The Markov-Switching Multifractal Model of Asset Returns
资产收益的马尔可夫切换多重分形模型AI 解读 ↓
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资产收益的马尔可夫切换多重分形模型
- 研究问题
- 如何在马尔可夫切换多重分形收益模型中估计连续分布或大量波动成分，并在最大似然计算受限时预测波动率？
- 方法与思路
- 作者提出广义矩估计与线性预测，以绕开最大似然对离散波动成分及成分数量的限制；原则上允许连续分布和任意成分数。
- 材料陈述的贡献
- 摘要称 GMM 在二项与对数正态模型的模拟中表现合理，线性预测相对最优预测的损失较小；增加成分改善部分序列的预测。
- 阅读关注点
- 阅读全文时应核对矩条件、参数识别与估计性质，并查看线性预测的目标、最优预测基准及增加成分带来的计算成本。
- 阅读边界
- 摘要未给出矩条件、样本与预测评估方案；“任意成分数”是原则性适用范围，部分序列的预测改善不能外推为全面优势。
原文摘要
Multifractal processes have recently been proposed as a new formalism for modeling the time series of returns in finance. The major attraction of these processes is their ability to generate various degrees of long memory in different powers of returns—a feature that has been found in virtually all financial data. Initial difficulties stemming from nonstationarity and the combinatorial nature of the original model have been overcome by the introduction of an iterative Markov-switching multifractal model which allows for estimation of its parameters via maximum likelihood (ML) and Bayesian forecasting of volatility. However, applicability of MLE is restricted to cases with a discrete distribution of volatility components. From a practical point of view, ML also becomes computationally unfeasible for large numbers of components even if they are drawn from a discrete distribution. Here we propose an alternative generalized method of moments (GMM) estimator together with linear forecasts which in principle is applicable for any continuous distribution with any number of volatility components. Monte Carlo studies show that GMM performs reasonably well for the popular binomial and lognormal models and that the loss incurred with linear compared to optimal forecasts is small. Extending the number of volatility components beyond what is feasible with MLE leads to gains in forecasting accuracy for some time series.