},
      title = {Forecast Comparison of Seasonal Autoregressive Integrated Moving Average (SARIMA) and Self Exciting Threshold Autoregressive (SETAR) Models},
      journal = {American Journal of Theoretical and Applied Statistics},
      volume = {6},
      number = {6},
      pages = {278-283},
      doi = {10.11648/j.ajtas.20170606.13},
      url = {https://doi.org/10.11648/j.ajtas.20170606.13},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.ajtas.20170606.13},
      abstract = {Financial and Economic time series literatures have shown that financial and economic time series data exhibit non-linearity in their behavior. In order to be mindful of such behavior as applied to Nigeria inflation rates, this study therefore, applies a two stages non-linear self-exciting threshold autoregressive model (SETAR) to Nigeria inflation rates. The results obtained for both in-sample and out-of-sample forecast performances for SETAR model were compared with results of linear seasonal autoregressive integrated moving average (SARIMA). On the basis of in-sample forecast performance of linear SARIMA and non-linear SETAR, using performance measure indices like MAE and RMSE, the results obtained indicated that non-linear SETAR model performed better than linear SARIMA. So also for the out-of-sample forecast performance using multi-step ahead forecast performance, the results also indicated that non-linear SETAR out performed linear SARIMA.},
     year = {2017}
    }
    

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    T1  - Forecast Comparison of Seasonal Autoregressive Integrated Moving Average (SARIMA) and Self Exciting Threshold Autoregressive (SETAR) Models
    AU  - Akintunde Mutairu Oyewale
    AU  - Olalude Gbenga Adelekan
    AU  - Oseghale Osezuwa Innocient
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    DO  - 10.11648/j.ajtas.20170606.13
    T2  - American Journal of Theoretical and Applied Statistics
    JF  - American Journal of Theoretical and Applied Statistics
    JO  - American Journal of Theoretical and Applied Statistics
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    EP  - 283
    PB  - Science Publishing Group
    SN  - 2326-9006
    UR  - https://doi.org/10.11648/j.ajtas.20170606.13
    AB  - Financial and Economic time series literatures have shown that financial and economic time series data exhibit non-linearity in their behavior. In order to be mindful of such behavior as applied to Nigeria inflation rates, this study therefore, applies a two stages non-linear self-exciting threshold autoregressive model (SETAR) to Nigeria inflation rates. The results obtained for both in-sample and out-of-sample forecast performances for SETAR model were compared with results of linear seasonal autoregressive integrated moving average (SARIMA). On the basis of in-sample forecast performance of linear SARIMA and non-linear SETAR, using performance measure indices like MAE and RMSE, the results obtained indicated that non-linear SETAR model performed better than linear SARIMA. So also for the out-of-sample forecast performance using multi-step ahead forecast performance, the results also indicated that non-linear SETAR out performed linear SARIMA.
    VL  - 6
    IS  - 6
    ER  - 

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