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catalog contributor b12210745.
catalog contributor b12210746.
catalog contributor b12210747.
catalog created "2001.".
catalog date "2001".
catalog date "2001.".
catalog dateCopyrighted "2001.".
catalog description "1.1 Basic ideas of state space analysis 1 -- 1.2 Linear Gaussian model 1 -- 1.3 Non-Gaussian and nonlinear models 3 -- 1.4 Prior knowledge 4 -- 1.6 Other books on state space methods 5 -- 1.7 Website for the book 5 -- I Linear Gaussian State Space Model -- 2 Local level model 9 -- 2.2 Filtering 11 -- 2.2.1 Kalman Filter 11 -- 2.3 Forecast errors 13 -- 2.3.1 Cholesky decomposition 14 -- 2.3.2 Error recursions 15 -- 2.4 State smoothing 16 -- 2.4.1 Smoothed state 16 -- 2.4.2 Smoothed state variance 17 -- 2.5 Disturbance smoothing 19 -- 2.5.1 Smoothed observation disturbances 20 -- 2.5.2 Smoothed state disturbances 20 -- 2.5.4 Cholesky decomposition and smoothing 22 -- 2.6 Simulation 22 -- 2.7 Missing observations 23 -- 2.8 Forecasting 25 -- 2.9 Initialisation 27 -- 2.10 Parameter estimation 30 -- 2.10.1 Loglikelihood evaluation 30 --".
catalog description "125 -- 6.3.3 Givens rotations 126 -- 6.3.4 Square root smoothing 127 -- 6.3.5 Square root filtering and initialisation 127 -- 6.3.6 Ilustration: local linear trend model 128 -- 6.4 Univariate treatment of multivariate series 128 -- 6.4.2 Details of univariate treatment 129 -- 6.4.3 Correlation between observation equations 131 -- 6.4.4 Computational efficiency 132 -- 6.4.5 Illustration: vector splines 133 -- 6.5 Filtering and smoothing under linear restrictions 134 -- 6.6 Algorithms of SsfPack 134 -- 6.6.2 SsfPack function 135 -- 6.6.3 Illustration: spline smoothing 136 -- 7 Maximum likelihood estimation 138 -- 7.2 Likelihood evaluation 138 -- 7.2.1 Loglikelihood when initial conditions are known 138 -- 7.2.2 Diffuse loglikelihood 139 -- 7.2.3 Diffuse loglikelihood evaluated via augmented Kalman filter 140 -- 7.2.4".
catalog description "188 -- 10.6.4 Trade frequencies: Poisson distribution 188 -- 11 Importance sampling 189 -- 11.2 Basic ideas of importance sampling 190 -- 11.3 Linear Gaussian approximating models 191 -- 11.4 Linearisation based on first two derivatives 193 -- 11.4.1 Exponentional family models 195 -- 11.4.2 Stochastic volatility model 195 -- 11.5 Linearisation based on the first derivative 195 -- 11.5.1 t-distribution 197 -- 11.5.2 Mixture of normals 197 -- 11.5.3 General error distribution 197 -- 11.6 Linearisation for non-Gaussian state components 198 -- 11.6.1 t-distribution for state errors 199 -- 11.7 Linearisation for nonlinear models 199 -- 11.7.1 Multiplicative models 201 -- 11.8 Estimating the conditional mode 202 -- 11.9 Computational aspects of importance sampling 204 -- 11.9.2 Practical implementation of importance sampling 204 -- 11.9.3 Antithetic variables 205 -- 11.9.4".
catalog description "2.10.2 Concentration of loglikelihood 31 -- 2.11 Steady state 32 -- 2.12 Diagnostic checking 33 -- 2.12.1 Diagnostic tests for forecast errors 33 -- 2.12.2 Detection of outliers and structural breaks 35 -- 2.13 Appendix: Lemma in multivariate normal regression 36 -- 3 Linear Gaussian state space models 38 -- 3.2 Structural time series models 39 -- 3.2.1 Univariate models 39 -- 3.2.2 Multivariate models 44 -- 3.2.3 Stamp 45 -- 3.3 ARMA models and ARIMA models 46 -- 3.4 Exponential smoothing 49 -- 3.5 State space versus Box-Jenkins approaches 51 -- 3.6 Regression with time-varying coefficients 54 -- 3.7 Regression with ARMA errors 54 -- 3.8 Benchmarking 54 -- 3.9 Simultaneous modelling of series from different sources 56 -- 3.10 State space models in continuous time 57 -- 3.10.1 Local level model 57 -- 3.10.2 Local linear trend model 59 -- 3.11".
