On Order and Regime Determination of SETAR Model in Modelling Nonlinear Stationary Time Series Data Structure: Application to Lafia Rainfall Data, Nasarawa State, Nigeria

Nicholas Pindar Dibal; Akeyede Imam; Mustafa Babagana Abubakar

doi:doi:10.11648/j.ajtas.20211002.11

| Peer-Reviewed

On Order and Regime Determination of SETAR Model in Modelling Nonlinear Stationary Time Series Data Structure: Application to Lafia Rainfall Data, Nasarawa State, Nigeria

Nicholas Pindar Dibal, Akeyede Imam, Mustafa Babagana Abubakar

Published in American Journal of Theoretical and Applied Statistics (Volume 10, Issue 2)

Received: 9 January 2021 Accepted: 16 January 2021 Published: 3 March 2021

Views: Downloads:

Download PDF

Share This Article

Twitter
Linked In
Facebook

Abstract

The linear time series model refers to the class of models for which fixed correlation parameters can fully explain the dependency between two random variables, but many real-life circumstances, such as monthly unemployment results, supplies and demands, interest rate, exchange rate, share prices, rainfall, etc., violate the assumption of linearity. For fitting and forecasting of nonlinear time series data, the self-exiting threshold autoregressive (SETAR) model was suggested. Using R to generate random nonlinear autoregressive data, a Monte Carlo simulation was performed, the SETAR model was fitted to the simulated data and Lafia rainfall data, Nasarawa State, Nigeria to determine the best regime orders and/or scheme number to make future forecast. Using Mean Square Error (MSE) and Akaike Information Criteria (AIC), the relative performance of models was examined. At a specific autoregressive order, regime order, sample size and step ahead, the model with minimum criteria was considered as the best. The results show that the best autoregressive and regime orders to be chosen are 3rd and 2nd [SETAR (3, 2)] respectively for fitting and forecasting nonlinear autoregressive time series data with small and moderate sample sizes. As the sample size increases, the output of the four models increases. Finally, it is shown that when sample size and number of steps forward are increased, the efficiency and forecasting capacity of the four models improves.

Published in	American Journal of Theoretical and Applied Statistics (Volume 10, Issue 2)
DOI	10.11648/j.ajtas.20211002.11
Page(s)	89-98
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, Regime Order, Autoregressive Order, Nonlinear Time Series

