Discretely Observed Brownian Motion Goverened byTelegrapher's Process: Estimation and Applications to Finance

Abstract Regime-switching models are commonly used in financial econometrics to capturechanges in market dynamics over time. However, classic Markov regime-switching models cannot handle irregularly spaced time series. To address this limitation,we propose a continuous-time regime-switching model with two states that can handle irregularly spaced time series. The model uses a Brownian motion with state-specific drift and volatility in each state, and a telegrapher's process with exponential holding times to characterize unobserved states. We develop inferences for model parameters using the hidden Markov model with discretely spaced time series, and facilitate exact likelihood evaluation with dynamicprogramming and occupation time results. Our simulation study validates the performance of the method, and in application to a collection of stock prices,we find that our model is competitive with the popular GARCH model.