Modeling Time-Varying Volatility in Nigerian Stock Returns Using a State Space Framework

References

[1] Abbara O, Zevallos M (2023a). Estimation and forecasting of long memory stochastic volatility models. Studies in Nonlinear Dynamics & Econometrics, 27(1), 1–24. https://doi.org/10.1515/snde-2020-0106

[2] Abbara O, Zevallos M (2023b). Maximum likelihood inference for asymmetric stochastic volatility models. Econometrics, 11(1), Article 1. https://doi.org/10.3390/econometrics11010001

[3] Adegboyo OS, Sarwar K (2025). Modelling and forecasting of Nigeria stock market volatility. Future Business Journal, 11(1), Article 124. https://doi.org/10.1186/s43093-025-00536-4

[4] Adi AA, Adimani WE, Adda SP (2023). Modelling volatility of sub-indices returns of Nigerian Stock Exchange using GARCH model. Empirical Economic Review, 6(2), 116–134. https://doi.org/10.29145/eer.62.06

[5] Ahmed I, Adenomon MO, Abdullahi HM, Nweze NO (2025). Modelling the volatility of stock exchange market capitalization returns in Nigeria using GARCH models. Science World Journal, 20(3), 1218–1224. https://doi.org/10.4314/swj.v20i3.42

[6] Asai M (2023). Estimation of realized asymmetric stochastic volatility models using Kalman filter. Econometrics, 11(3), Article 18. https://doi.org/10.3390/econometrics11030018

[7] Azman S, Pathmanathan D, Thavaneswaran A (2022). Forecasting the volatility of cryptocurrencies in the presence of COVID-19 with the state-space model and Kalman filter. Mathematics, 10(17), Article 3190. https://doi.org/10.3390/math10173190

[8] Bégin JF, Zafari G (2025). Estimation of multifactor stochastic volatility jump-diffusion models: A marginalized filter approach. Econometrics and Statistics. Advance online publication. https://doi.org/10.1016/j.ecosta.2025.03.002

[9] Chau TTT, Ailliot P, Monbet V, Tandeo P (2023). Comparison of simulation-based algorithms for parameter estimation and state reconstruction in nonlinear state-space models. Discrete and Continuous Dynamical Systems - S, 16(2), 240–264. https://doi.org/10.3934/dcdss.2022054

[10] Chen CWS, Lin EMH, Huang TFJ (2022). Bayesian quantile forecasting via the realized hysteretic GARCH model. Journal of Forecasting, 41(7), 1317–1337. https://doi.org/10.1002/for.2876

[11] Conrad C, Kleen O (2020). Two are better than one: Volatility forecasting using multiplicative component GARCH-MIDAS models. Journal of Applied Econometrics, 35(1), 19–45. https://doi.org/10.1002/jae.2742

[12] Cornelius A, OlaOluwa YS, Johnson OF, Damola AM, Omoyeni OT (2024). Trading volume, intraday and overnight volatility of stock returns in the Nigerian Stock Exchange. Asian Journal of Probability and Statistics, 26(9), 110–122. https://doi.org/10.9734/ajpas/2024/v26i9649

[13] Damian C, Frey R (2024). Detecting rough volatility: A filtering approach. Quantitative Finance, 24(10), 1493–1508. https://doi.org/10.1080/14697688.2024.2399284

[14] Emenogu NG, Adenomon MO, Nweze NO (2020). On the volatility of daily stock returns of Total Nigeria Plc: Evidence from GARCH models, value-at-risk and backtesting. Financial Innovation, 6(1), Article 18. https://doi.org/10.1186/s40854-020-00178-1

[15] Fałdziński M, Fiszeder P, Orzeszko W (2021). Forecasting volatility of energy commodities: Comparison of GARCH models with support vector regression. Energies, 14(1), Article 6. https://doi.org/10.3390/en14010006

[16] Gbadebo AD (2023). Exchange rate volatility and Nigerian stock market development. International Journal of Professional Business Review, 8(9), Article e03078. https://doi.org/10.26668/businessreview/2023.v8i9.3078