References

[1]	Akeyede, I., Adeleke, B. L. and Yahya, W. B. (2015). On forecast Strength of some linear and nonlinear time series models for stationary data structure, American Journal of Mathematics and Statistics, 5 (4): 163-177 DOI: 10.5923/j.ajms.20150504.01.
[2]	Clements, M. P. and Smith, J. (1999). A Monte Carlo study of the forecasting performance of empirical SETAR models, Journal of Applied Econometrics, 14, 123-141.
[3]	De Goojier, J. G. (2001). On threshold moving-average models. Journal of Time Series Analysis, 19, 1–18. MR1624163.
[4]	Dickey, D. A. and Fuller, W. A. (1979). Distribution of the estimators for autoregressive Time series with a unit root, Journal of American Statistical Association, 74, 427-431.
[5]	Dufrenot, G., Guegan, D. and Peguin-Feissolle, A. (2005). Long memory dynamics in a SETAR model-applications to stock markets. Journal of International Financial Markets, Institutions and Money, Elsevier, 15 (5), 391-406.
[6]	Fırat, E. H. (2017). SETAR (Self-exciting Threshold Autoregressive) Non-linear Currency Modelling in EUR/USD, EUR/TRY and USD/TRY Parities. Mathematics and Statistics 5 (1): 33-55, DOI: 10.13189/ms.2017.050105.
[7]	Franses, P. H. and van Dijk, D. (2000). Non-linear time series models in empirical finance, Cambridge, New York.
[8]	Gibson, D. and Nur, D. (2011). Threshold Autoregressive Models in Finance: A Comparative Approach, Proceedings of the Fourth Annual ASEARC Conference, 17-18 February, University of Western Sydney, Paramatta, Australia.
[9]	Grabowski, D., Staszewska-Bystrova, A. and Winker, P. (2017). Generating prediction bands for path forecasts from SETAR models. Studies in Nonlinear Dynamics & Econometrics, 21 (5), 20160066, ISSN (Online) 1558 3708, DOI: https://doi.org/10.1515/snde-2016-0066.
[10]	Hansen, B. E. (1996). Inference when a nuisance parameter is not identified under the null hypothesis, Journal of Econometrica 64, 413-30.
[11]	Keenan, D. M. (1985). A Tukey nonadditivity-type test for time series nonlinearity, Biometrika 72, 39-44.
[12]	Tong, H. (1978). On a threshold model, Pattern Recognition and Signal Processing, Amsterdam: Sijthoff & Noordhoff, 101-41.
[13]	Tong, H. and Lim, K. S. (1980). Threshold autoregression, limit cycles and cyclical data (with discussion), Journal of the Royal Statistical Society, Series B, Vol. 42 (3), 245-292.
[14]	Tong, H. (1983). Threshold models in nonlinear time series analysis, Lecture Notes in Statistics, No. 21, Heidelberg: Springer, 62-64.
[15]	Tong, H. (1990). Nonlinear Time Series: A Dynamical System Approach. Oxford: Oxford University Press.
[16]	Tong, H. and Yeung, I. (1991). Threshold autoregressive modelling in continuous time. Statistica Sinica, 1 (1991), 411-430.
[17]	Tong, H. (2011). "Threshold models in time series analysis —30 years on. Statistics and Its Inference 2 (2). 1-36, DOI 10.4310/SII. 2011.v4.n2.a1.
[18]	Tsay, R. S. (1986). Nonlinearity tests for time series, Biometrika 73, 461-466.
[19]	Tsay, R. S. (2010). Analysis of Financial Time Series; 3^rd Edition, Published by John Wiley & Sons, Inc., Hoboken, New Jersey. Published simultaneously in Canada.
[20]	Watier, L. and Richardson, S. (1995). Modeling of an epidemiological time series by a threshold autoregressive model. The Statistician 44 (3): 353-364.

Cite This Article

Plain Text BibTeX RIS

APA Style

Nicholas Pindar Dibal, Akeyede Imam, Mustafa Babagana Abubakar. (2021). On Order and Regime Determination of SETAR Model in Modelling Nonlinear Stationary Time Series Data Structure: Application to Lafia Rainfall Data, Nasarawa State, Nigeria. American Journal of Theoretical and Applied Statistics, 10(2), 89-98. https://doi.org/10.11648/j.ajtas.20211002.11

Copy | Download

ACS Style

Nicholas Pindar Dibal; Akeyede Imam; Mustafa Babagana Abubakar. On Order and Regime Determination of SETAR Model in Modelling Nonlinear Stationary Time Series Data Structure: Application to Lafia Rainfall Data, Nasarawa State, Nigeria. Am. J. Theor. Appl. Stat. 2021, 10(2), 89-98. doi: 10.11648/j.ajtas.20211002.11

Copy | Download

AMA Style

Nicholas Pindar Dibal, Akeyede Imam, Mustafa Babagana Abubakar. On Order and Regime Determination of SETAR Model in Modelling Nonlinear Stationary Time Series Data Structure: Application to Lafia Rainfall Data, Nasarawa State, Nigeria. Am J Theor Appl Stat. 2021;10(2):89-98. doi: 10.11648/j.ajtas.20211002.11