catalog description "Bivariate structural time series analysis 167 -- 9.4 Box-Jenkins analysis 169 -- 9.5 Spline smoothing 172 -- 9.6 Approximate methods for modelling volatility 175 -- II Non-Gaussian And Nonlinear State Space Models -- 10 Non-Gaussian and nonlinear state space models 179 -- 10.2 General non-Gaussian model 179 -- 10.3 Exponential family models 180 -- 10.3.1 Poisson density 181 -- 10.3.2 Binary density 181 -- 10.3.3 Binomial density 181 -- 10.3.4 Negative binomial density 182 -- 10.3.5 Multinomial density 182 -- 10.4 Heavy-tailed distributions 183 -- 10.4.1 t-Distribution 183 -- 10.4.2 Mixture of normals 184 -- 10.4.3 General error distribution 184 -- 10.5 Nonlinear models 184 -- 10.6 Financial models 185 -- 10.6.1 Stochastic volatility models 185 -- 10.6.2 General autoregressive conditional heteroscedasticity 187 -- 10.6.3 Durations: exponential distribution".
catalog description "Diffuse initialisation 206 -- 11.9.5 Treatment of t-distribution without importance sampling 208 -- 11.9.6 Treatment of Gaussian mixture distributions without importance sampling 210 -- 12 Analysis from a classical standpoint 212 -- 12.2 Estimating conditional means and variances 212 -- 12.3 Estimating conditional densities and distribution functions 213 -- 12.4 Forecasting and estimating with missing observations 214 -- 12.5 Parameter estimation 215 -- 12.5.2 Estimation of likelihood 215 -- 12.5.3 Maximisation of loglikelihood 216 -- 12.5.4 Variance matrix of maximum likelihood estimate 217 -- 12.5.5 Effect of errors in parameter estimation 217 -- 12.5.6 Mean square error matrix due to simulation 217 -- 12.5.7 Estimation when the state disturbances are Gaussian 219 -- 12.5.8 Control variables 219 -- 13 Analysis from a Bayesian standpoint 222 -- 13.2".
catalog description "Examples of initial conditions for some models 110 -- 5.6.1 Structural time series models 110 -- 5.6.2 Stationary ARMA models 111 -- 5.6.3 Nonstationary ARIMA models 112 -- 5.6.4 Regression model with ARMA errors 114 -- 5.6.5 Spline smoothing 115 -- 5.7 Augmented Kalman filter andd smoother 115 -- 5.7.2 Augmented Kalman filter 115 -- 5.7.3 Filtering based on the augmented Kalman filter 116 -- 5.7.4 Illustration: the local linear trend model 118 -- 5.7.5 Comparisons of computational efficiency 119 -- 5.7.6 Smoothing based on the augmented Kalman filter 120 -- 6 Further computational aspects 121 -- 6.2 Regression estimation 121 -- 6.2.2 Inclusion of coefficient vector in state vector 122 -- 6.2.3 Regression estimation by augmentation 122 -- 6.2.4 Least squares and recursive residuals 123 -- 6.3 Square root filter and smoother 124 -- 6.3.2 Square root form of variance updating".
catalog description "Includes bibliographical references (p. [241]-247) and indexes.".
catalog description "Likelihood when elements of initial state vector are fixed but unknown 141 -- 7.3 Parameter estimation 142 -- 7.3.2 Numerical maximisation algorithms 142 -- 7.3.3 Score vector 144 -- 7.3.4 EM algorithm 147 -- 7.3.5 Parameter estimation when dealing with diffuse initial conditions 149 -- 7.3.6 Large sample distribution of maximum likelihood estimates 150 -- 7.3.7 Effect of errors in parameter estimation 150 -- 7.4 Goodness of fit 152 -- 7.5 Diagnostic checking 152 -- 8 Bayesian analysis 155 -- 8.2 Posterior analysis of state vector 155 -- 8.2.1 Posterior analysis conditional on parameter vector 155 -- 8.2.2 Posterior analysis when parameter vector is unknown 155 -- 8.2.3 Non-informative priors 158 -- 8.3 Markov chain Monte Carlo methods 159 -- 9 Illustrations of the use of the linear Gaussian model 161 -- 9.2 Structural time series models 161 -- 9.3".
