A stochastic-volatility filter losing on stochastic-volatility data tells traders about the estimator before it tells them about frontier-market risk. That is the result worth taking from Egba's paper. Nigeria has little bearing on it, and the headline needs to be read with that distinction in mind.
The forecasting contest
Egba compares three models on a daily series containing 3,912 returns, from 4 January 2010 to 31 December 2024. Estimation uses the first 3,129 observations, ending 30 December 2021. The remaining 783 form a chronological holdout. Gaussian maximum likelihood fits GARCH(1,1) and EGARCH(1,1), each with a constant mean.
The third model puts log variance in a latent AR(1) process and observes the log of squared returns. Its observation noise follows a skewed log-chi-square distribution. Egba substitutes a mean-adjusted Gaussian with variance π²/2, then applies a Kalman filter. This produces an approximate likelihood, a limitation Egba acknowledges.
During the holdout, the filters update while coefficients remain fixed at their training estimates. Each one-step variance forecast is evaluated against the corresponding day's squared return. The main loss is QLIKE: GARCH records 1.1071, EGARCH 1.1076 and the state-space SV model 1.1428. Diebold-Mariano tests use a five-lag Newey-West variance. They place SV's loss above GARCH (DM = 2.404, p =.016) and EGARCH (DM = 2.398, p =.017). The GARCH comparison with EGARCH yields DM = −0.106, p =.916. The abstract closes with "Latent-state flexibility did not produce lower one-step-ahead QLIKE loss in this daily design."
Where do Nigerian prices enter?
They do not.
The methodology explains that "using seed 140626, a pre-sample index level of 25,000 points was advanced by the generated returns." An AR(1) log-variance process generates the series, with persistence 0.978 and innovation SD 0.19. Return shocks and volatility shocks have correlation −0.28. Daily drift is 0.00070. The generator also inserts two decaying volatility pulses, beginning on 16 March 2020 and 1 June 2022. The second arrives during the holdout.
Egba is open about this. The abstract describes a "constructed daily series", and the limitations say the results "do not establish forecast performance on observed NGX closes." He deserves credit for those disclosures. The title nevertheless promises Nigerian stock returns. And the literature review presents the exercise as asking whether Shuaibu's monthly Nigerian ranking "carries over" to daily data. A seeded path cannot settle that question.
The discussion retreats from that framing. It says the difference "does not establish that either model class is universally superior" and calls for evaluation using observed daily NGX returns and alternative filters because the result is sensitive to design. The title and literature review thus reach further than the discussion. Kurtosis of 6.207 and skew of −0.322 are properties of the generator. The NGX scale supplies a starting number.
Recovering persistence still leaves SV behind
The fitted SV persistence is within one standard error of its true value, although estimated state variance is about 25% low. Estimated φ reaches 0.9813 (SE 0.0054), compared with the true 0.978. In percentage units, true long-run log variance is zero; its estimate is 0.0827 (SE 0.1603). Estimated state variance q is 0.0270 (SE 0.0072). The generator's true value is 0.19², about 0.036.
The fitted model leaves out two things. The estimates table lists μh, φ and q, without a correlation parameter corresponding to the generator's −0.28. Log-squared returns also discard each shock's sign. EGARCH picks up the planted leverage through γ = −0.0262 (SE 0.0117, p =.024). Another suspect is the Gaussian substitute for log-chi-square noise, which Egba identifies as a limitation.
Egba explicitly says the state-space result depends on the observation equation and filter chosen. He does not spell out the particular mismatch: the fitted SV omits a leverage term, whereas the generator includes a −0.28 correlation. The losing entrant is therefore a three-parameter Kalman approximation that discards shock signs. The data themselves came from the SV model class.
How much does a 3% QLIKE gap establish?
SV loses by 0.0357 QLIKE, roughly 3% of GARCH's loss. Just 0.0005 separates GARCH and EGARCH. The paper runs three pairwise tests without a multiplicity correction. The reported p-values (.016 and.017) straddle the Bonferroni threshold of 0.0167 for three tests, leaving the significance claim marginal after accounting for multiplicity. There is also just one seed and one path. No Monte Carlo spread across draws accompanies the result.
Changing the loss changes the ranking. EGARCH leads on RMSE with 2.4182, followed by GARCH at 2.4277 and SV at 2.4524. On MAE, SV leads with 1.2813, ahead of EGARCH at 1.3379 and GARCH at 1.3445. Egba says no pairwise tests were reported for RMSE or MAE. Those rankings consequently carry no inferential weight, and he confines his claim to QLIKE.
Finishing last on QLIKE and first on MAE suggests forecasts that sit low. Against squared returns, MAE rewards forecasts near the median, below the mean; QLIKE penalizes underprediction heavily. We did not find mean forecast levels in the paper. The explanation remains a hypothesis. It resembles our crypto finding, where the loss mostly set the forecast level.
The Student-t check improves SV's QLIKE by 0.0064 to 1.1364, leaving it last. Its MAE increases to 1.3413, still narrowly below EGARCH-t at 1.3420. Because the generator uses standard-normal shocks, a fat-tail check has limited scope here anyway.
We could not test the result ourselves. We carry neither the NGX All-Share Index nor a Nigerian equity universe. Repeating seed 140626 would reproduce a simulation. Substituting US equities would test another market.
Keep GARCH as the QLIKE benchmark
Egba recommends retaining GARCH as the QLIKE benchmark and trying EGARCH when asymmetry matters. That makes sense as a starting point. He also says observed exchange data, a trading-day calendar and intraday realized variance are needed for validation before the rankings inform market or risk decisions. The evidence warrants that restraint: one constructed path, one 783-day window, a one-step horizon and parameters held fixed for three years.
Much of the next study is already in Egba's discussion. It calls for observed NGX closes on a trading-day calendar and an intraday realized-variance proxy. The particle or Bayesian filtering listed as future work would give SV a fair entrant, with evaluation across multiple forecast horizons. We would also include an SV leverage term, rolling re-estimation and many seeds to distinguish skill from a fortunate draw.
One finding would change our view. An exact-likelihood SV with leverage that still loses to GARCH by something like 0.0357 QLIKE on real NGX data would leave the class with a problem. For now, the evidence reaches one Gaussian approximation on one simulated draw.