STAT 510: Applied Time Series Analysis

Overview

Time series data are intriguing yet complicated information to work with. While this course will provide students with a basic understanding of the nature and basic processes used to analyze such data, you will quickly realize that this is a small first step in being able to confidently understand what trends might exist within a set of data and the complexities of being able to use this information to make predictions or forecasts. Yet, whether it is financial, medical or weather related, this type of data is quite frequently found in much of our daily lives.

Syllabus

The objective of this course is to learn and apply statistical methods for the analysis of data that have been observed over time. Our challenge in this course is to account for the correlation between measurements that are close in time. Topics covered in this course include methods for:

Modeling univariate time series data with Autoregressive and Moving Average Models (denoted as ARIMA models, sometimes called Box Jenkins models).
Tools for model identification, model estimation, and assessment of the suitability of the model.
Using a model for forecasting and determining prediction intervals for forecasts.
Smoothing methods and trend/seasonal decomposition methods. Smoothing methods include moving averages, exponential smoothing, and Lowess smoothers.
Relationships between time series variables, cross correlation, lagged regression models
Intervention Analysis (basically before/after analysis of a time series to assess effect of a new policy, treatment, etc.)
Longitudinal Analysis and Repeated Measures Models for comparing treatments when the response is a time series.
Vector Autoregressive Models for Multivariate Time Series
ARCH Models for changing variation and periods of volatility in a series
Analyzing the frequency domain - Periodograms, Spectral Density, Identifying the important periodic components of a series.

We will need to use a statistical software program to analyze time series data. The course assignments and notes include R code to analyze our data. If you are unfamiliar with R (or need to brush up), please take some time to follow through the following introduction:

Introduction to R