This research project aims to advance the development of statistical methodology and theory for analyzing nonstationary time series. A nonstationary time series is a sequence of data points collected at successive time points with certain aspects changing over time or being nonstationary. Nonstationary time series appear very frequently in various scientific fields including economics, engineering, environmental science, finance, and medical science among others. Ignoring nonstationarity and dependence, two important features of nonstationary time series, can lead to erroneous conclusions. Therefore, the research project is expected to promote scientific research in not only statistics but also other disciplines that involve the analysis of nonstationary time series.
In order to capture the temporal dynamics resulting from the nonstationarity, the parameters are allowed to change over time and modeled as deterministic but unknown functions of time, which are intrinsically infinite dimensional. To avoid potential misspecifications of parametric models, nonparametric methods are used to estimate and make inference about the underlying parameter functions. The research to be performed involves parameter estimation, hypothesis testing, and variable selection for regression models with time-varying parameters. By allowing a general class of nonstationary and dependent processes, the methods to be developed and the asymptotic results to be established can be widely applicable, and we are able to understand and quantify the effect of nonstationarity and dependence on the asymptotic behavior of parameter estimators and test statistics of interest.
