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Vine copula base modelling and forecasting of multivariate realized volatility time-series

多元已实现波动率时间序列的 Vine copula 基础建模和预测

基本信息

批准号：
263890942
负责人：
Professorin Dr. Claudia Czado
金额：
--
依托单位：
Lehrstuhl für Statistik
依托单位国家：
德国
项目类别：
Research Grants
财政年份：
2015
资助国家：
德国
起止时间：
2014-12-31 至 2020-12-31
项目状态：
已结题

来源：
https://gepris.dfg.de/gepris/projekt/263890942?language=en
关键词：
Vine copula base modelling forecasting

项目摘要

Reliable forecasts of stock market volatility are necessary in portfolio management and the evaluation of risks. Due to the increasing availability of high-frequency data, the use of squared returns to estimate the ex-post realized volatility (RV) has become one of the standard methods in empirical finance.Within the project we will tackle both the modeling approaches for univariate times series of realized variances and for matrix variate time series of realized covariance matrices. The currently most popular univariate model for realized volatility modeling is the HAR regression. The performance of the model is convincing, but the choice of the explanatory factors (measured at daily frequency) in the model is merely heuristic. Within the first part of the project we addressed the nonlinear modeling of temporal dependence of the factors. In the second phase of the project we will concentrate on statistical approaches such as principle component analysis, factor analysis and neural networks, which will help us to determine the optimal aggregation of historical data for factor building. Similar problem remains if we consider the initial intraday information. The realized volatilities are estimated in the simplest case using the sum of squared intra-day returns. It is of key interest to address the proper aggregation and transformation of intra-day returns too.The method we advocated for the realized covariance matrices in the first phase of the project was based on partial correlations. It shows good performance, but we would like to improve further its performance and ensure more robust forecasts. For this we want to investigate a new selection method which chooses the subset of standard and partial correlations, which form the partial correlation vine, based on the forecasting performance of the marginal models associated to the univariate partial correlation time-series. We expect that this way of proceeding will lead to an improved forecasting performance. So far we have not considered model sparsity of the partial correlation vines. In general, model sparsity in a vine copula model can be achieved by setting certain pair-copulas to the independence copula. This corresponds to a partial correlation value of zero in a partial correlation vine. So-called truncated vines set all pair-copulas of trees above a certain level to the independence copula. We will study several choices of setting this truncation level.

对股票市场波动的可靠预测在投资组合管理和风险评估中是必要的。随着高频数据的日益增多，使用收益率平方估计事后已实现波动率（RV）已成为实证金融学的标准方法之一。在本项目中，我们将讨论已实现方差的单变量时间序列和已实现协方差矩阵的矩阵变量时间序列的建模方法。目前最流行的已实现波动率建模的单变量模型是HAR回归。该模型的性能是令人信服的，但模型中的解释因子（以每日频率测量）的选择仅仅是启发性的。在该项目的第一部分，我们解决了时间依赖的因素的非线性建模。在该项目的第二阶段，我们将集中于统计方法，如主成分分析，因子分析和神经网络，这将有助于我们确定最佳的历史数据的汇总因素建设。如果我们考虑最初的日内信息，类似的问题仍然存在。在最简单的情况下，使用日内收益率的平方和来估计已实现的波动率。对日内收益进行适当的聚合和转换也是一个关键的问题。我们在项目的第一阶段提出的实现协方差矩阵的方法是基于偏相关的。它显示出良好的性能，但我们希望进一步提高其性能，并确保更可靠的预测。为此，我们要研究一种新的选择方法，选择的标准和偏相关的子集，形成偏相关藤，基于与单变量偏相关时间序列的边际模型的预测性能。我们希望这种方法能够提高预测性能。到目前为止，我们还没有考虑模型稀疏的偏相关葡萄树。一般来说，葡萄树copula模型的稀疏性可以通过将某些对copula设置为独立copula来实现。这对应于部分相关曲线中的零部分相关值。所谓的截断葡萄树将一定水平以上的树的所有对copula设置为独立copula。我们将研究设置此截断水平的几种选择。