Forecasting multifractal volatility
为泊松多重分形过程开发了预测未来收益分布的解析方法，该过程能捕捉金融时间序列的厚尾、波动持续性和矩缩放特征，适用于需要密度预测的实证研究。
This paper develops analytical methods to forecast the distribution of future returns for a new continuous-time process, the Poisson multifractal. The process captures the thick tails, volatility persistence, and moment scaling exhibited by many nancial time series. It can be interpreted as a stochastic volatility model with multiple frequencies and a Markov latent state. We assume for simplicity that the forecaster knows the true generating process with certainty but only observes past returns. The challenge in this environment is long memory and the corresponding innite dimension of the state space. We introduce a discretized version of the model that has a nite state space and an analytical solution to the conditioning problem. As the grid step size goes to zero, the discretized model weakly converges to the continuous-time process, implying the consistency of the density forecasts. JEL Classication: C22; C53; F31 Keywords: Forecasting; Long memory; Multiple frequencies; Stoch...