[17] Gong C, Stoffer DS (2021). A note on efficient fitting of stochastic volatility models. Journal of Time Series Analysis, 42(2), 186–200. https://doi.org/10.1111/jtsa.12561

[18] Gregoir S, Meddahi N (2025). Towards identification of shocks in linear state-space models: Application to stochastic volatility model. Journal of Time Series Analysis, 46(6), 1205–1223. https://doi.org/10.1111/jtsa.70012

[19] Guzman IE, Ccori PC (2020). A new method for sequential learning of states and parameters for state-space models: The particle swarm learning optimization. Journal of Statistical Computation and Simulation, 90(11), 2057–2079. https://doi.org/10.1080/00949655.2020.1762600

[20] Haruna Umar Y, Adeoye M (2020). A Markov regime switching approach of estimating volatility using Nigerian stock market. American Journal of Theoretical and Applied Statistics, 9(4), Article 80. https://doi.org/10.11648/j.ajtas.20200904.11

[21] Harvey DI, Leybourne SJ, Zu Y (2024). Tests for equal forecast accuracy under heteroskedasticity. Journal of Applied Econometrics, 39(5), 850–869. https://doi.org/10.1002/jae.3050

[22] Kalovwe SK, Mwaniki JI, Simwa RO (2021). On stock returns volatility and trading volume of the Nairobi Securities Exchange Index. RMS: Research in Mathematics & Statistics, 8(1), Article 1889765. https://doi.org/10.1080/27658449.2021.1889765

[23] Kawakatsu H (2023). Simple factor realized stochastic volatility models. Journal of Time Series Econometrics, 15(1), 79–110. https://doi.org/10.1515/jtse-2021-0049

[24] Lux T (2022). Inference for nonlinear state-space models: A comparison of different methods applied to Markov-switching multifractal models. Econometrics and Statistics, 21, 69–95. https://doi.org/10.1016/j.ecosta.2020.03.001

[25] Mahatma Y, Hadi I (2021). Stochastic volatility estimation of stock prices using the Ensemble Kalman Filter. InPrime: Indonesian Journal of Pure and Applied Mathematics, 3(2), 136–143. https://doi.org/10.15408/inprime.v3i2.20256

[26] Mao X, Czellar V, Ruiz E, Veiga H (2020). Asymmetric stochastic volatility models: Properties and particle filter-based simulated maximum likelihood estimation. Econometrics and Statistics, 13, 84–105. https://doi.org/10.1016/j.ecosta.2019.08.002

[27] Mohammed T, Umar YH, Adams SO (2022). Modeling the volatility for some selected beverages stock returns in Nigeria (2012–2021): A GARCH model approach. Matrix Science Mathematic, 6(2), 41–51. https://doi.org/10.26480/msmk.02.2022.41.51

[28] Nemushungwa AI (2024). Assessing the forecasting performance of GARCH models in the presence of instabilities. Universal Journal of Accounting and Finance, 12(1), 13–23. https://doi.org/10.13189/ujaf.2024.120102

[29] Olugbode MA, Shittu OI (2024). Transition E-GARCH model for modeling and forecasting volatility of equity stock returns in Nigeria Stock Exchange. International Journal of Research and Innovation in Social Science, 7(12), 2120–2134. https://doi.org/10.47772/ijriss.2023.7012162

[30] Özgül A (2025). GAS or GARCH: A comparison of density and VaR forecasts in Turkish FX and stock markets. Istanbul Business Research, 54(1), 58–86. https://doi.org/10.26650/ibr.2025.54.1577152

[31] Pallotta A, Ciciretti V (2024). Should you use GARCH models for forecasting volatility? A comparison to GRU neural networks. Studies in Nonlinear Dynamics & Econometrics, 28(5), 725–738. https://doi.org/10.1515/snde-2022-0025

[32] Pérez-Vieites S, Míguez J (2021). Nested Gaussian filters for recursive Bayesian inference and nonlinear tracking in state-space models. Signal Processing, 189, Article 108295. https://doi.org/10.1016/j.sigpro.2021.108295

[33] Rezende T (2022). A new filtering inference procedure for a GED state-space volatility model. Journal of Statistical Planning and Inference, 221, 55–68. https://doi.org/10.1016/j.jspi.2022.02.009

