Science Journal of Applied Mathematics and Statistics

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ETS - ARIMA Intervention Modelling of Bangladesh Taka/Nigerian Naira Exchange Rates

Received: 20 November 2023    Accepted: 18 December 2023    Published: 11 January 2024
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Abstract

In real-world scenarios, numerous external events disrupt many time series, causing fluctuations in the series' mean level. When modeling such series using the traditional ARIMA model, this can result in distortions in the model's parameter estimations, the structure of the fitted model, and future value projections. Any unusual values in the series that might have arisen as a result of the special event could be adjusted using the Box-Tiao intervention modeling technique. This study investigates time series intervention modelling based on ETS and ARIMA models aimed at studying the response of the comparative value of the Bangladesh Taka to the Nigerian Naira due to the 2016 economic recession. The dataset for this study is the daily exchange rate of Bangladesh Taka to Nigerian Naira from January to December 2016. The BDT/NGN2016 exchange rates have been considered, with a step intervention being the introduction of the economic recession in June 2016. Results revealed an initial impact of 0.5217. The intervention caused a 68.49% depreciation in the value of the Naira exchanged with the Bangladesh Taka in the exchange rate market, with a decay rate of 0.6. The intervention effect was persistent, with a long-run effect of 1.2862. Hence, the intervention had a gradual start and a permanent effect.

DOI 10.11648/j.sjams.20241201.11
Published in Science Journal of Applied Mathematics and Statistics (Volume 12, Issue 1, February 2024)
Page(s) 1-12
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

