Time variation in market efficiency: Empirical evidence from B3 sectoral indices (2016-2024)
Published:
Mar 6, 2026
Volume:
24
Keywords:
Market efficiency
Long memory
Fractional integration
Volatility
B3
Abstract
This study investigates the time-varying degree of (in)efficiency in the Brazilian stock market by analyzing long-range dependence in the returns and volatilities of seven B3 sectoral indices from January 2016 to July 2024. The semiparametric Geweke and Porter-Hudak (GPH) estimator of the fractional integration parameter is employed, combined with rolling window procedures and Bai-Perron structural break tests. The results show that returns predominantly exhibit short memory behavior, consistent with the weak form of the Efficient Market Hypothesis. In contrast, volatilities display temporary long memory during the peak of the COVID-19 pandemic, followed by a gradual reduction in persistence. The findings are consistent with the Fractal Market Hypothesis and the Adaptive Market Hypothesis, suggesting that systemic shocks temporarily affect market efficiency dynamics without generating permanent structural changes.
How to cite
Eduardo Ataide dos Santos, Edson Zambon Monte. Time variation in market efficiency: Empirical evidence from B3 sectoral indices (2016-2024). Brazilian Review of Finance, v. 24, n. 1, 2026. p. e202603. DOI: 10.12660/rbfin.v24n1.2026.97549.
References
BAI, J., & PERRON, P. (1998). Estimating and testing linear models with multiple structural changes. Econometrica, 66(1), 47–78. https://doi.org/10.2307/2998540
BAI, J., & PERRON, P. (2003). Computation and analysis of multiple structural change models. Journal of Applied Econometrics, 18(1), 1–22. https://doi.org/10.1002/jae.659
BAILLIE, R. T., BOLLERSLEV, T., & MIKKELSEN, H. O. (1996). Fractionally integrated generalized autoregressive conditional heteroskedasticity. Journal of Econometrics, 74(1), 3–30. https://doi.org/10.1016/S0304-4076(95)01749-6
BHATTACHARYA, S. N., et al. (2018). Long memory in stock returns and volatility: Evidence from emerging markets. Journal of International Financial Markets, Institutions and Money, 53, 215–234. https://doi.org/10.1016/j.intfin.2017.12.005
CAJUEIRO, D. O., & TABAK, B. M. (2004). The Hurst exponent over time: Testing the assertion that emerging markets are becoming more efficient. Physica A, 336(3–4), 521–537. https://doi.org/10.1016/j.physa.2004.01.031
CAVALCANTE, J., & ASSAF NETO, A. (2004). Long-range dependence in the Brazilian stock market. Emerging Markets Finance and Trade, 40(2), 54–60. https://doi.org/10.1080/1540496X.2004.11052564
CHARFEDDINE, L., & KHEDIRI, K. B. (2016). Time varying market efficiency of the GCC stock markets. Physica A, 444, 487–504. https://doi.org/10.1016/j.physa.2015.09.038
COMTE, F., & RENAULT, E. (1998). Long memory in continuous-time stochastic volatility models. Mathematical Finance, 8(4), 291–323. https://doi.org/10.1111/1467-9965.00057
COSTA, A. C., & VASCONCELOS, G. F. R. (2003). Dependência de longo prazo no mercado acionário brasileiro. Revista Brasileira de Economia, 57(3), 447–466. https://doi.org/10.1590/S0034-71402003000300002
FAMA, E. F. (1970). Efficient capital markets: A review of theory and empirical work. The Journal of Finance, 25(2), 383–417. https://doi.org/10.2307/2325486
FAMA, E. F. (1991). Efficient capital markets: II. The Journal of Finance, 46(5), 1575–1617. https://doi.org/10.2307/2328565
GEWEKE, J., & PORTER-HUDAK, S. (1983). The estimation and application of long memory time series models. Journal of Time Series Analysis, 4(4), 221–238. https://doi.org/10.1111/j.1467-9892.1983.tb00371.x
GIL-ALANA, L. A., & CLAUDIO-QUIROGA, G. (2020). The COVID-19 impact on the Asian stock markets. Asian Economics Letters, 1(2). https://doi.org/10.46557/001c.17656
HENRY, O. T. (2002). Long memory in stock returns: Some international evidence. Applied Financial Economics, 12(10), 725–729. https://doi.org/10.1080/09603100010025733
HULL, M., & McGROARTY, F. (2014). Do emerging markets become more efficient as they develop? Long memory persistence in equity indices. Emerging Markets Review, 18, 45–61. https://doi.org/10.1016/j.ememar.2013.11.001
KAHNEMAN, D., & TVERSKY, A. (1979). Prospect theory: An analysis of decision under risk. Econometrica, 47(2), 263–291. https://doi.org/10.2307/1914185
LAHMIRI, S., & BEKIROS, S. (2020). The impact of COVID-19 pandemic upon stability and sequential irregularity of equity and cryptocurrency markets. Chaos, Solitons & Fractals, 138. https://doi.org/10.1016/j.chaos.2020.109936
LO, A. W. (2004). The adaptive markets hypothesis. The Journal of Portfolio Management, 30(5), 15–29. https://doi.org/10.3905/jpm.2004.442611
LO, A. W. (2005). Reconciling efficient markets with behavioral finance: The adaptive markets hypothesis. Journal of Investment Consulting, 7(2), 21–44. Available at SSRN: https://ssrn.com/abstract=1702447
MACIEL, L. S. (2023). Brazilian stock-market efficiency before and after COVID-19: The roles of fractality and predictability. Global Finance Journal, 58, 100887. https://doi.org/10.1016/j.gfj.2022.100887
MALKIEL, B. G. (2003). The efficient market hypothesis and its critics. Journal of Economic Perspectives, 17(1), 59–82. https://doi.org/10.1257/089533003321164958
MANDELBROT, B. (1963). The variation of certain speculative prices. The Journal of Business, 36(4), 394–419. https://doi.org/10.1086/294632
MONTE, E. Z. (2023). A long-memory analysis for the CBOE Brazil ETF volatility index. International Journal of Emerging Markets, 18(11), 5155–5171. https://doi.org/10.1108/IJOEM-03-2021-0352
MÜLLER, U. A., et al. (1993). Fractals and intrinsic time: A challenge to econometricians. In Proceedings of the XXXIXth International AEA Conference on Real Time Econometrics. European Communities.
PETERS, E. E. (1994). Fractal market analysis: Applying chaos theory to investment and economics. John Wiley & Sons.
REISEN, V. A., CRIBARI-NETO, F., & JENSEN, M. J. (2003). Long memory inflationary dynamics: The case of Brazil. Studies in Nonlinear Dynamics & Econometrics, 7(3). https://doi.org/10.2202/1558-3708.1183
R CORE TEAM. (2025). R: A language and environment for statistical computing. R Foundation for Statistical Computing. Available at https://www.R-project.org/. Accessed on January 16, 2026.
SHILLER, R. J. (2000). Irrational exuberance. Princeton University Press.
SHIMOTSU, K., & PHILLIPS, P. C. B. (2005). Exact local Whittle estimation of fractional integration. The Annals of Statistics, 33, 1890–1933. https://doi.org/10.1214/009053605000000309
VERA-VALDÉS, J. E. (2021). The COVID-19 pandemic and its effects on the long memory of Latin American stock markets. Chaos, Solitons & Fractals, 142. https://doi.org/10.1016/j.chaos.2020.110377