  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.
