Robust State-Space and Markov Regime-Switching Analysis of a Transformed Lafarge Africa Plc Monthly Price Scenario

This study develops a new, reproducible framework for analysing a transformed monthly price scenario associated with Lafarge Africa Plc. Unlike polynomial-trend and simple present-value approaches, the proposed methodology combines log-return transformation, a two-state Markov regime-switching model, a local-linear-trend state-space model, benchmark forecasting, residual diagnostics, and downside-risk estimation. The input series contains 36 monthly observations from January 2023 to December 2025 and was deliberately transformed so that it does not reproduce the source values directly; consequently, the findings are interpreted as a methodological case study rather than as a verified record of actual traded prices. Monthly log returns were computed using $r_t=\log\left(\frac{P_t}{P_{t-1}}\right)$, where $P_t$ denotes the transformed monthly price at time $t$. The transformed price has a mean of NGN 65.344, a median of NGN 63.125, and a standard deviation of NGN 10.847. Monthly log returns are stationary under the Augmented Dickey–Fuller (ADF) test, while the Ljung–Box and ARCH-LM diagnostics do not detect statistically significant residual serial correlation or conditional heteroskedasticity at conventional significance levels. Returns nevertheless exhibit pronounced positive skewness and excess kurtosis, motivating regime-switching and tail-risk analyses. A two-regime Markov specification is employed to estimate time-varying latent market states, whereas a local-linear-trend state-space model generates probabilistic forecasts through Kalman filtering. In a six-month holdout evaluation, the ARIMA(1,1,1) benchmark achieved the lowest forecasting error with an RMSE of 2.276 and a MAPE of 3.961%, compared with 6.576 and 11.029%, respectively, for the structural state-space model. Historical 95% Value-at-Risk (VaR) and Expected Shortfall (ES) were estimated at 9.083% and 10.808%, respectively. The findings demonstrate that forecasting performance should be evaluated separately from structural interpretability: while ARIMA provides superior point forecasts for the transformed dataset, the regime-switching and state-space models offer richer insights into latent market dynamics, uncertainty quantification, and downside financial risk. The proposed framework provides a transparent and reproducible methodology for advanced financial time-series modelling and investment risk assessment.