Full Paper View Go Back

Intervention Model Based on Exponential Smoothing Methods and ARIMA Modelling of the Nigerian Naira Exchange Rates

Elisha J. Inyang1

Section:Research Paper, Product Type: Journal-Paper
Vol.11 , Issue.1 , pp.24-33, Feb-2024


Online published on Feb 28, 2024


Copyright © Elisha J. Inyang . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

View this paper at   Google Scholar | DPI Digital Library


XML View     PDF Download

How to Cite this Paper

  • IEEE Citation
  • MLA Citation
  • APA Citation
  • BibTex Citation
  • RIS Citation

IEEE Style Citation: Elisha J. Inyang, “Intervention Model Based on Exponential Smoothing Methods and ARIMA Modelling of the Nigerian Naira Exchange Rates,” International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.11, Issue.1, pp.24-33, 2024.

MLA Style Citation: Elisha J. Inyang "Intervention Model Based on Exponential Smoothing Methods and ARIMA Modelling of the Nigerian Naira Exchange Rates." International Journal of Scientific Research in Mathematical and Statistical Sciences 11.1 (2024): 24-33.

APA Style Citation: Elisha J. Inyang, (2024). Intervention Model Based on Exponential Smoothing Methods and ARIMA Modelling of the Nigerian Naira Exchange Rates. International Journal of Scientific Research in Mathematical and Statistical Sciences, 11(1), 24-33.

BibTex Style Citation:
@article{Inyang_2024,
author = {Elisha J. Inyang},
title = {Intervention Model Based on Exponential Smoothing Methods and ARIMA Modelling of the Nigerian Naira Exchange Rates},
journal = {International Journal of Scientific Research in Mathematical and Statistical Sciences},
issue_date = {2 2024},
volume = {11},
Issue = {1},
month = {2},
year = {2024},
issn = {2347-2693},
pages = {24-33},
url = {https://www.isroset.org/journal/IJSRMSS/full_paper_view.php?paper_id=3424},
publisher = {IJCSE, Indore, INDIA},
}

RIS Style Citation:
TY - JOUR
UR - https://www.isroset.org/journal/IJSRMSS/full_paper_view.php?paper_id=3424
TI - Intervention Model Based on Exponential Smoothing Methods and ARIMA Modelling of the Nigerian Naira Exchange Rates
T2 - International Journal of Scientific Research in Mathematical and Statistical Sciences
AU - Elisha J. Inyang
PY - 2024
DA - 2024/02/28
PB - IJCSE, Indore, INDIA
SP - 24-33
IS - 1
VL - 11
SN - 2347-2693
ER -

55 Views    158 Downloads    11 Downloads
  
  

Abstract :
Nigeria`s poor handling of the currency crisis has made exchange rates the country`s main issue. This is made worse by her near total reliance on imports for consumption and her need for foreign cash from the export of crude oil. Consequently, Nigeria`s economic success is heavily reliant on the fluctuations of other global currencies. The study is aimed at modelling exchange rates between the Nigerian naira and the Pakistani rupee during a financial slump using an intervention modelling approach constructed on exponential smoothing methods and the ARIMA model with a view to making comparisons. The dataset used in this study is the daily exchange rates of Pakistani rupees to Nigerian naira spanning from January to December 2016. Results revealed that the 2016 economic downturn had a negative impact on the naira, with a percentage change of 47.51. This implies that rupees appreciated over the naira such that Rs1 PKR = 1.9524 NGN compared to the periods before and after the intervention occurred. The economic recession was considered a step function with a delay of 1 period and a gradual-permanent effect with a decay rate of 0.60. Comparatively speaking, nonetheless, the ARIMA-intervention model outperformed the ETS-intervention model.

Key-Words / Index Term :
Exponential smoothing methods, ARIMA, Intervention model, Exchange rates.

