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: