| Description |
This dissertation aims to develop statistical methods for change point detection in functional time series. Change point problems originally arose from the area of quality control, where one observes the production line and would like to detect the deviations from the acceptable products. Briefly speaking, the change point problem is the detection and estimation of the point at which the statistical properties of a sequence of observations change. It is important to detect such changes in many different areas, such as finance, bioinformatics, and medical images. Functional time series are obtained by splitting a continuous time record, such as stock price, into daily or annual curves. They might exhibit dependencies that invalidate statistical procedures that assume independent and identically distributed observations. Previous research focused primarily on change point detection in functional time series that are homoscedastic. We provide a CUSUM (cumulative sums) type hypothesis testing to check if there exists a change point in the mean structure of the heteroscedastic functional time series. We first prove several limit theorems for the test statistic under the null hypothesis and then explore its asymptotic behavior under the alternative. We apply the new methodology to determine whether there exists change points in the Daily Treasury Yield Curve Rates of the US in 2008, 2012 and 2017. We also provide a CUSUM type estimator for the location of the change in the means of the functional time series at the end of the dissertation. |