References :
[1] Box, G. and Jenkins, G. “Time Series Analysis: Forecasting and Control,” Holden – Day, San Francisco, 1970.
[2] Holt, C. C. “Forecasting Trends and Seasonals by Exponentially Weighted Averages,” O.N.R. Memorandum, Camegies Institute of Technology, Vol. 52, 1957.
[3] Brown, R. G. “Statistical Forecasting for Inventory Control,” McGraw-Hill, New York, 1959.
[4] Winters, P. R. “Forecasting Sales by Exponentially Weighted Averages,” Management Sciences, Vol. 6, pp.324 – 342, 1960.
[5] Seong, B. and Lee, K. “Intervention Analysis Based on Exponential Smoothing Methods: Application to 9/11 and COVID – 19 Effects,” Economic Modelling, 2020. https: //doi.org/10.1016/j.econmod.2020.11.014.
[6] Box, G. E. P. and Tiao, G. C. “Intervention Analysis with Application to Economic and Environmental Problems,” Journal of American Statistical Association, Vol. 70, No. 349, pp.70-79, 1975.
[7] Anyanwu, F. A., Ananwude, A. C., and Okoye, N. T. “Exchange Rate Policy and Nigeria’s Economic Growth: A Granger Causality Impact Assessment,” International Journal of Applied Economics, Finance and Accounting, Vol. 1, No. 1, pp.1 – 13, 2017.
[8] Danladi, J. D. and Uba, U. P. “Does the Volatility of Exchange Rate Affect the Economic Performance of Countries in the West African Monetary Zone? A Case of Nigeria and Ghana,” British Journal of Economics, Management & Trade, Vol. 11, Issue. 3, pp.1 – 10, 2016.
[9] Etuk, H. E. and Eleki, A. G. “Intervention Analysis of Daily Yuan – Naira Exchange Rates.CARD,” International Journal of Science and Advanced Innovative Research (IJSAIR), Vol. 1, No. 3, December 2016.
[10] Girard, D. Z. “Intervention Time Series Analysis of Pertussis Vaccination in England and Wales,” Health Policy, Vol. 54, pp.13 – 25, 2000.
[11] Yang, L. “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.
[12] Nelson, J. P. “Consumer Bankruptcies and the Bankruptcy Reform Act: A Time – Series Intervention Analysis, 1960 – 1997,” Journal of Financial Services Research, Vol. 17, No. 2, pp.181 – 200, 2000.
[13] Shittu, O. I. and Inyang, E. J. “Statistical Assessment of Government’s Interventions on Nigerian Crude Oil Prices,” A Publication of Professional Statisticians Society of Nigeria, Proceedings of 3rd International Conference, Vol. 3, pp.519 – 524, 2019.
[14] Lam, C. Y., Ip, W. H., and Lau, C. W. “A Business Process Activity Model and Performance Measuremen Using a Time Series ARIMA Intervention Analysis,” Expert Systems with Applications, Vol. 36, pp.925 – 932, 2009.
[15] Etuk, E. H., Dimkpa, M., Sibeate, P., and Onyeka, N. G. “Intervention Analysis of Daily Yen/Naira Exchange Rates,” Management and Administrative Sciences Review, Vol. 6, Issue. 1, 2017.
[16] Sharma, P. and Khare, M. “Application of Intervention Analysis for Assessing the
Effectiveness of CO Pollution Control Legislation in India,” Transportation Research, Part D 4 , 427 – 432, 1999.
[17] Etuk, E. H. and Udoudo, U. P. “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.
[18] Deutsch, S. J. and Alt, F. B. “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, 1977.
[19] Etuk, E. H. and Ntagu, O. K. “Modelling of the Intervention of Daily Swiss Franc (CHF)/Nigerian Naira (NGN) Exchange Rates,” International Journal of Science and Advanced Innovative Research, Vol. 3, No. 1, 2018.
[20] Min, J. C. H. “Forecasting Japanese Tourism Demand in Taiwan using an Intervention Analysis,” International Journal of Culture, Tourism and Hospital Research, Vol. 2, Issue. 3, pp.197 – 216, 2008.
[21] Etuk, E. H. and George, D. S. “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, 2020.
[22] Mrinmoy, R., Ramasubramanian, V., Amrender, K. and Anil, R. “Application of Time Series Intervention Modelling for Modelling and Forecasting Cotton Yield,” Statistics and Applications, Vol. 12, No. 1& 2, pp. 61 – 70, 2014.
[23] Etuk, E. H. and Chukwukelo, V. N. “Intervention Analysis of Daily Moroccan Dirham/Nigerian Naira Exchange Rates,” International Journal of Management Studies, Business & Entrepreneurship Research, Vol. 3, No. 1, 2018.
[24] Darkwah, K. F., Okyere, G. A., and Boakye, A. “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.
[25] Etuk, E. H., Onyeka, G. N., and Leesie, L. “An Autoregressive Integrated Moving Average Intervention Model of 2016 Brazilian Real and Nigerian Naira Exchange Rates,” Journal of Basic and Applied Research International, Vol. 27, No. 9, pp.1 – 7, 2021.