catalog description "Posterior analysis of functions of the state vector 222 -- 13.3 Computational aspects of Bayesian analysis 225 -- 13.4 Posterior analysis of parameter vector 226 -- 13.5 Markov chain Monte Carlo methods 228 -- 14 Non-Gaussian and nonlinear illustrations 230 -- 14.2 Poisson density: van drivers killed in Great Britain 230 -- 14.3 Heavy-tailed density: outlier in gas consumption in UK 233 -- 14.4 Volatility: pound/dollar daily exchange rates 236 -- 14.5 Binary density: Oxford-Cambridge boat race 237 -- 14.6 Non-Gaussian and nonlinear analysis using SsfPack 238.".
catalog description "Simulating observation disturbances 84 -- 4.7.2 Derivation of simulation smoother for observation disturbances 87 -- 4.7.3 Simulation smoothing recursion 89 -- 4.7.4 Simulating state disturbances 90 -- 4.7.5 Simulating state vectors 91 -- 4.7.6 Simulating multiple samples 92 -- 4.8 Missing observations 92 -- 4.9 Forecasting 93 -- 4.10 Dimensionality of observational vector 94 -- 4.11 General matrix form for filtering and smoothing 95 -- 5 Initialisation of filter and smoother 99 -- 5.2 Exact initial Kalman filter 101 -- 5.2.1 Basic recursions 101 -- 5.2.2 Transition to the usual Kalman filter 104 -- 5.2.3 A convenient representation 105 -- 5.3 Exact initial state smoothing 106 -- 5.3.1 Smoothed mean of state vector 106 -- 5.3.2 Smoothed variance of state vector 107 -- 5.4 Exact initial disturbance smoothing 109 -- 5.5 Exact initial simulation smoothing 110 -- 5.6".
catalog description "Spline smoothing 61 -- 3.11.1 Spline smoothing in discrete time 61 -- 3.11.2 Spline smoothing in continuous time 62 -- 4 Filtering, smoothing and forecasting 64 -- 4.2 Filtering 65 -- 4.2.1 Derivation of Kalman filter 65 -- 4.2.2 Kalman filter recursion 67 -- 4.2.3 Steady state 68 -- 4.2.4 State estimation errors and forecast errors 68 -- 4.3 State smoothing 70 -- 4.3.1 Smoothed state vector 70 -- 4.3.2 Smoothed state variance matrix 72 -- 4.3.3 State smoothing recursion 73 -- 4.4 Disturbance smoothing 73 -- 4.4.1 Smoothed disturbances 73 -- 4.4.2 Fast state smoothing 75 -- 4.4.3 Smoothed disturbance variance matrices 75 -- 4.4.4 Disturbance smoothing recursion 76 -- 4.5 Covariance matrices of smoothed estimators 77 -- 4.6 Weight functions 81 -- 4.6.2 Filtering weights 81 -- 4.6.3 Smoothing weights 82 -- 4.7 Simulation smoothing 83 -- 4.7.1".
catalog extent "xvii, 253 p. :".
catalog identifier "0198523548".
catalog isPartOf "Oxford statistical science series ; 24".
catalog issued "2001".
catalog issued "2001.".
catalog language "eng".
catalog publisher "Oxford ; New York : Oxford University Press,".
catalog subject "519.5/5 21".
catalog subject "QA280 .D87 2001".
catalog subject "State-space methods.".
catalog subject "Time-series analysis.".
catalog tableOfContents "1.1 Basic ideas of state space analysis 1 -- 1.2 Linear Gaussian model 1 -- 1.3 Non-Gaussian and nonlinear models 3 -- 1.4 Prior knowledge 4 -- 1.6 Other books on state space methods 5 -- 1.7 Website for the book 5 -- I Linear Gaussian State Space Model -- 2 Local level model 9 -- 2.2 Filtering 11 -- 2.2.1 Kalman Filter 11 -- 2.3 Forecast errors 13 -- 2.3.1 Cholesky decomposition 14 -- 2.3.2 Error recursions 15 -- 2.4 State smoothing 16 -- 2.4.1 Smoothed state 16 -- 2.4.2 Smoothed state variance 17 -- 2.5 Disturbance smoothing 19 -- 2.5.1 Smoothed observation disturbances 20 -- 2.5.2 Smoothed state disturbances 20 -- 2.5.4 Cholesky decomposition and smoothing 22 -- 2.6 Simulation 22 -- 2.7 Missing observations 23 -- 2.8 Forecasting 25 -- 2.9 Initialisation 27 -- 2.10 Parameter estimation 30 -- 2.10.1 Loglikelihood evaluation 30 --".
