  In this paper, we address the problem of probabilistic forecasting using an
adaptive volatility method rooted in classical time-varying volatility models
and leveraging online stochastic optimization algorithms. These principles were
successfully applied in the M6 forecasting competition under the team named
AdaGaussMC. Our approach takes a unique path by embracing the Efficient Market
Hypothesis (EMH) instead of trying to beat the market directly. We focus on
evaluating the efficient market, emphasizing the importance of online
forecasting in adapting to the dynamic nature of financial markets. The three
key points of our approach are: (a) apply the univariate time-varying
volatility model AdaVol, (b) obtain probabilistic forecasts of future returns,
and (c) optimize the competition metrics using stochastic gradient-based
algorithms. We contend that the simplicity of our approach contributes to its
robustness and consistency. Remarkably, our performance in the M6 competition
resulted in an overall 7th ranking, with a noteworthy 5th position in the
forecasting task. This achievement, considering the perceived simplicity of our
approach, underscores the efficacy of our adaptive volatility method in the
realm of probabilistic forecasting.
