Abstract
This paper introduces the concept of the realized hierarchical Archimedean copula (rHAC). The proposed approach inherits the ability of the copula to capture the dependencies among financial time series, and combines it with additional information contained in high-frequency data. The considered model does not suffer from the curse of dimensionality, and is able to accurately predict high-dimensional distributions. This flexibility is obtained by using a hierarchical structure in the copula. The time variability of the model is provided by daily forecasts of the realized correlation matrix, which is used to estimate the structure and the parameters of the rHAC. Extensive simulation studies show the validity of the estimator based on this realized correlation matrix, and its performance, in comparison to the benchmark models. The application of the estimator to one-day-ahead Value at Risk (VaR) prediction using high-frequency data exhibits good forecasting properties for a multivariate portfolio.
Highlights
One of the main objectives of quantitative research is the modelling and approximation of multivariate distributions
We show the validity of the clustering estimator (CE) presented in Algorithms 2 and 3 and compare it to the adaptation of the method of Segers and Uyttendaele (2014) (SU) and the approach of Okhrin et al (2013) (OOS) which was improved by Górecki et al (2014) and was implemented in the R package HAC by Okhrin and Ristig (2014)
In order to compare different methods, CE is applied to the Kendall’s correlation matrix and to the linear correlation matrix estimated in the usual manner over the whole sample path that corresponds to the correlation matrices of the daily log-returns
Summary
One of the main objectives of quantitative research is the modelling and approximation of multivariate distributions. Models based on high-frequency data yield superior predictions in comparison to approaches based on daily data. Many researchers have implemented the obtained realized measures to model financial time series. Most of those studies, employ models where the realized correlation matrix directly characterizes the multivariate distribution, see, for example, Bauer and Vorkink (2011), Chiriac and Voev (2011), Jin and Maheu (2012), or address GARCH type models, for example, Hansen et al (2014), Bauwens et al (2012), Noureldin et al (2012), Bollerslev et al (2016)
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