This paper proves the weak efficiency hypothesis when proving the maritingala hypothesis on return differences for the General Index of the Colombian Stock Exchange (IGBC) . A first order conditional dependency structure by using the Autoregressive Fractionally Integrated Moving Averages model ARFIMA, and onsecond order with the Hyperbolical Asymmetric Autoregressive Potential Conditionally Heteroscedastic model, HYAPARCH, which captures all the stylized facts in the empiric research is considered. The results reject the weak efficiency hypothesis when showing that the returns generation process seems to obey to and Autoregressive Fractionally Integrated model ARFI in conditional average anda Hyperbolical Asymmetric Conditionally Heteroscedastic model, HYAGARCH, in conditional variance