Regularization for High-dimensional Time Series Models
Yan Yi Sun · OhioLink ETD Center (Ohio Library and Information Network) · 2011
Analyzing multivariate time series has been a very important topic in economics, finance, engineering, social and natural sciences.Compared to univariate models, the multivariate models better represent the dynamics and correlations of the component series.Many popular univariate models such as autoregressive conditional heteroscedasticity (ARCH), generalized ARCH (GARCH), and capital asset pricing model (CAPM), are all under investigations for the extension to their multivariate counterparts.However, when increasing the data dimension, the number of parameters in the multivariate model easily explodes.This brings in various issues such as unsatisfactory estimation efficiency, heavy computational burden, and poor model interpretability, and becomes the bottleneck of high-dimensional time series analysis.In an attempt to address the problem, this dissertation studies a regularization technique for high-dimensional time series by penalty, which simultaneously performs variable selection and parameter estimation.The idea of regularization, including the shrinkage type of estimators, has a long history in statistics.Recent emergence of a large amount of high-dimensional data My deepest gratitude goes to my advisor Dr James Deddens.I feel extremely fortunate to have an advisor who gave me the freedom and support to do the research I like, and meanwhile was always there to listen and help when I faltered.He was the one to criticize me the most severely when I underperformed.He was also the one to give me the warmest praise when I excelled.I would like to thank Dr Xiaodong Lin for introducing me to this promising and fruitful research area.His helpful comments to revise our joint paper are much appreciated.