Hybrid change point detection for time series via support vector regression and CUSUM method

Abstract

This study considers the change point testing problem regarding time series based on the location and scale-based cumulative sum (LSCUSUM) test constructed with the residuals obtained from support vector regression (SVR)-autoregressive moving average (ARMA) models. For this, we first estimate the model parameters in SVR–ARMA models from a training time series sample, in which a long AR model is fitted to the data to obtain residuals. We then use these as initial values of the error terms in SVR–ARMA (p,q) models and obtain the forecasting values recursively until the updated error terms converge to a certain limit. Finally, we select an optimal order of p,q with the root mean square error (RMSE) and use the forecasting errors from this selected model as the residuals for constructing the LSCUSUM test. Monte Carlo simulations are performed to evaluate the validity of the test. A real data example is provided for illustration.