Flexible Cholesky GARCH model with time dependent coefficients

TL;DR

This paper introduces a stochastic, time-dependent coefficient extension to the Cholesky GARCH model, improving the estimation of high-dimensional covariance matrices in multivariate time series.

Contribution

It proposes a novel stochastic structure for dependency components in Cholesky GARCH using state-space modeling and Kalman filtering, enhancing model flexibility and accuracy.

Findings

Lower MSE compared to other models

Better performance based on MAE and MSE

Effective in high-dimensional dependence modeling

Abstract

Study of instantaneous dependence among several variable is important in many of the high-dimensional sciences. Multivariate GARCH models are as a standard approach for modelling time-varying covariance matrix such phenomena. Cholesky GARCH is one of these approaches where the time-varying covariance matrix can be written parsimoniously, containing variance components through a diagonal matrix and dependency components through a unit lower triangular matrix with regression coefficients as entries. In this paper, we proposed a stochastic structure for dependency components in Cholesky GARCH model by considering linear regression model as a state-space model and using kalman filtering for estimating regression coefficients. We find that the MSE of stochastic Cholesky GARCH model is smaller than the MSE of other models also show that the stochastic Cholesky GARCH has better performance in compare to another models based on MAE and MSE criterions for the real data.