Discretely observed Brownian motion governed by telegraph signal process: Estimation and application to finance

Regime-switching models are commonly used in financial econometrics to capture changes in market dynamics over time. However, classic Markov regime-switching models cannot deal with irregularly spaced time series. To address this limitation, we propose a continuous-time regime-switching model with two states that can handle situations where data points are collected at non-equidistant times. The model employs a Brownian motion with state-specific drift and volatility and a telegraph signal process with exponential holding times to characterize unobserved states. We develop an estimation procedure for the model parameters using the hidden Markov model tools and occupation time results for telegraph signal process. Computationally effective exact likelihood evaluation is achieved with help of a recursive forward algorithm. Our simulation study validates the performance of our method. An analysis of estimates from regular and irregular grids for simulations that utilize trading days and calendar days was also added. In application to a collection of stock prices, we find that our model is competitive with a popular GARCH model.