ETS Model, ARIMA, Intervention Modelling, Bangladesh Taka/Nigerian Naira

References
[1] Akaike, H. (1974). A New Look at the Statistical Model Identification. I. E. E. E. Transactions of Automatic Control, AC, 19, 716–723.
[2] BGT/NGN (2016). https://www.exchangerates.org.uk/BGT-NGN-spot-exchange-rates-history-2016.html
[3] Box, G. and Jenkins, G. (1970). Time Series Analysis: Forecasting and Control. Holden – Day, San Francisco.
[4] Box, G. E. P. and Jenkins, G. M. (1976). Time Series Analysis: Forecasting and Control, Revised Edition, San Francisco: Holden Day.
[5] Box, G. E. P., Reinsel, G. C., and Jenkins, G. M. (1994). Time Series Analysis: Forecasting and Control. 3rd Ed. Prentice – Hall, England Cliffs, N. J.
[6] Box, G. E. P. and Tiao, G. C. (1975). Intervention Analysis with Application to Economic and Environmental Problems. Journal of American Statistical Association, Vol,. 70, No. 349. Pp. 70-79.
[7] Brown, R. G. (1959). Statistical Forecasting for Inventory Control. McGraw-Hill, New York.
[8] Darkwah, K. F., Okyere, G. A., and Boakye, A. (2012). Intervention Analysis of serious Crimes in the Eastern Region of Ghana. International Journal of Business and Social Research (IJBSR), Vol. 2, No. 7, December 2012.
[9] Deutsch, S. J. and Alt, F. B. (1977). The Effect of Massachusetts’ Gun Control Law on Gun –related Crimes in the City of Boston. Evaluation Quarterly, Vol. 1, No. 4, pp. 543–568, November 1977.
[10] Etuk, E. H. and Amadi, E. H. (2016). Intervention Analysis of Daily GBP – USA Exchange Rates Occassioned by BREXIT. International Journal of Management, Accounting and Economics, 3(12), 797–805.
[11] Etuk, E. H. and Chukwukelo, V. N. (2018). Intervention Analysis of Daily Moroccan Dirham/Nigerian Naira Exchange Rates. International Journal of Management Studies, Business & Entrepreneurship Research. Vol. 3, No. 1, March 2018.
[12] Etuk, H. E. and Eleki, A. G. (2016). Intervention Analysis of Daily Yuan – Naira Exchange Rates. CARD International Journal of Science and Advanced Innovative Research (IJSAIR), Vol. 1, No. 3, December 2016.
[13] Etuk, E. H. and George, D. S. (2020). Interrupted Time Series Modelling of Daily Malaysian Ringitt MYR/Liberian Dollar LRD Exchange Rates. International Journal of Science and Advance Innovative Research, Vol. 5, No. 2, June 2020.
[14] Etuk, E. H., Dimkpa, M., Sibeate, P., and Onyeka, N. G. (2017). Intervention Analysis of Daily Yen/Naira Exchange Rates. Management and Administrative Sciences Review, Vol. 6, Issue 1., January 2017.
[15] Etuk, E. H., Inyang, E. J. and Udoudo, U. P. (2022). Impact of Declaration of Cooperation on the Nigerian Crude Oil Production. International Journal of Statistics and Applied Mathematics 2022; 7(2): 165–169.
[16] Etuk, E. H., Onyeka, G. N., and Leesie, L. (2021). An Autoregressive Integrated Moving Average Intervention Model of 2016 Brazilian Real and Nigerian Naira Exchange Rates. Journal of Basic and Applied Research International, 27 (9): 1–7, 2021.
[17] Etuk, E. H. and Ntagu, O. K. (2018). Modelling of the Intervention of Daily Swiss Franc (CHF)/Nigerain Naira (NGN) Exchange Rates. International Journal of Science and Advanced Innovative Research, Vol. 3, No. 1, March 2018.
[18] Etuk, E. H. and Udoudo, U. P. (2018). Intervention Analysis of Daily Indian Rupee/Nigerian Naira Exchange Rates. Noble International Journal of Business and Management Research. Vol. 02, No. 06, pp: 47–52, 2018.
[19] Girard, D. Z. (2000). Intervention Time Series Analysis of Pertussis Vaccination in England and Wales. Health Policy, 54, 13–25.
[20] Holt, C. C. (1957). Forecasting Trends and Seasonals by Exponentially Weighted Averages. O. N. R. Memorandum 52/1957, Camegies Instute of Technology.
[21] Inyang, E. J., Etuk, E. H., Nafo, N. M., and Da-Wariboko, Y. A. Time Series Intervention Modelling Based on ESM and ARIMA Models: Daily Pakistan Rupee/Nigerian Naira Exchange Rate. Asian Journal of Probability and Statistics, Vol. 25, No. 3, pp. 1-17, 2023; Article no. AJPAS.106693. ISSN: 2582-0230. DOI: 10.9734/AJPAS/2023/v25i3560
[22] Inyang, E. J., Nsien, E. F., Clement, E. P., and Danjeh, A. G. (2022). Statistical Investigation of the impact of global oil politics: An Interrupted Time Series Approach. JP Journal of Mathematical Sciences, Vol. 32, Iss 1& 2, pp. 1–13.
[23] Jaganathan, S. (2021). Modeling and Predicting Demand During Pandemics Using Time Series Models. https://www.linkedin.com/pulse/modelling-predicting-demand-during-pandemics-using-time-series-jaganathan.
[24] Jarrett, J. E. and Kyper, E. (2011). ARIMA Modelling with Intervention to Forecast and Analyze Chinese Stock Prices. Int. j. eng. bus. Manag., Vol. 3, 53–58.
[25] Lai, S. L. and Lu, W. L. (2005). Impact Analysis of September 11 on Air Travel Demand in the USA. Journal of Air Transport Management, 11(6), 455–458.
[26] Lam, C. Y., Ip, W. H., and Lau, C. W. (2009). A Business Process Activity Model and Performance Measuremen Using a Time Series ARIMA Intervention Analysis. Expert Systems with Aplications, 36, 925–932.
[27] Makridakis, S., Wheelwright, S. C., and Hyndman, R. J. (1998). Forecasting Methods and Applications, 3rd Edition, John Wiley, New York.
[28] Min, J. C. H. (2008). Forecasting Japanese Tourism Demad in Taiwan using an Intervention Analysis. International Journal of Culture, Tourism and Hospital Research, Vol. 2, Iss 3, pp. 197–216.
[29] Moffat, I. U. and Inyang, E. J. (2022). Impact Assessment of Gap on Nigerian Crude Oil Production: A Box-Tiao Intervention Approach. Asian Journal of Probability and Statistics, 17(2), 52–60. https://doi.org/10.9734/ajpas/2022/v17i230419
[30] Mrinmoy, R., Ramasubramanian, V., Amrender, K. and Anil, R. (2014). Application of Time Series Intervention Modelling for Modelling and Forcasting Cotton Yield. Statistics and Applications. Vol. 12, No. 1& 2, pp. 61–70.
[31] Nelson, J. P. (2000). Consumer Bankruptcies and the Bankruptcy Reform Act: A Time – Series Intervention Analysi, 1960 – 1997. Journal of Financial Services Research, 17:2, 181–200, 2000.
[32] Seong, B. and Lee, K. (2020). Intervention Analysis Based on Exponential Smoothing Methods: Application to 9/11 and COVID–19 Effects. Economic Modelling, https://doi.org/10.1016/j.econmod.2020.11.014.
[33] Sharma, P. and Khare, M. (1999). Application of Intervention Analysis for Assessing the Effectiveness of CO Pollution Control Legislation in India. Transportation Research Part D 4 (1999), 427–432.
[34] Shittu, O. I. and Inyang, E. J. (2019). Statistical Assessment of Government’s Interventions on Nigerian Crude Oil Prices. A Publication of Professional Statisticians Society of Nigeria, Proceedings of 3rd International Conference. 2019; 3: 519-524.
[35] Trapero, J. R., Pedregal, D. J., Fildes, R., and Kourentzes, N. (2013). Analysis of Judgmental Adjustments in the Presence of Promotions. International Journal of Forecasting, 29(2), 234–243.
[36] Winters, P. R. (1960). Forecasting Sales by Exponentially Weighted Averages. Management Sciences, 6, 324–342.
[37] Yang, L. (2014). Pricing Virtual Goods: Using Intervention Analysis and Products’ Usage Data. A Thesis Presented to the University of Waterloo in Fulfillment of the Thesis Requirement of the Degree of Master of Applied Science in Management Sciences, 2014.
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  • APA Style

