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We propose a continuous-time Markov-switching generalized autoregressiveconditional heteroskedasticity (COMS-GARCH) process for handling irregularlyspaced time series (TS) with multiple volatilities states. We employ a Gibbssampler in the Bayesian framework to estimate the COMS-GARCH model parameters,the latent state path and volatilities. To improve the inferential robustnessand computational efficiency for obtaining the maximum a posteriori estimatesfor the state path and volatilities, we suggest a multi-path sampling schemeand incorporate the Bernoulli noise injection in the computational algorithm.We provide theoretical justifications for the improved stability and robustnesswith the Bernoulli noise injection through the concept of ensemble learning andthe low sensitivity of the objective function to external perturbation in theTS. We apply the proposed COMS-GARCH process and the computational procedure tosimulated TS, a real currency exchange rate TS, and a real blood volumeamplitude TS. The empirical results demonstrate that the COMS-GARCH process andthe computational procedure are able to predict volatility regimes andvolatilities in a TS with satisfactory accuracy.

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