Comparative Analysis of Information Criteria with a Forecast-Based Criterion for Optimal ARIMA Model Identification: Empirical Evidence using Naira- Franc Exchange Rate

PDF

Published: 2023-04-27

Page: 123-133


Amaefula Chibuzo G. *

Department of Mathematics and Statistics, Federal University Otuoke, Bayelsa State, Nigeria.

*Author to whom correspondence should be addressed.


Abstract

The study compares Akaike information criterion (AIC), Schwarz Bayesian information criterion (SBIC), Hannan Quinn (HQ) and Forecast Prediction Error (FPE) with a forecast output-based criterion (AFC) in identifying an optimal autoregressive integrated moving average (ARIMA) model for predicting Naira-Franc Exchange Rate (NFEXR). The comparison is conditioned on no autocorrelated residuals in the identified model. Monthly data set used spanned from 2008M1-2020M12. The order of integration test indicates NFEXR is stationary after first differencing. Estimation was based on an iterative algorithm for calculating least squares estimates of model parameters. Six probable specifications of ARIMA (p, 1, q) are evaluated by all the information criteria under study. The computational analytical results indicate that the models chosen by AIC, SBIC, HQ and FPE are inadequate and could not satisfy the condition of no autocorrelated residuals. And ARIMA (0, 1, 2) specification, having the minimum value of AFC and satisfying the condition of no autocorrelation in the model residuals is identified as the optimal model. However, AFC is apt in model identification and ARIMA (0, 1, 2) can be useful in monitoring and predicting of NFEXR for robust portfolio investment, economic gain and trade relationship between the two countries.

Keywords: AFC, ARIMA Identification, Information criteria, NFEXR


How to Cite

G., A. C. (2023). Comparative Analysis of Information Criteria with a Forecast-Based Criterion for Optimal ARIMA Model Identification: Empirical Evidence using Naira- Franc Exchange Rate. Asian Journal of Pure and Applied Mathematics, 5(1), 123–133. Retrieved from https://globalpresshub.com/index.php/AJPAM/article/view/1802

Downloads

Download data is not yet available.

References

Olokor F. Franco-Nigeria Trade Dropped to $2.3bn in 2020 – France. Punch [cited Apr 14]; 2021.

Available:https://punchng.com/franco-nigeria-trade-dropped-to-2-3bn-in-2020-france/

Huang W, Lai L. K, Nakamori, Y and Wang, S. Forecasting foreign exchange rates with Artificial Neural Networks: A review, International Journal of 27 Information Technology & Decision Making. 2004;3(1):145-65.

Shittu OI. Modeling exchange rate in Nigeria in the presence of financial and political instability: an intervention analysis approach. Middle East Fin Econ ISSN. 2009;2889(5):1450.

Ramzan S, Ramzan S, Zahid F. M. Modeling and forecasting exchange rate dynamics in Pakistan using ARCH family models. Electron J Appl Stat Anal. 2012;5(1):15-9. DOI: 10.1285/i20705948v5n1p15

Onasanya OK, Adeniji OE. Forecasting of exchange rate between naira and US dollar using time domain model. Int J Dev Econ Sustain. 2013;1:45-55.

Medel C, Camilleri G, Hsu H, Kania S, Touloumtzoglou M. Robustness in foreign exchange rate forecasting models: economics – based modeling after the financial crisis, Munich Personal RePEc Archive (MPRA):Paper No. 65290; 2015. Available:http://mpra.ub.uni-muenchen.de/65290/

Tindaon S. Forecasting the NTD/USD exchange rate using Autoregressive Model. Taiwan: Department of International Business, Chung Yuan Christian University; 2015.

Okon EJ, Ikpang IN. Modeling and forecasting exchange rate values between naira and US dollar to assess the effect of COVID-19 pandemic period on the rate. Asian J Probab Stat. 2020;8(1):55-65. DOI: 10.9734/ajpas/2020/v8i130200

Amaefula CG. Modelling naira – rupee exchange rate: An Arima framework Asian journal of economics, finance and management AJEFM. 2022;8(1):24-33.

Central Bank of Nigeria; 2021. Statistical Belletin. Available:http://www.cbn.gov.ng

Box DE, Jenkins GM. Time series analysis, forecasting and control. rev ed. Holden-Day; 1974.

Amaefula CG. A simple integration order test: An alternative to unit root testing. EJMATH. 2021;2(3):77-85.

DOI: 10.24018/ejmath.2021.2.3.22

Akaike H. A new look at the statistical model identification. IEEE Trans Autom Control. 1969;21:234-7.

Akaike H. Fitting autoregressive models for prediction, Annals of the Institute of Statistical Mathematics AC-19. 1974;364-85.

Schwarz G. Estimating the dimensions of a model. Ann Statist. 1978;6(2):461-4, as well as in. DOI: 10.1214/aos/1176344136

Hannan EJ, Quinn BG. The determination of the order of an autoregression. J R Stat Soc B. 1979;41(2):190-5.

DOI: 10.1111/j.2517-6161.1979.tb01072.x, P. 190

Amaefula CG. Optimal identification of subclass of autoregressive integrated moving average model using sum of square deviation forecasts criterion. Int J Stat Syst. 2011;6(1):35-40.