Fast Converging and Robust Optimal Path Selection in Continuous-time Markov-switching GARCH Model
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We propose CROPS, a fast Converging and Robust Optimal Path Selection algorithm for accurate identification of the underlying path that characterizes the volatility and structural changes in continuous-time and high-frequency time series (TS). We set up the continuous-time Markov-switching generalized autoregressive conditional heteroskedasticity (COMS-GARCH) process, based on which we study the properties and advantages of CROPS in handling irregular spacing and structural changes simultaneously in TS data. We employ the Gibbs sampler in the Bayesian framework to obtain the maximum a posterior estimates for the model parameters and identify the optimal path for the COMS-GARCH process. We incorporate the Bernoulli noise injection technique into the CROPS procedure improve the generalizability of the state path and volatility prediction based on an sequential ensemble of sub-TS data. We also establish the stability in the objective function in the presence of random perturbation in the observed TS. The properties of the CROPS procedure in COMS-GARCH are illustrated through simulation studies and demonstrated in a real currency exchange rate TS data set.
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