Time-varying Scalar Component VARMA: A State-space Solution to Structural Instability in Macroeconomic Forecasting

International audience Macroeconomic relationships in Nigeria are unstable due to oil-price shocks, policy reforms, and exchange-rate realignments, making traditional VAR and VARMA models unreliable when parameters shift over time. Classical VARMA suffers from identification and small-sample problems, while VAR assumes constant parameters and poorly captures structural changes, leading to weak long-horizon forecasts. This study develops and estimates a Time-Varying Scalar Component VARMA (TV-SCVARMA) model that maintains VAR parsimony, incorporates MA dynamics, and allows parameters to evolve stochastically with variables (K=5). Using quarterly data on real GDP growth, inflation, money supply [M1 & M2], and exchange rate (2010Q1–2024Q1) obtained from the Central Bank of Nigeria and the National Bureau of Statistics, parameters were estimated via a state-space framework with Kalman filter–based maximum likelihood. Forecast performance was assessed using Root Mean Squared Errors (RMSE). Results show that the TV-SCVARMA model delivers the lowest RMSE, rapid convergence, and stable forecasts, while classical VARMA performs poorly. The study concludes that time-varying models are better suited for forecasting in unstable economies and recommends TV-SCVARMA for macroeconomic policy analysis, with future work extending the model to stochastic volatility or Bayesian estimation for extreme-shock environments.