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In many branches of science relevant observations are taken sequentially over time. Bayesian Analysis of Time Series discusses how to use models that explain the probabilistic characteristics of these time series and then utilizes the Bayesian approach to make inferences about their parameters. This is done by taking the prior information and via Bayes theorem implementing Bayesian inferences of estimation, testing hypotheses, and prediction. The methods are demonstrated using both R and WinBUGS. The R package is primarily used to generate observations from a given time series model, while the WinBUGS packages allows one to perform a posterior analysis that provides a way to determine the characteristic of the posterior distribution of the unknown parameters.

Features

Presents a comprehensive introduction to the Bayesian analysis of time series.
Gives many examples over a wide variety of fields including biology, agriculture, business, economics, sociology, and astronomy.
Contains numerous exercises at the end of each chapter many of which use R and WinBUGS.
Can be used in graduate courses in statistics and biostatistics, but is also appropriate for researchers, practitioners and consulting statisticians.
About the author

Lyle D. Broemeling, Ph.D., is Director of Broemeling and Associates Inc., and is a consulting biostatistician. He has been involved with academic health science centers for about 20 years and has taught and been a consultant at the University of Texas Medical Branch in Galveston, The University of Texas MD Anderson Cancer Center and the University of Texas School of Public Health. His main interest is in developing Bayesian methods for use in medical and biological problems and in authoring textbooks in statistics. His previous books for Chapman & Hall/CRC include Bayesian Biostatistics and Diagnostic Medicine, and Bayesian Methods for Agreement.



Table of Contents
Table of Contents

1. Introduction to the Bayesian Analysis of Time Series
Introduction
Bayesian Analysis
Fundamentals of Time Series Analysis
Basic Random Models
Time Series and Regression
Time Series and Stationarity
Time Series and Spectral Analysis
Dynamic Linear Model
The Shift Point Problem
Residuals and Diagnostic Tests
References


2. Bayesian Analysis
Introduction
Bayes' Theorem
Prior Information
The Binomial Distribution
The Normal Distribution
Posterior Information
The Binomial Distribution
The Normal Distribution
The Poisson Distribution
Inference
Introduction
Estimation
Testing Hypotheses
Predictive Inference
Introduction
The Binomial Population
Forecasting from a Normal Population
Checking Model Assumptions
Introduction
Forecasting from an Exponential, but Assuming a Normal Population
A Poisson Population
The Wiener Process
Testing the Multinomial Assumption
Computing
Introduction
Monte Carlo Markov Chains
Introduction
The Metropolis Algorithm
Gibbs Sampling
The Common Mean of Normal Populations
An Example
Comments and Conclusions
Exercises
References

3. Preliminary Considerations for Time Series
Time Series
Airline Passenger Bookings
Sunspot Data
Los Angeles Annual Rainfall
Graphical Techniques
Plot of Air Passenger Bookings
Sunspot Data
Graph of Los Angeles Rainfall Data
Trends, Seasonality, and Trajectories
Decomposition
Decompose Air Passenger Bookings
Average Monthly Temperatures for Debuque, Iowa
Graph of Los Angeles Rainfall Data
Mean, Variance, Correlation and General Sample Characteristic of a Time Series
Other Fundamental Considerations
Summary and Conclusions
Exercises
References

4. Basic Random Models
Introduction
White Noise
A Random Walk
Another Example
Goodness of Fit
Predictive Distributions
Comments and Conclusions
Exercises
References

5. Time Series and Regression
Introduction
Linear Models
Linear Regression with Seasonal Effects and Autoregressive Models
Bayesian Inference for a Non-Linear Trend in Time Series
Nonlinear Trend with Seasonal Effects
Regression with AR(2) Errors
Simple Linear Regression Model
Nonlinear Regression with Seasonal Effects
Comments and Conclusions
Exercises
References

6. Time Series and Stationarity
Moving Average Models
Regression Models with Moving Average Errors
Regression Model with MA Errors and Seasonal Effects
Autoregressive Moving Average Models
Another Approach for the Bayesian analysis of MA Processes
Second Order Moving Average Process
Quadratic Regression With MA(2) Residuals
Regression Model With MA(2) Errors and Seasonal Effects
Forecasting with Moving Average Processes
Another Example
Testing Hypotheses
Forecasting with a Moving Average Time Series
Exercises
References

7. Time Series and Spectral Analysis
Introduction
The Fundamentals
Unit of Measurement of Frequency
The Spectrum
Examples
Bayesian Spectral Analysis of Autoregressive Moving Average Series
MA(1) Process
MA(2) Series
The AR(1) Time Series
AR(2)
ARMA(1,1) Time Series
Sunspot Cycle
Comments and Conclusions
Exercises
References

8. Dynamic Linear Models
Introduction
Discrete Time Linear Dynamic Systems
Estimation of the States
Filtering
Smoothing
Prediction
The Control problem
Example
The Kalman Filter
The Control Problem
Adaptive Estimation
An Example of Adaptive Estimation
Testing Hypotheses
Summary
Exercises
References

9. The Shift Point Problem in Time Series
Introduction
A Shifting Normal Sequence
Structural Change in an Autoregressive Time Series
One Shift in a MA(1) Time Series
Changing Models in Econometrics
Regression Model with Autocorrelated Errors
Another Example of Structural Change
Testing Hypotheses
Analyzing Threshold Autoregression with the Bayesian Approach
A Numerical Example of Threshold Autoregression
Comments and Conclusions
Exercises
References

10. Residuals and Diagnostic Tests
Introduction
Diagnostic Checks for Autoregressive Models
Residuals for Model of Color Data
Residuals and Diagnostic Checks for Regression Models with AR(1) Errors
Diagnostic Tests for Regression Models with Moving Average Time Series
Comments and Conclusions
Exercises
References