Time-Varying Effects of Inflation on Stock Market Returns in Nigeria: Evidence from a State-Space Model and Kalman Filter

This paper examines whether inflation’s conditional relationship with Nigerian stock returns changes over time using 239 monthly observations from February 2005 to December 2024. Returns are measured as 100 times the monthly log change in the Nigerian Exchange All-Share Index, with lagged headline inflation, exchange-rate changes, changes in the Central Bank of Nigeria Monetary Policy Rate, and Brent crude price changes as predictors. A linear state-space model lets only the inflation coefficient follow a random walk and is estimated by maximum likelihood with the Kalman filter. An expanding-window, one-month-ahead forecast comparison covers 72 observations from January 2019 to December 2024. The estimated state-innovation variance is 0.014; a bootstrap likelihood-ratio statistic of 5.21 (p = .028) rejects the constant-coefficient restriction at 5%. The filtered inflation coefficient ranges from −0.12 to 0.09 and crosses zero, while its 95% interval covers zero during substantial portions of the sample. Forecast RMSE and MAE are 3.92 and 2.74 percentage points for the time-varying model, compared with 4.10 and 2.88 for the constant-coefficient benchmark. The Clark–West statistic (1.73; one-sided asymptotic p = .042) supports a forecast improvement at 5% under the standard-normal reference.