[34] Sahiner M (2022). Forecasting volatility in Asian financial markets: Evidence from recursive and rolling window methods. SN Business & Economics, 2(10), Article 157. https://doi.org/10.1007/s43546-022-00329-9

[35] Shuaibu H (2026). Forecasting Nigerian equity volatility: A comparative assessment of GARCH, EGARCH, and stochastic volatility models. Gusau Journal of Business Administration, 5(1), 355–367. https://doi.org/10.57233/gujoba.v5i1.30

[36] Szczepocki P (2023). Estimation of Yu and Meyer bivariate stochastic volatility model by iterated filtering. Przegląd Statystyczny, 2022(4), 1–19. https://doi.org/10.59139/ps.2022.04.1

[37] Tasi’u M, Umar AA, Abdulaziz U, David RO (2024). Forecasting performance of some GARCH models on holiday-induced volatility in Nigeria Stock Exchange price returns under different error distributions. FUDMA Journal of Sciences, 8(6), 349–353. https://doi.org/10.33003/fjs-2024-0806-3118

[38] Toby A, Austen G (2021). Volatility modelling of stock returns in the petroleum marketing sector of the Nigerian Stock Exchange. American Journal of Finance, 6(1), 71–97. https://doi.org/10.47672/ajf.777

[39] Ugomma CA (2024). Evaluation of stock price volatility of MTN and Airtel in Nigeria stock markets. European Journal of Theoretical and Applied Sciences, 2(2), 692–701. https://doi.org/10.59324/ejtas.2024.2(2).60

[40] Uguru NE, Enwere GM, Amos W (2024). The nexus between exchange rate volatility and Nigerian stock prices: An EGARCH approach. African Journal of Economics and Sustainable Development, 7(1), 56–72. https://doi.org/10.52589/ajesd-atak411m

[41] Wawire AK, Simiyu CN, Laiboni M, Ochenge R (2026). Horizon- and regime-dependent performance of GARCH-type models: Evidence from volatility forecasting in a frontier market. International Journal of Financial Studies, 14(6), Article 148. https://doi.org/10.3390/ijfs14060148

[42] Xu Y, Lien D (2022). Forecasting volatilities of oil and gas assets: A comparison of GAS, GARCH, and EGARCH models. Journal of Forecasting, 41(2), 259–278. https://doi.org/10.1002/for.2812

@article{1724124,
      author = {Ovieneyi Lawrence Egba},
      title = {Modeling Time-Varying Volatility in Nigerian Stock Returns Using a State Space Framework},
      journal = {Iconic Research And Engineering Journals},
      year = {2026},
      volume = {10},
      number = {4},
      pages = {3570-3583},
      issn = {2456-8880},
      url = {https://www.irejournals.com/formatedpaper/1724124.pdf},
      abstract = {This study compared a state-space stochastic-volatility model with GARCH(1,1) and EGARCH(1,1) for daily returns represented at the scale of the Nigerian Exchange All-Share Index. The constructed daily series covered 4 January 2010 to 31 December 2024 and contained 3,912 observations. Models were estimated on 3,129 observations, with 783 held out for chronological one-step-ahead forecast evaluation. The state-space specification represented log variance as a latent autoregressive process and used a Kalman filter with a Gaussian approximation to the log-squared-return observation. GARCH and EGARCH passed the reported residual checks. Among the return-density models, EGARCH had the lower in-sample AIC and GARCH the lower BIC. GARCH recorded the lowest holdout QLIKE loss (1.1071), followed by EGARCH (1.1076) and state-space SV (1.1428). EGARCH had the lowest RMSE (2.4182), while state-space SV had the lowest MAE (1.2813). Diebold-Mariano tests found higher QLIKE loss for state-space SV than for either benchmark; the GARCH-EGARCH difference was not statistically distinguishable. The QLIKE ranking was unchanged under the error-distribution robustness checks. Latent-state flexibility did not produce lower one-step-ahead QLIKE loss in this daily design.},
      keywords = {Nigerian stock returns; volatility forecasting; GARCH; EGARCH; state-space model; stochastic volatility},
      month = {October},
  }