    Inyang, E. J., Nafo, N. M., Wegbom, A. I., Da-Wariboko, Y. A. (2024). ETS - ARIMA Intervention Modelling of Bangladesh Taka/Nigerian Naira Exchange Rates. Science Journal of Applied Mathematics and Statistics, 12(1), 1-12. https://doi.org/10.11648/j.sjams.20241201.11

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    ACS Style

    Inyang, E. J.; Nafo, N. M.; Wegbom, A. I.; Da-Wariboko, Y. A. ETS - ARIMA Intervention Modelling of Bangladesh Taka/Nigerian Naira Exchange Rates. Sci. J. Appl. Math. Stat. 2024, 12(1), 1-12. doi: 10.11648/j.sjams.20241201.11

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    AMA Style

    Inyang EJ, Nafo NM, Wegbom AI, Da-Wariboko YA. ETS - ARIMA Intervention Modelling of Bangladesh Taka/Nigerian Naira Exchange Rates. Sci J Appl Math Stat. 2024;12(1):1-12. doi: 10.11648/j.sjams.20241201.11

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  • @article{10.11648/j.sjams.20241201.11,
      author = {Elisha John Inyang and Ngia Matthew Nafo and Anthony Ike Wegbom and Yvonne Asikiye Da-Wariboko},
      title = {ETS - ARIMA Intervention Modelling of Bangladesh Taka/Nigerian Naira Exchange Rates},
      journal = {Science Journal of Applied Mathematics and Statistics},
      volume = {12},
      number = {1},
      pages = {1-12},
      doi = {10.11648/j.sjams.20241201.11},
      url = {https://doi.org/10.11648/j.sjams.20241201.11},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjams.20241201.11},
      abstract = {In real-world scenarios, numerous external events disrupt many time series, causing fluctuations in the series' mean level. When modeling such series using the traditional ARIMA model, this can result in distortions in the model's parameter estimations, the structure of the fitted model, and future value projections. Any unusual values in the series that might have arisen as a result of the special event could be adjusted using the Box-Tiao intervention modeling technique. This study investigates time series intervention modelling based on ETS and ARIMA models aimed at studying the response of the comparative value of the Bangladesh Taka to the Nigerian Naira due to the 2016 economic recession. The dataset for this study is the daily exchange rate of Bangladesh Taka to Nigerian Naira from January to December 2016. The BDT/NGN2016 exchange rates have been considered, with a step intervention being the introduction of the economic recession in June 2016. Results revealed an initial impact of 0.5217. The intervention caused a 68.49% depreciation in the value of the Naira exchanged with the Bangladesh Taka in the exchange rate market, with a decay rate of 0.6. The intervention effect was persistent, with a long-run effect of 1.2862. Hence, the intervention had a gradual start and a permanent effect.
    },
     year = {2024}
    }
    

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  • TY  - JOUR
    T1  - ETS - ARIMA Intervention Modelling of Bangladesh Taka/Nigerian Naira Exchange Rates
    AU  - Elisha John Inyang
    AU  - Ngia Matthew Nafo
    AU  - Anthony Ike Wegbom
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    DO  - 10.11648/j.sjams.20241201.11
    T2  - Science Journal of Applied Mathematics and Statistics
    JF  - Science Journal of Applied Mathematics and Statistics
    JO  - Science Journal of Applied Mathematics and Statistics
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    EP  - 12
    PB  - Science Publishing Group
    SN  - 2376-9513
    UR  - https://doi.org/10.11648/j.sjams.20241201.11
    AB  - In real-world scenarios, numerous external events disrupt many time series, causing fluctuations in the series' mean level. When modeling such series using the traditional ARIMA model, this can result in distortions in the model's parameter estimations, the structure of the fitted model, and future value projections. Any unusual values in the series that might have arisen as a result of the special event could be adjusted using the Box-Tiao intervention modeling technique. This study investigates time series intervention modelling based on ETS and ARIMA models aimed at studying the response of the comparative value of the Bangladesh Taka to the Nigerian Naira due to the 2016 economic recession. The dataset for this study is the daily exchange rate of Bangladesh Taka to Nigerian Naira from January to December 2016. The BDT/NGN2016 exchange rates have been considered, with a step intervention being the introduction of the economic recession in June 2016. Results revealed an initial impact of 0.5217. The intervention caused a 68.49% depreciation in the value of the Naira exchanged with the Bangladesh Taka in the exchange rate market, with a decay rate of 0.6. The intervention effect was persistent, with a long-run effect of 1.2862. Hence, the intervention had a gradual start and a permanent effect.
    
    VL  - 12
    IS  - 1
    ER  - 

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Author Information
  • Department of Statistics, University of Uyo, Uyo, Nigeria

  • Department of Mathematics, Rivers State University, Port Harcourt, Nigeria

  • Department of Mathematics, Rivers State University, Port Harcourt, Nigeria

  • Department of Mathematics, Rivers State University, Port Harcourt, Nigeria

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