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 erence 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 R>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 Li.