Comparative Forecasting of MTN Nigeria Stock Prices and Trading Volume using Box–Jenkins Models and a Reduced Factorial Design

Abstract

This study compares Box-Jenkins forecasting structures (ARMA(p,q), ARIMA(p,d,q), and SARIMA(p,d,q)(P,D,Q)s) for the daily closing stock price and trading volume of MTN Nigeria Communications Plc (MTNN) on the Nigerian Exchange Group (NGX), and decomposes the structural drivers of accuracy using a factorial design. Using 249 daily observations from 26 May 2025 to 26 May 2026, eight candidate configurations spanning AR order (p ∈ {1,2}), differencing order (d ∈ {0,1}) and seasonal AR order (P ∈ {0,1}) were evaluated for trading volume, forming a complete 2³ factorial design; for stock price, only six of the eight combinations were estimated – the two SARIMA specifications without differencing (d = 0, P = 1) were not fitted – so the price analysis is a reduced, non-orthogonal design, and its factorial effects are reported with that limitation stated explicitly. Models were estimated on a training sample of 227 observations and evaluated out-of-sample using rolling one-step-ahead forecasts across 22 validation observations. By RMSE, ARIMA(1,1,0) produced the most accurate stock price forecasts (RMSE = 24.21 NGN; MAPE = 1.71%), although ARMA(1,0) and ARMA(2,0) achieved lower MAE and MAPE; SARIMA(2,1,0)(1,0,0)₅ produced the most accurate trading-volume forecasts on all four criteria (RMSE = 3,177,444; MAPE = 44.69%). No single model was superior across both series or across all criteria: for price, first-order differencing was the dominant structural factor; for volume, AR order and the interaction between differencing and seasonal AR order were the dominant factors.