Change-point detection algorithms in autoregressive process
The change-point detection method is helpful in autoregressive time series modeling. The instability in the underlying model parameters may affect the forecasting accuracy and lead to biased data analysis. This thesis is trying to answer two questions: (a) whether the given correlated time series data is generated from a stationary stochastic process or different processes; (b) if the time series sequence is generated from different mechanisms, where are the starting points of each new mechanism. We have developed three algorithms to seek the solution, which can be categorized into two groups: the global segmentation group, including CE.AR algorithm and local segmentation group, including MCP2 method (Multiple Comparisons Procedure for Multiple Change Point) and HarmonicCPT algorithm. In Chapter 3, we develop the CE.AR method to estimate the unknown number and the locations of change-points in autoregressive time series. In order to find the optimal value of a performance function based on the Minimum Description Length principle, we modified the Cross-Entropy algorithm for the combinatorial optimization problem. Our numerical experiments show that the proposed approach is very efficient in detecting multiple change-points when the underlying process has moderate to substantial variations in the mean and the autocorrelation coefficient. However, due to the heavy computational cost, CE.AR method is not suitable for long sequence time series data. Therefore, we move to the approximate segmentation direction and develop the MCP2 method, which can be found in Chapter 4. The first step is to use a likelihood ratio scan based estimation technique to identify the potential change points to segment the time series. Next, modified parametric spectral discrimination tests are used to validate the proposed segments. The numerical study shows that our method performs not very well under stationary AR(1) scenarios. Therefore, in order to further improve the detection power, we shift our focus on testing if there is no change point in the sequence. Hence, in Chapter 5, we introduced the Harmonic mean p-value technique to combine all the p-values. The numerical study is conducted to demonstrate the performance of the proposed method across various scenarios and compared with other methods. The review of previous research on non-stationary time series segmentation methods is provided at the beginning, in Chapter 2.