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

Overview

This study addresses parameter instability in Nigerian macroeconomic forecasting by developing a Time-Varying Scalar Component VARMA (TV-SCVARMA) model. Traditional VAR and VARMA specifications assume constant parameters and fail to accommodate structural breaks induced by oil-price volatility, policy interventions, and exchange-rate regime shifts. The proposed framework combines the parsimony of VAR with moving-average dynamics while permitting stochastic parameter evolution, addressing identification and small-sample estimation challenges endemic to classical VARMA specifications.

Methods and approach

The TV-SCVARMA model was estimated using a state-space representation with Kalman filter-based maximum likelihood inference. The empirical specification incorporates five macroeconomic variables: real GDP growth, inflation, M1 money supply, M2 money supply, and the exchange rate. Data spanning 2010Q1 to 2024Q1 were sourced from the Central Bank of Nigeria and the National Bureau of Statistics. Parameter evolution was modeled as stochastic processes, enabling dynamic adjustment to structural shifts. Forecast accuracy was evaluated through Root Mean Squared Error comparisons against classical VARMA and VAR benchmarks across multiple horizons.

Key Findings

The TV-SCVARMA specification demonstrated superior out-of-sample forecast performance relative to traditional approaches, achieving the lowest RMSE across the assessment period. The model exhibited rapid convergence and maintained stability in long-horizon forecasts despite the presence of macroeconomic turbulence. Classical VARMA exhibited substantially weaker forecasting capacity, while constant-parameter VAR models failed to capture structural dynamics. These findings indicate that permitting parameter time-variation materially improves predictive accuracy in environments characterized by recurrent exogenous shocks.

Implications

The results establish that time-varying specifications are necessary for reliable macroeconomic forecasting in small open economies subject to commodity-price fluctuations and policy regime changes. The TV-SCVARMA framework provides a methodologically sound foundation for central bank policy analysis and scenario simulation in unstable macroeconomic environments. Practitioners should transition from constant-parameter specifications to adaptive models that accommodate parameter evolution when forecasting horizons extend beyond immediate periods. The approach is particularly relevant for emerging markets experiencing repeated structural breaks rather than steady-state conditions.