Xing Liu, supervised by Dr Din-Houn Lau
Key words: time series, iterative weighted least squares, change-point detection
R codes for the UROP project, conducted in summer 2018.
Implementing regression models on streaming data is a popular topic in diverse areas, e.g., finance and structure engineering. This report provides a revision of a number of celebrated online regression and monitoring techniques, which are useful and popular tools for modeling streaming data.
We begin this project by introducing the recursive least-square algorithm, together with the iterative formulae for some important goodness-of-fit measures. We then consider the problem of isolated departures (outliers) by investigating the leverage and the studentized residual. In the second part of the report, we study various change-point detection methods and develop further on the Quandt's test, followed by an analysis of their performance on both synthetic data and a chromosome study. It turns out that this newly proposed modified Quandt's test produces competitive empirical results on both experiments.