The course covers modeling, estimation and inference of non-stationary time series from a state-of-the-art statistical perspective. In particular, we shall deal with fundamental modeling, structural approximation, Gaussian approximation, statistical inference of trends, quantile curves, time-varying spectra and functional data analysis related to non-stationary time series. With the recent advances in various fields, a systematic account of non-stationary time series analysis is needed.
Undergraduate time series analysis at the level of Brock and Davis (2002).
Reference: Brockwell, Peter J., and Richard A. Davis, eds. Introduction to time series and forecasting. New York, NY: Springer New York, 2002.
Zhou, Z. & Wu, W. B. (2009). Local Linear Quantile Estimation for Non-stationary Time Series. The Annals of Statistics, 37 2696-2729.
Zhou, Z. (2013). Heteroscedasticity and Autocorrelation Robust Structural Change Detection. Journal of the American Statistical Association, 108 726-740.
Zhou, Z. (2014) Inference of Weighted V-statistics for Non-stationary Time Series and Its Applications. The Annals of Statistics 42 87-114.
Ding, X. and Zhou, Z. (2021) Auto-Regressive Approximations to Non-stationary Time Series, with Inference and Applications. https://arxiv.org/abs/2112.00693
Target Audience: Graduate students
Teaching Language: English