Bayesian analysis of time series

Content: Table of Contents1. Introduction to the Bayesian Analysis of Time SeriesIntroductionBayesian AnalysisFundamentals of Time Series AnalysisBasic Random ModelsTime Series and RegressionTime Series and StationarityTime Series and Spectral AnalysisDynamic Linear ModelThe Shift Point ProblemResiduals and Diagnostic TestsReferences2. Bayesian AnalysisIntroductionBayes\' TheoremPrior InformationThe Binomial DistributionThe Normal DistributionPosterior InformationThe Binomial DistributionThe Normal DistributionThe Poisson DistributionInferenceIntroductionEstimationTesting HypothesesPredictive InferenceIntroductionThe Binomial PopulationForecasting from a Normal PopulationChecking Model AssumptionsIntroductionForecasting from an Exponential, but Assuming a Normal PopulationA Poisson PopulationThe Wiener ProcessTesting the Multinomial AssumptionComputingIntroductionMonte Carlo Markov ChainsIntroductionThe Metropolis AlgorithmGibbs SamplingThe Common Mean of Normal PopulationsAn ExampleComments and ConclusionsExercisesReferences3. Preliminary Considerations for Time SeriesTime SeriesAirline Passenger BookingsSunspot DataLos Angeles Annual RainfallGraphical TechniquesPlot of Air Passenger BookingsSunspot DataGraph of Los Angeles Rainfall DataTrends, Seasonality, and TrajectoriesDecompositionDecompose Air Passenger BookingsAverage Monthly Temperatures for Debuque, IowaGraph of Los Angeles Rainfall DataMean, Variance, Correlation and General Sample Characteristic of a Time SeriesOther Fundamental ConsiderationsSummary and ConclusionsExercisesReferences4. Basic Random ModelsIntroductionWhite NoiseA Random WalkAnother ExampleGoodness of FitPredictive DistributionsComments and ConclusionsExercisesReferences5. Time Series and RegressionIntroductionLinear ModelsLinear Regression with Seasonal Effects and Autoregressive ModelsBayesian Inference for a Non-Linear Trend in Time SeriesNonlinear Trend with Seasonal EffectsRegression with AR(2) ErrorsSimple Linear Regression ModelNonlinear Regression with Seasonal EffectsComments and ConclusionsExercisesReferences6. Time Series and StationarityMoving Average ModelsRegression Models with Moving Average ErrorsRegression Model with MA Errors and Seasonal EffectsAutoregressive Moving Average ModelsAnother Approach for the Bayesian analysis of MA ProcessesSecond Order Moving Average ProcessQuadratic Regression With MA(2) ResidualsRegression Model With MA(2) Errors and Seasonal EffectsForecasting with Moving Average ProcessesAnother ExampleTesting HypothesesForecasting with a Moving Average Time SeriesExercisesReferences7. Time Series and Spectral AnalysisIntroductionThe FundamentalsUnit of Measurement of Frequency The SpectrumExamplesBayesian Spectral Analysis of Autoregressive Moving Average SeriesMA(1) ProcessMA(2) SeriesThe AR(1) Time SeriesAR(2)ARMA(1,1) Time SeriesSunspot CycleComments and ConclusionsExercisesReferences8. Dynamic Linear ModelsIntroductionDiscrete Time Linear Dynamic SystemsEstimation of the StatesFilteringSmoothingPredictionThe Control problemExampleThe Kalman FilterThe Control ProblemAdaptive EstimationAn Example of Adaptive EstimationTesting HypothesesSummaryExercisesReferences9. The Shift Point Problem in Time SeriesIntroductionA Shifting Normal SequenceStructural Change in an Autoregressive Time Series  One Shift in a MA(1) Time SeriesChanging Models in EconometricsRegression Model with Autocorrelated ErrorsAnother Example of Structural ChangeTesting HypothesesAnalyzing Threshold Autoregression with the Bayesian ApproachA Numerical Example of Threshold AutoregressionComments and ConclusionsExercisesReferences10. Residuals and Diagnostic TestsIntroductionDiagnostic Checks for Autoregressive ModelsResiduals for Model of Color DataResiduals and Diagnostic Checks for Regression Models with AR(1) ErrorsDiagnostic Tests for Regression Models with Moving Average Time SeriesComments and ConclusionsExercisesReferences