Bayesian Hierarchical Models and Moment Bounds for High-Dimensional Time Series
In this dissertation, I explore two statistical tasks involving high-dimensional time series.The first task is to forecast high-dimensional time series using Bayesian hierarchical models (BHM). The data under modeling is related to smoking epidemic and human mortality measures obtained from multiple populations around the world. I propose a BHM for estimating and forecasting the all-age smoking attributable fraction (ASAF), which serves as a summarizing statistical measure of the effect of smoking on mortality. The projected ASAF is used to forecast the dynamics of the between-gender gap of life expectancy at birth. In addition, I propose a general framework to incorporate smoking-related information into life expectancy at birth forecast. The framework includes forecasting an age-specific smoking attributable fraction (ASSAF), a non-smoking life expectancy at birth, and a male-female life expectancy gap. Assessed by out-of-sample validation, the new framework improves forecast accuracy and calibration compared with other commonly considered methods for mortality forecasts. The second task is to obtain expectation bounds for the deviation of large sample auto-covariance matrices from their means under weak data dependence. While the accuracy of covariance matrix estimation corresponding to independent data has been well understood, much less is known in the case of dependent data. We make a step towards filling this gap, and establish deviation bounds that depend only on the parameters controlling the ”intrinsic dimension” of the data up to some logarithmic terms. Our results have immediate impacts on high dimensional time series analysis, and we apply them to the high dimensional linear VAR(d) model, the vector-valued ARCH model, and a model used in Banna et al. (2016).
- Statistics