Bayesian Statistics: Time Series Analysis

This module defines stationary time series processes, the autocorrelation function and the autoregressive process of order one or AR(1). Parameter estimation via maximum likelihood and Bayesian inference in the AR(1) are also discussed.

This module extends the concepts learned in Week 1 about the AR(1) process to the general case of the AR(p). Maximum likelihood estimation and Bayesian posterior inference in the AR(p) are discussed.

Normal Dynamic Linear Models (NDLMs) are defined and illustrated in this module using several examples. Model building based on the forecast function via the superposition principle is explained. Methods for Bayesian filtering, smoothing and forecasting for NDLMs in the case of known observational variances and known system covariance matrices are discussed and illustrated.

This module covers Fourier representation, building NDLMs with multiple components, filtering, smoothing and forecasting with unknown observational variance, and system covariance matrix specification via discount factors.

In this final project you will use normal dynamic linear models to analyze a time series dataset downloaded from Google trend.