Endogenous Markov Switching Regression Models for High-Frequency Data Under Microstructure Noise

We present a novel method in analyzing microstructure noise of high-frequency data as a measurement error problem within an endogenous Markov-switching regression model. In this model, the regression disturbance and the latent state variable controlling the regime are correlated. We show that under endogeneity the popular realized variance estimator is biased and no longer converges to the integrated regime dependent volatility. Exploring intraday return data on foreign exchange rates, we find significant endogeneity at high frequencies. Similar to the popular volatility signature plot suggested by Andersen, Bollerslev, Diebold, and Labys (2000b), we propose an endogeneity plot, which indicates as to which sampling frequency the assumption of exogeneity of the state variable controlling the regime remains valid.