[26] Jarrett, J. E. and Kyper, E. “ARIMA Modelling with Intervention to Forecast and Analyze Chinese Stock Prices,” Int. j. eng. bus. Manag., Vol. 3, pp.53 – 58, 2011.
[27] Etuk, E. H. and Amadi, E. H. “Intervention Analysis of Daily GBP – USA Exchange Rates Occasioned by BREXIT,” International Journal of Management, Accounting and Economics, Vol. 3, No. 12, pp.797 – 805, 2016.
[28] Lai, S. L. and Lu, W. L. “Impact Analysis of September 11 on Air Travel Demand in the USA,” Journal of Air Transport Management, Vol. 11, No. 6, pp.455 – 458, 2005.
[29] Moffat, I. U. and Inyang, E. J. “Impact Assessment of Gap on Nigerian Crude Oil Production: A Box-Tiao Intervention Approach,” Asian Journal of Probability and Statistics, Vol. 17, Issue. 2, pp.52 – 60, 2022. https://doi.org/10.9734/ajpas/2022/v17i230419
[30] Etuk, E.H.,Inyang, E. J. and Udoudo, U. P. “Impact of Declaration of Cooperation on the Nigerian Crude Oil Production,” International Journal of Statistics and Applied Mathematics, Vol. 7, Issue. 2, pp.165 – 169, 2022.
[31] Inyang, E. J., Nsien, E. F., Clement, E. P., and Danjeh, A. G. “Statistical Investigation of the impact of global oil politics: An Interrupted Time Series Approach,” JP Journal of Mathematical Sciences, Vol. 32, Issue. 1& 2, pp. 1 – 13, 2022.
[32] Adeleye, N. F., Ilo, H. O., and Gbadamosi, T. O., “Time Series Analysis of Crude Oil Production in Nigeria between the Years 2010 to 2020,” International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol. 10, Issue. 2, pp. 38 – 45, 2023.
[33] Parvez, S. M. and Azim, N. H. A., “Analyzing Bangladesh’s Present Patterns in Population Growth and Prediction by ARIMA and Exponential Smoothing Model,“ International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol. 10, Issue. 3, pp. 41 – 48, 2023.
[34] 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. DOI: 10.9734/AJPAS/2023/v25i3560
[35] Inyang, E. J., Nafo, N. M., Wegbom, A. I., Da-Wariboko, Y. A. “ETS - ARIMA Intervention Modelling of Bangladesh Taka/Nigerian Naira Exchange Rates,” Science Journal of Applied Mathematics and Statistics, Vol. 12, Issue. 1, pp.1 – 12, 2024. https://doi.org/10.11648/j.sjams.20241201.11
[36] Jaganathan, S. “Modeling and Predicting Demand During Pandemics Using Time Series Models,” 2021. https://www.linkedin.com/pulse/modelling-predicting-demand-during-pandemics-using-time-series-jaganathan.
[37] Trapero, J. R., Pedregal, D. J., Fildes, R., and Kourentzes, N. “Analysis of Judgmental Adjustments in the Presence of Promotions,” International Journal of Forecasting, Vol. 29, Issue. 2, pp.234 – 243, 2013.
[38] PKR/NGN, 2016. https://www.exchangerates.org.uk/PKR-NGN-spot-exchange-rates-history-2016.html
[39] R Core Team “R: A Language and Environment for Statistical Computing,” R Foundation for Statistical Computing, Vienna, Austria, 2022. URL https://www.R-project.org/.
[40] Box, G. E. P. and Jenkins, G. M. (1976). Time Series Analysis: Forecasting and Control, Revised Edition, San Francisco: Holden Day.
[41] Box, G. E. P., Reinsel, G. C., and Jenkins, G. M. “Time Series Analysis: Forecasting and Control,” 3rd Ed. Prentice – Hall, England Cliffs, N. J., 1994.
[42] Shittu, O. I. and Yaya, O. S. “Introduction to Time Series Analysis,” Department of Statistics, University of Ibadan, Ibadan, Nigeria, 2016.
[43] Dickey, D. A. and Fuller, W. A. “Distribution of Estimators for Autoregressive Time Series with a Unit Root,” Journal of the American Statistical Association, Vol. 74, pp.427 – 431, 1979.
[44] Akaike, H. “A New Look at the Statistical Model Identification,” I. E. E. E. Transactions of Automatic Control, AC, Vol. 19, pp.716 – 723, 1974.
[45] Schwarz, G. E. “Estimating the Dimension of a Model,” Annals of Statistics, Vol. 6, Issue. 2, pp.461 – 464, 1978. Doi: 10.1214/aos/117644136, MR 0468014.
[46] Clement, E. P. “Using Normalized Bayesian Information Criterion (BIC) to improve Box-Jenkins model Building,” American Journal of Mathematics and Statistics, Vol. 4, Issue. 5, pp.214 – 221, 2014. DOI: 10.5923/k.ajms.20140405.02
[47] Ljung, G. M. and Box, G. E. P. “On a Measure of Lack of Fit in Time Series Models,” Biometrika, Vol. 66, pp.265 – 270, 1978.
[48] Stellwagen, E. and Tashman, L. “ARIMA: The Models of Box and Jenkins,” Forecasting Methods Tutorials, 2013.

Authorization Required

 

You do not have rights to view the full text article.
Please contact administration for subscription to Journal or individual article.
Mail us at  support@isroset.org or view contact page for more details.

Go to Navigation