Copy | Download

@article{10.11648/j.ajtas.20211002.11,
  author = {Nicholas Pindar Dibal and Akeyede Imam and Mustafa Babagana Abubakar},
  title = {On Order and Regime Determination of SETAR Model in Modelling Nonlinear Stationary Time Series Data Structure: Application to Lafia Rainfall Data, Nasarawa State, Nigeria},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {10},
  number = {2},
  pages = {89-98},
  doi = {10.11648/j.ajtas.20211002.11},
  url = {https://doi.org/10.11648/j.ajtas.20211002.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20211002.11},
  abstract = {The linear time series model refers to the class of models for which fixed correlation parameters can fully explain the dependency between two random variables, but many real-life circumstances, such as monthly unemployment results, supplies and demands, interest rate, exchange rate, share prices, rainfall, etc., violate the assumption of linearity. For fitting and forecasting of nonlinear time series data, the self-exiting threshold autoregressive (SETAR) model was suggested. Using R to generate random nonlinear autoregressive data, a Monte Carlo simulation was performed, the SETAR model was fitted to the simulated data and Lafia rainfall data, Nasarawa State, Nigeria to determine the best regime orders and/or scheme number to make future forecast. Using Mean Square Error (MSE) and Akaike Information Criteria (AIC), the relative performance of models was examined. At a specific autoregressive order, regime order, sample size and step ahead, the model with minimum criteria was considered as the best. The results show that the best autoregressive and regime orders to be chosen are 3rd and 2nd [SETAR (3, 2)] respectively for fitting and forecasting nonlinear autoregressive time series data with small and moderate sample sizes. As the sample size increases, the output of the four models increases. Finally, it is shown that when sample size and number of steps forward are increased, the efficiency and forecasting capacity of the four models improves.},
 year = {2021}
}

Copy | Download

TY  - JOUR
T1  - On Order and Regime Determination of SETAR Model in Modelling Nonlinear Stationary Time Series Data Structure: Application to Lafia Rainfall Data, Nasarawa State, Nigeria
AU  - Nicholas Pindar Dibal
AU  - Akeyede Imam
AU  - Mustafa Babagana Abubakar
Y1  - 2021/03/03
PY  - 2021
N1  - https://doi.org/10.11648/j.ajtas.20211002.11
DO  - 10.11648/j.ajtas.20211002.11
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  - 89
EP  - 98
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20211002.11
AB  - The linear time series model refers to the class of models for which fixed correlation parameters can fully explain the dependency between two random variables, but many real-life circumstances, such as monthly unemployment results, supplies and demands, interest rate, exchange rate, share prices, rainfall, etc., violate the assumption of linearity. For fitting and forecasting of nonlinear time series data, the self-exiting threshold autoregressive (SETAR) model was suggested. Using R to generate random nonlinear autoregressive data, a Monte Carlo simulation was performed, the SETAR model was fitted to the simulated data and Lafia rainfall data, Nasarawa State, Nigeria to determine the best regime orders and/or scheme number to make future forecast. Using Mean Square Error (MSE) and Akaike Information Criteria (AIC), the relative performance of models was examined. At a specific autoregressive order, regime order, sample size and step ahead, the model with minimum criteria was considered as the best. The results show that the best autoregressive and regime orders to be chosen are 3rd and 2nd [SETAR (3, 2)] respectively for fitting and forecasting nonlinear autoregressive time series data with small and moderate sample sizes. As the sample size increases, the output of the four models increases. Finally, it is shown that when sample size and number of steps forward are increased, the efficiency and forecasting capacity of the four models improves.
VL  - 10
IS  - 2
ER  -

Copy | Download

Author Information

Nicholas Pindar Dibal

Department of Mathematical Sciences, University of Maiduguri, Maiduguri, Nigeria
Akeyede Imam

Department of Mathematics, Federal University Lafia, Lafia, Nigeria
Mustafa Babagana Abubakar

Directorate of Academic Planning, Federal University Lafia, Lafia, Nigeria

Download PDF

Sections

Plain Text BibTeX RIS

APA Style

Nicholas Pindar Dibal, Akeyede Imam, Mustafa Babagana Abubakar. (2021). On Order and Regime Determination of SETAR Model in Modelling Nonlinear Stationary Time Series Data Structure: Application to Lafia Rainfall Data, Nasarawa State, Nigeria. American Journal of Theoretical and Applied Statistics, 10(2), 89-98. https://doi.org/10.11648/j.ajtas.20211002.11

Copy | Download

ACS Style

Nicholas Pindar Dibal; Akeyede Imam; Mustafa Babagana Abubakar. On Order and Regime Determination of SETAR Model in Modelling Nonlinear Stationary Time Series Data Structure: Application to Lafia Rainfall Data, Nasarawa State, Nigeria. Am. J. Theor. Appl. Stat. 2021, 10(2), 89-98. doi: 10.11648/j.ajtas.20211002.11

