Forecasting multifractal volatility
Forecasting multifractal volatility
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DOI：
10.1016/s0304-4076(01)00069-0
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发表时间：
2001-11-01
影响因子：
6.3
通讯作者：
Fisher, A
中科院分区：
文献类型：
--
作者：
Calvet, L;Fisher, A
本文发展了一种新的连续时间过程--泊松多重分形的分析方法来预测未来收益率的分布。该过程捕捉了许多金融时间序列所表现出的厚尾、波动持续性和矩标度。它可以被解释为一个具有多个频率和马尔可夫潜态的随机波动模型。为了简单起见，我们假设预测者确切地知道真实的生成过程，但只观察过去的收益。在这种环境中的挑战是长内存和相应的无限维的状态空间。我们介绍了一个离散化版本的模型，有一个有限的状态空间和分析解决方案的条件问题。当网格步长为零时，离散化模型弱收敛到连续时间过程，这意味着密度预测的一致性。(C)2001年由Elsevier Science S.A.出版
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 financial 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 infinite dimension of the state space. We introduce a discretized version of the model that has a finite 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. (C) 2001 Published by Elsevier Science S.A.