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 |
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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. |
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Copyright © The Author(s), 2021. Published by Science Publishing Group |
SETAR Model, Regime Order, Autoregressive Order, Nonlinear Time Series
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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
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
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
@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} }
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 -