Copy | Download

AMA Style

Nicholas Pindar Dibal, Akeyede Imam, Mustafa Babagana Abubakar. On Order and Regime Determination of SETAR Model in Modelling Nonlinear Stationary Time Series Data Structure: Application to Lafia Rainfall Data, Nasarawa State, Nigeria. Am J Theor Appl Stat. 2021;10(2):89-98. doi: 10.11648/j.ajtas.20211002.11

Copy | Download

@article{10.11648/j.ajtas.20211002.11,
  author = {Nicholas Pindar Dibal and Akeyede Imam and Mustafa Babagana Abubakar},
  title = {On Order and Regime Determination of SETAR Model in Modelling Nonlinear Stationary Time Series Data Structure: Application to Lafia Rainfall Data, Nasarawa State, Nigeria},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {10},
  number = {2},
  pages = {89-98},
  doi = {10.11648/j.ajtas.20211002.11},
  url = {https://doi.org/10.11648/j.ajtas.20211002.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20211002.11},
  abstract = {The linear time series model refers to the class of models for which fixed correlation parameters can fully explain the dependency between two random variables, but many real-life circumstances, such as monthly unemployment results, supplies and demands, interest rate, exchange rate, share prices, rainfall, etc., violate the assumption of linearity. For fitting and forecasting of nonlinear time series data, the self-exiting threshold autoregressive (SETAR) model was suggested. Using R to generate random nonlinear autoregressive data, a Monte Carlo simulation was performed, the SETAR model was fitted to the simulated data and Lafia rainfall data, Nasarawa State, Nigeria to determine the best regime orders and/or scheme number to make future forecast. Using Mean Square Error (MSE) and Akaike Information Criteria (AIC), the relative performance of models was examined. At a specific autoregressive order, regime order, sample size and step ahead, the model with minimum criteria was considered as the best. The results show that the best autoregressive and regime orders to be chosen are 3rd and 2nd [SETAR (3, 2)] respectively for fitting and forecasting nonlinear autoregressive time series data with small and moderate sample sizes. As the sample size increases, the output of the four models increases. Finally, it is shown that when sample size and number of steps forward are increased, the efficiency and forecasting capacity of the four models improves.},
 year = {2021}
}

Copy | Download

TY  - JOUR
T1  - On Order and Regime Determination of SETAR Model in Modelling Nonlinear Stationary Time Series Data Structure: Application to Lafia Rainfall Data, Nasarawa State, Nigeria
AU  - Nicholas Pindar Dibal
AU  - Akeyede Imam
AU  - Mustafa Babagana Abubakar
Y1  - 2021/03/03
PY  - 2021
N1  - https://doi.org/10.11648/j.ajtas.20211002.11
DO  - 10.11648/j.ajtas.20211002.11
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  - 89
EP  - 98
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20211002.11
AB  - The linear time series model refers to the class of models for which fixed correlation parameters can fully explain the dependency between two random variables, but many real-life circumstances, such as monthly unemployment results, supplies and demands, interest rate, exchange rate, share prices, rainfall, etc., violate the assumption of linearity. For fitting and forecasting of nonlinear time series data, the self-exiting threshold autoregressive (SETAR) model was suggested. Using R to generate random nonlinear autoregressive data, a Monte Carlo simulation was performed, the SETAR model was fitted to the simulated data and Lafia rainfall data, Nasarawa State, Nigeria to determine the best regime orders and/or scheme number to make future forecast. Using Mean Square Error (MSE) and Akaike Information Criteria (AIC), the relative performance of models was examined. At a specific autoregressive order, regime order, sample size and step ahead, the model with minimum criteria was considered as the best. The results show that the best autoregressive and regime orders to be chosen are 3rd and 2nd [SETAR (3, 2)] respectively for fitting and forecasting nonlinear autoregressive time series data with small and moderate sample sizes. As the sample size increases, the output of the four models increases. Finally, it is shown that when sample size and number of steps forward are increased, the efficiency and forecasting capacity of the four models improves.
VL  - 10
IS  - 2
ER  -

Copy | Download