Selection of Linear Time Series Model on the Basis of Out-of-Sample Prediction Criteria

Background: In linear time series, the in-sample model selection and the out-of-sample model selection are the two common approaches to model selection. However, empirical evidence based on out-of-sample forecast performance is generally considered more trustworthy than evidence based on in-sample performance, which is deficient in providing information about future observations.

Aim: The aim of the study is to select the best linear time series model suitable to predict Nigeria exchange rates for the period 2002-2018.

Materials and Methods: Data on naira to pound and naira to euro exchange rates from January 2002 to December 2018, comprising of 204 data points were considered. The data were divided into two portions; the first portion which comprises of 192 observations was used for model building while the second portion with 12 observations was used for out-of-sample prediction evaluation. The Box-Jenkins ARIMA iterative procedure was used in model building while the mean square error (MSE), root mean square error (RMSE), mean absolute error (MAE) and Theil’s U coefficient were the measures of accuracy adopted in selecting the best out-of sample model.

Results: Our results revealed that, based on in-sample model selection, ARIMA (0, 1, 1) and ARIMA (1, 1, 0) were the appropriate models with minimum information criteria. However, on the basis of out-sample forecast performance evaluation criteria, ARIMA (1, 1, 0) and ARIMA (1, 1, 2) were found to be appropriate out-of-sample models with minimum forecast evaluation criteria. In all, our results showed that, the out-of sample models performed better than their in-sample counterparts in their ability to forecast future values.

Conclusion: So far, this study revealed that out-of-sample is a better model selection criterion than the in-sample counterpart as evident in its ability to predict future values which is the very essence for modelling in time series.