Semiparametric Inference for Integer-Valued Time Series

点击翻译按钮获取中文摘要

Discrete time series appear in a wide variety of settings. Energy forecasters may wish to understand patterns in the average number of windy days per month over time as a means to predicting wind power. Hydrologists may wish to forecast future river crests based on estimates of average number of rainy days. Public health officials may want to assess whether there is a declining trend in the number of cases of influenza over time after a major medical intervention such as mass immunizations.  One objective of statistical modeling of the dynamics of a time series is to predict future values of the series. Forecasting of river crests based on estimates of mean number of rainy days is an example of the latter objective. Yet another objective is to understand the relationship between typical values of the time series and a set of explanatory variables while adjusting for the dependent nature of the data. Estimating the trend in the average number of cases of a disease after an intervention is an example of the former objective; this approach is known as regression modeling. This research program is primarily concerned with time series regression modeling for discrete data. Usual time series regression modeling problems are studied as well as regression problems pertaining to "big data". When a large number of predictors are collected, not all variables will be fully relevant in explaining the mean counts. I will examine a "big data" technique known as "shrinkage estimation" that incorporates information from variables with partial relevance with a view towards improving prediction power of the regression model. Typical statistical models for count time series data make assumptions about the data generating mechanism giving rise to the data; these assumptions are in practice difficult to verify. In my research program, I relax assumptions about how discrete-valued time series data arise and study the advantages as well as the disadvantages from such a regression modeling approach. I adopt an estimating function theory modeling framework for model parameter estimation as it provides a unifying approach to discrete-valued time series estimation. The estimating function theory framework encompasses many of the statistical models proposed for explaining the dynamics for integer-valued time series. Furthermore, the methodology is easy to implement in contrast to some of the methods that require more stringent assumptions about the data generating mechanism. The findings from this research program will allow researchers to compare and contrast estimates derived from both the less restrictive methodology with that of existing methodology. If the results from both methodologies are very different, then the end users of the methodology will be able to use the results from this research program as an endpoint with confidence in their statistical conclusions.