catalog tableOfContents "125 -- 6.3.3 Givens rotations 126 -- 6.3.4 Square root smoothing 127 -- 6.3.5 Square root filtering and initialisation 127 -- 6.3.6 Ilustration: local linear trend model 128 -- 6.4 Univariate treatment of multivariate series 128 -- 6.4.2 Details of univariate treatment 129 -- 6.4.3 Correlation between observation equations 131 -- 6.4.4 Computational efficiency 132 -- 6.4.5 Illustration: vector splines 133 -- 6.5 Filtering and smoothing under linear restrictions 134 -- 6.6 Algorithms of SsfPack 134 -- 6.6.2 SsfPack function 135 -- 6.6.3 Illustration: spline smoothing 136 -- 7 Maximum likelihood estimation 138 -- 7.2 Likelihood evaluation 138 -- 7.2.1 Loglikelihood when initial conditions are known 138 -- 7.2.2 Diffuse loglikelihood 139 -- 7.2.3 Diffuse loglikelihood evaluated via augmented Kalman filter 140 -- 7.2.4".
catalog tableOfContents "188 -- 10.6.4 Trade frequencies: Poisson distribution 188 -- 11 Importance sampling 189 -- 11.2 Basic ideas of importance sampling 190 -- 11.3 Linear Gaussian approximating models 191 -- 11.4 Linearisation based on first two derivatives 193 -- 11.4.1 Exponentional family models 195 -- 11.4.2 Stochastic volatility model 195 -- 11.5 Linearisation based on the first derivative 195 -- 11.5.1 t-distribution 197 -- 11.5.2 Mixture of normals 197 -- 11.5.3 General error distribution 197 -- 11.6 Linearisation for non-Gaussian state components 198 -- 11.6.1 t-distribution for state errors 199 -- 11.7 Linearisation for nonlinear models 199 -- 11.7.1 Multiplicative models 201 -- 11.8 Estimating the conditional mode 202 -- 11.9 Computational aspects of importance sampling 204 -- 11.9.2 Practical implementation of importance sampling 204 -- 11.9.3 Antithetic variables 205 -- 11.9.4".
catalog tableOfContents "2.10.2 Concentration of loglikelihood 31 -- 2.11 Steady state 32 -- 2.12 Diagnostic checking 33 -- 2.12.1 Diagnostic tests for forecast errors 33 -- 2.12.2 Detection of outliers and structural breaks 35 -- 2.13 Appendix: Lemma in multivariate normal regression 36 -- 3 Linear Gaussian state space models 38 -- 3.2 Structural time series models 39 -- 3.2.1 Univariate models 39 -- 3.2.2 Multivariate models 44 -- 3.2.3 Stamp 45 -- 3.3 ARMA models and ARIMA models 46 -- 3.4 Exponential smoothing 49 -- 3.5 State space versus Box-Jenkins approaches 51 -- 3.6 Regression with time-varying coefficients 54 -- 3.7 Regression with ARMA errors 54 -- 3.8 Benchmarking 54 -- 3.9 Simultaneous modelling of series from different sources 56 -- 3.10 State space models in continuous time 57 -- 3.10.1 Local level model 57 -- 3.10.2 Local linear trend model 59 -- 3.11".
catalog tableOfContents "Bivariate structural time series analysis 167 -- 9.4 Box-Jenkins analysis 169 -- 9.5 Spline smoothing 172 -- 9.6 Approximate methods for modelling volatility 175 -- II Non-Gaussian And Nonlinear State Space Models -- 10 Non-Gaussian and nonlinear state space models 179 -- 10.2 General non-Gaussian model 179 -- 10.3 Exponential family models 180 -- 10.3.1 Poisson density 181 -- 10.3.2 Binary density 181 -- 10.3.3 Binomial density 181 -- 10.3.4 Negative binomial density 182 -- 10.3.5 Multinomial density 182 -- 10.4 Heavy-tailed distributions 183 -- 10.4.1 t-Distribution 183 -- 10.4.2 Mixture of normals 184 -- 10.4.3 General error distribution 184 -- 10.5 Nonlinear models 184 -- 10.6 Financial models 185 -- 10.6.1 Stochastic volatility models 185 -- 10.6.2 General autoregressive conditional heteroscedasticity 187 -- 10.6.3 Durations: exponential distribution".
