Time Series and Spectral Methods for Imputation, Regression, and Environmental Health

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Progress in statistical methods is vital for making sense of an ever-increasing flow of data. Time series are a type of data consisting of repeated observations of a physical phenomena, indexed by a common factor. The proposed research deals with the reconstruction of missing samples in such time series, the estimation of the spectra of them, and the use of both in regression models. The research falls within two distinct statistical areas, both dealing with data: the first in the pre-analysis stage (interpolating raw time series), and the second in the analysis stage (development of models for analysis).The analysis of time series in the natural sciences is a key element in the interpretation of real-world phenomena. These analyses have increasing value and predictive power as the length of the data series increases. Unfortunately, such series are often plagued by missing records. Interpolation allows for the reconstruction of values for missing records, extending the inferential power of the overall series. One prong of the proposed research centres on the development of algorithms and theory for the interpolation of time series. The challenge with such algorithms is the complex nature of real-world time series, and developing models which allow for violations of simplistic assumptions is the primary objective of the research. The proposed research on model development consists of application of time series spectral methods to two problems: the estimation of limited timescale associations in additive models, and the estimation of lagged associations. The first of these is a problem of mixed data, with both predictor and response having elements driven by long-term effects (e.g., mortality records vary annually), but with the inference desired being that of the short-term effects: careful work is required to separate the two. The second of these problems is that of delayed effects, where predictors have time delayed associations with responses. The research proposed develops a novel modelling framework for estimation of these delayed effects, eliminating an identifiability issue of previous solutions.The work proposed here will address these problems relating to time series data, and lead to original research that will further the scientific use of complex time series. The work on time series interpolation will be of value to researchers seeking to analyze long time series, while the work on additive models will be of value to researchers for whom these models are a primary working tool for estimation of timescale-limited associations. A further impact will be to refine and improve the reliability of risk estimation for population health, which ultimately will affect the policies made by our government that pertain to the health of Canadians. Training is a major component of this research program, which will support 1 Phd and 7 MSc graduate students, as well as 8 undergraduate summer research students.