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

Akintunde Mutairu Oyewale; Olalude Gbenga Adelekan; Oseghale Osezuwa Innocient

doi:doi:10.11648/j.ajtas.20170606.13

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

Akintunde Mutairu Oyewale, Olalude Gbenga Adelekan, Oseghale Osezuwa Innocient

Published in American Journal of Theoretical and Applied Statistics (Volume 6, Issue 6)

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.

Published in	American Journal of Theoretical and Applied Statistics (Volume 6, Issue 6)
DOI	10.11648/j.ajtas.20170606.13
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), 2017. Published by Science Publishing Group

Keywords

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

References

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[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.
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[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.
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[15]	Tsay, R. S. (2005). Analysis of Financial Time Series 2ED. John Wiley & Sons, Inc., Hoboken, New Jersey.
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[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.

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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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AMA Style

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://article.sciencepublishinggroup.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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TY  - JOUR
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
Y1  - 2017/11/21
PY  - 2017
N1  - https://doi.org/10.11648/j.ajtas.20170606.13
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
SP  - 278
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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Author Information

Akintunde Mutairu Oyewale

Department of Statistics, School of Applied Sciences, The Federal Polytechnic, Ede, Nigeria
Olalude Gbenga Adelekan

Department of Statistics, School of Applied Sciences, The Federal Polytechnic, Ede, Nigeria
Oseghale Osezuwa Innocient

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

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APA Style

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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ACS Style

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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AMA Style

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://article.sciencepublishinggroup.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}
}

Copy | Download

TY  - JOUR
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
Y1  - 2017/11/21
PY  - 2017
N1  - https://doi.org/10.11648/j.ajtas.20170606.13
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
SP  - 278
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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