Text

theses

This dissertation studies several topics in time series modeling. The discussion on seasonal time series, compositional time series and spatial-temporal time series brings new insight to the existing methods. Innovative methodologies are developed for modeling and forecasting purposes. These topics are not isolated but to naturally support each other under rigorous discussions. A variety of real examples are presented from economics, social science and geoscience areas. The second chapter introduces a new class of seasonal time series models, treating the seasonality as a stable composition through time. With the objective of forecasting the sum of the next $ell$ observations, the concept of rolling season is adopted and a structure of rolling conditional distribution is formulated under the compositional time series framework. The probabilistic properties, the estimation and prediction, and the forecasting performance of the model are studied and demonstrated with simulation and real examples. The third chapter focuses on the discussion of compositional time series theories in multivariate models. It provides an idea to the modeling procedure of the multivariate time series that has sum constraints at each time. It also proposes a joint MLE method for threshold vector-error correction models. This chapter interprets the methodologies with an real example of the U.S. household consumption expenditures data. Threshold cointegration effects are analyzed on the U.S. real GDP growth rate. The estimation of TVECM is compared by the current two-step estimation method and the proposed joint MLE approach. Sensor allocation problem is studied in Chapter 4 under spatial-temporal models in Gaussian random fields. Given observations from existing sensors, the problem is solved by minimizing the integrated conditional variance based on different forecasting purposes. In this chapter, the time series are measured at different locations with both spatial and time series correlations. The spatial-temporal covariance structure is extensively discussed under both separable and nonseparable cases. The model is finally applied to the ozone level measurements in Harris County, Texas.

ETD_6711

Ph.D.

Includes bibliographical references

by Kun Chang

doi:10.7282/T3833V03

ETD doctoral

The author owns the copyright to this work.