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