# Bayesian Inference on QGARCH Model Using the Adaptive Construction Scheme

## TL;DR

This paper demonstrates that the adaptive construction scheme significantly improves Bayesian inference efficiency for the QGARCH model, effectively capturing asymmetry in time series data.

## Contribution

It introduces an adaptive proposal density method for Bayesian inference on the QGARCH model, enhancing sampling efficiency and accuracy.

## Key findings

- Effective sampling of QGARCH parameters with minimal correlations
- Adaptive scheme outperforms traditional methods in Bayesian estimation
- Demonstrated on artificial QGARCH data

## Abstract

We study the performance of the adaptive construction scheme for a Bayesian inference on the Quadratic GARCH model which introduces the asymmetry in time series dynamics. In the adaptive construction scheme a proposal density in the Metropolis-Hastings algorithm is constructed adaptively by changing the parameters of the density to fit the posterior density. Using artificial QGARCH data we infer the QGARCH parameters by applying the adaptive construction scheme to the Bayesian inference of QGARCH model. We find that the adaptive construction scheme samples QGARCH parameters effectively, i.e. correlations between the sampled data are very small. We conclude that the adaptive construction scheme is an efficient method to the Bayesian estimation of the QGARCH model.