# Estimation of multivariate asymmetric power GARCH models

## TL;DR

This paper introduces a new class of multivariate asymmetric power GARCH models that incorporate leverage effects, providing conditions for stationarity, asymptotic properties of estimators, and practical applications to financial data.

## Contribution

It proposes a flexible multivariate asymmetric power GARCH model with explicit stationarity conditions and derives the asymptotic behavior of estimators, enhancing financial time series modeling.

## Key findings

- Model includes various GARCH forms relevant to finance
- Explicit stationarity conditions derived
- Estimator properties confirmed through simulations and real data

## Abstract

It is now widely accepted that volatility models have to incorporate the so-called leverage effect in order to to model the dynamics of daily financial returns.We suggest a new class of multivariate power transformed asymmetric models. It includes several functional forms of multivariate GARCH models which are of great interest in financial modeling and time series literature. We provide an explicit necessary and sufficient condition to establish the strict stationarity of the model. We derive the asymptotic properties of the quasi-maximum likelihood estimator of the parameters. These properties are established both when the power of the transformation is known or is unknown. The asymptotic results are illustrated by Monte Carlo experiments. An application to real financial data is also proposed.