Change Point Detection in Beta Process with High Frequency Data

High frequency regression has received more and more attention recent years. This is the first paper about detecting the change points in the beta process of high frequency regression. As an intermediate modelling approach between the constant beta and continuous beta process, this paper employs the piecewise constant process to model the time-varying beta, which can ensure both parsimony and flexibility of the high frequency regression model at the same time. By extending the idea of self-normalization to the observations with time-varying covariance structure, we have developed the testing and estimation methodologies for the scenario of single change point in the multivariate beta process. The limiting null distribution and the asymptotic behavior of the power of the single change point test are derived. The convergence rate of the single change point estimate is also established. For the scenario of multiple change points, we have developed a new wild binary segmentation algorithm to detect the multiple change points. A novel data-driven approach is also designed to consistently estimate the number of change points. Monte Carlo simulation and empirical study show the accuracy and efficiency of our proposed methodologies