# Continuous-time Markov-switching GARCH Process with Robust and Efficient State Path and Volatility Estimation

## TL;DR

This paper introduces a robust Bayesian method for estimating a continuous-time Markov-switching GARCH model, effectively handling irregular data and multiple volatility states, with applications to finance and biomedical signals.

## Contribution

It develops a novel COMS-GARCH model with a multi-path sampling scheme and Bernoulli noise injection for improved robustness and efficiency in state and volatility estimation.

## Key findings

- Accurately predicts volatility regimes in simulated data.
- Demonstrates effective application to real currency exchange rate data.
- Shows robustness and efficiency improvements through Bernoulli noise injection.

## Abstract

We propose a continuous-time Markov-switching generalized autoregressive conditional heteroskedasticity (COMS-GARCH) process for handling irregularly spaced time series (TS) with multiple volatilities states. We employ a Gibbs sampler in the Bayesian framework to estimate the COMS-GARCH model parameters, the latent state path and volatilities. To improve the inferential robustness and computational efficiency for obtaining the maximum a posteriori estimates for the state path and volatilities, we suggest a multi-path sampling scheme and incorporate the Bernoulli noise injection in the computational algorithm. We provide theoretical justifications for the improved stability and robustness with the Bernoulli noise injection through the concept of ensemble learning and the low sensitivity of the objective function to external perturbation in the TS. We apply the proposed COMS-GARCH process and the computational procedure to simulated TS, a real currency exchange rate TS, and a real blood volume amplitude TS. The empirical results demonstrate that the COMS-GARCH process and the computational procedure are able to predict volatility regimes and volatilities in a TS with satisfactory accuracy.