A 0.18-point reduction in monthly forecast RMSE is all this paper offers a trader, and nobody has shown it can pay for a single trade.
Egba examines whether the inflation coefficient in a monthly Nigerian return regression varies over time, and whether that variation improves one-month forecasts. Nigerian studies disagree on the relationship. Some find a positive long-run association, others a negative one. Inflation could lift nominal cash flows while raising discount rates. A constant slope could therefore average two regimes into a coefficient close to zero. Tracking the drift should improve forecasts. Any trading value would come from that improvement: a better forecast of next month's NGX All-Share return, presumably used for a tactical tilt.
The regression uses the monthly NGX All-Share log return (times 100) and four predictors, each lagged one month. These are headline inflation, the log change in the official naira-dollar rate, the change in the Central Bank of Nigeria's Monetary Policy Rate, and the log change in Brent. The inflation slope alone varies, following a random walk whose innovation variance is qβ. The intercept and three control coefficients remain fixed. Maximum likelihood estimation through the Kalman filter uses 239 usable months, from February 2005 to December 2024. The null qβ = 0 lies on the parameter-space boundary, so the constancy test relies on a parametric bootstrap instead of a chi-square table.
The estimated qβ is 0.014 (SE 0.006), with a bootstrap LR of 5.21 (p =.028, 2,000 draws). The filtered slope ranges from -0.12 to 0.09. Initially negative, it approaches zero mid-sample and becomes positive during parts of the later period. The out-of-sample comparison covers 72 expanding-window forecasts, January 2019 to December 2024. RMSE is 3.92 and MAE is 2.74 for the time-varying model; the constant-slope model records 4.10 and 2.88. The one-sided Clark-West statistic reaches 1.73 (p =.042). Among the controls, only the exchange-rate change clears 5% (0.18, p =.046).
Rebuilding from Egba's paper
The paper supplies a fair amount of what a replication needs. It states the variable transformations and names the sources (NGX, NBS, CBN, EIA). The forecast split is precise: December 2018 ends the first estimation window. According to the paper, every forecast uses the filtered state at its origin, never the smoothed state. The state path therefore uses no later data. The paper also specifies diffuse initialization, dispersed starting values and observed-information standard errors.
Other details remain unresolved. Equations (1) and (2) contain only their numbers in the version we read, leaving an implementer to reconstruct the system from the prose. The inflation descriptions differ too. Table 1 calls the series a "monthly all-items headline inflation rate", whereas the text describes it as "the published year-on-year headline rate". We did not find a statement establishing whether qβ, H and the three control coefficients are re-estimated at each of the 72 origins. "Expanding-window" suggests they are; anyone rebuilding the model must make that choice.
We also did not find a description of how the parametric bootstrap generates errors. The author leaves "exact data downloads and revisions" to future work. One-month lags reduce timing ambiguity, the paper says, without establishing whether NBS CPI for month t-1 is available by month t.
The series need checking before modelling begins. Maximum reported inflation is 28.90%, although NBS headline readings exceeded 30% during 2024, within the sample. The official rate's largest monthly change is 18.20%, surprisingly small beside the 2023 unification. The series were either constructed differently from the text's description, or something needs fixing.
Does inflation explain the moving slope?
Inflation averages 13.90%, with a standard deviation of 5.21, and the slope multiplies that level. At the mean, a slope ranging from -0.12 to 0.09 shifts the fitted monthly return from about -1.67 to +1.25 points. Compare that with a fixed intercept of only 0.31 (SE 0.26) and a mean return of 0.74. Multiplying a slow-moving level by a random-walk coefficient produces something much like a random-walk intercept. A replication should fit that alternative. If a drifting intercept matches the likelihood, calling the state an inflation slope adds little information.
Evidence for the sign change is weak. The 95% band includes zero over what the paper calls "substantial portions of the sample". Its conclusion nevertheless says the association "changes sign", despite the abstract's own band including zero for long stretches. Rejecting qβ = 0 establishes movement in the slope. An allocator would need evidence of when it is reliably negative or positive.
Constant variance leaves ARCH effects behind
At 12 lags, the ARCH LM statistic is 23.9, p =.03. Yet H, the observation variance, remains fixed at 31.70. Egba acknowledges the risk explicitly: "a random-walk state may mistake volatility for coefficient change." The proposed extensions cover mean-reverting states, alternative inflation measures and sectoral returns. All leave the residual variance fixed. Allowing stochastic volatility in H and then re-estimating qβ is the test that would settle this concern.
The bootstrap could make matters worse. Under the null, a parametric bootstrap typically generates homoskedastic errors. If that happened here, the reference distribution would miss the heteroskedasticity detected by the diagnostics. In that case, p =.028 is likely too small.
The forecast evidence is thin too.
On 72 observations, a Clark-West statistic of 1.73 clears 5% against an asymptotic normal distribution, at p =.042. Both forecast errors (3.92 and 4.10) are below the full-sample return SD of 5.82. This suggests that the 2019 to 2024 evaluation window was calmer than the sample overall. The paper gives no return SD for that window. Its full-sample observation variance, H = 31.70, implies a residual SD of about 5.63, again above both out-of-sample RMSEs. We saw no comparisons using alternative start dates.
What would justify capital?
The author states the limits candidly, describing the gain as "modest and specific to the January 2019 to December 2024 evaluation window". The paper also says investors would need transaction-cost-aware tests before using the forecasts as a trading signal. It measures neither returns nor turnover, and identifies no executable instrument for the NGX All-Share.
We could not test the result ourselves. Our data include no Nigerian headline CPI, official naira-dollar rate or policy rate, and no tradable Nigerian equity instrument. We also lack the EIA Brent spot series. Substituting WTI futures would change the predictor.
Our view would change if the inflation slope retained its qβ and its Clark-West advantage after allowing H to vary. Until someone runs that comparison, a 0.18-point RMSE improvement over 72 months remains a forecasting footnote.