catalog tableOfContents "Diffuse initialisation 206 -- 11.9.5 Treatment of t-distribution without importance sampling 208 -- 11.9.6 Treatment of Gaussian mixture distributions without importance sampling 210 -- 12 Analysis from a classical standpoint 212 -- 12.2 Estimating conditional means and variances 212 -- 12.3 Estimating conditional densities and distribution functions 213 -- 12.4 Forecasting and estimating with missing observations 214 -- 12.5 Parameter estimation 215 -- 12.5.2 Estimation of likelihood 215 -- 12.5.3 Maximisation of loglikelihood 216 -- 12.5.4 Variance matrix of maximum likelihood estimate 217 -- 12.5.5 Effect of errors in parameter estimation 217 -- 12.5.6 Mean square error matrix due to simulation 217 -- 12.5.7 Estimation when the state disturbances are Gaussian 219 -- 12.5.8 Control variables 219 -- 13 Analysis from a Bayesian standpoint 222 -- 13.2".
catalog tableOfContents "Examples of initial conditions for some models 110 -- 5.6.1 Structural time series models 110 -- 5.6.2 Stationary ARMA models 111 -- 5.6.3 Nonstationary ARIMA models 112 -- 5.6.4 Regression model with ARMA errors 114 -- 5.6.5 Spline smoothing 115 -- 5.7 Augmented Kalman filter andd smoother 115 -- 5.7.2 Augmented Kalman filter 115 -- 5.7.3 Filtering based on the augmented Kalman filter 116 -- 5.7.4 Illustration: the local linear trend model 118 -- 5.7.5 Comparisons of computational efficiency 119 -- 5.7.6 Smoothing based on the augmented Kalman filter 120 -- 6 Further computational aspects 121 -- 6.2 Regression estimation 121 -- 6.2.2 Inclusion of coefficient vector in state vector 122 -- 6.2.3 Regression estimation by augmentation 122 -- 6.2.4 Least squares and recursive residuals 123 -- 6.3 Square root filter and smoother 124 -- 6.3.2 Square root form of variance updating".
catalog tableOfContents "Likelihood when elements of initial state vector are fixed but unknown 141 -- 7.3 Parameter estimation 142 -- 7.3.2 Numerical maximisation algorithms 142 -- 7.3.3 Score vector 144 -- 7.3.4 EM algorithm 147 -- 7.3.5 Parameter estimation when dealing with diffuse initial conditions 149 -- 7.3.6 Large sample distribution of maximum likelihood estimates 150 -- 7.3.7 Effect of errors in parameter estimation 150 -- 7.4 Goodness of fit 152 -- 7.5 Diagnostic checking 152 -- 8 Bayesian analysis 155 -- 8.2 Posterior analysis of state vector 155 -- 8.2.1 Posterior analysis conditional on parameter vector 155 -- 8.2.2 Posterior analysis when parameter vector is unknown 155 -- 8.2.3 Non-informative priors 158 -- 8.3 Markov chain Monte Carlo methods 159 -- 9 Illustrations of the use of the linear Gaussian model 161 -- 9.2 Structural time series models 161 -- 9.3".
catalog tableOfContents "Posterior analysis of functions of the state vector 222 -- 13.3 Computational aspects of Bayesian analysis 225 -- 13.4 Posterior analysis of parameter vector 226 -- 13.5 Markov chain Monte Carlo methods 228 -- 14 Non-Gaussian and nonlinear illustrations 230 -- 14.2 Poisson density: van drivers killed in Great Britain 230 -- 14.3 Heavy-tailed density: outlier in gas consumption in UK 233 -- 14.4 Volatility: pound/dollar daily exchange rates 236 -- 14.5 Binary density: Oxford-Cambridge boat race 237 -- 14.6 Non-Gaussian and nonlinear analysis using SsfPack 238.".
catalog tableOfContents "Simulating observation disturbances 84 -- 4.7.2 Derivation of simulation smoother for observation disturbances 87 -- 4.7.3 Simulation smoothing recursion 89 -- 4.7.4 Simulating state disturbances 90 -- 4.7.5 Simulating state vectors 91 -- 4.7.6 Simulating multiple samples 92 -- 4.8 Missing observations 92 -- 4.9 Forecasting 93 -- 4.10 Dimensionality of observational vector 94 -- 4.11 General matrix form for filtering and smoothing 95 -- 5 Initialisation of filter and smoother 99 -- 5.2 Exact initial Kalman filter 101 -- 5.2.1 Basic recursions 101 -- 5.2.2 Transition to the usual Kalman filter 104 -- 5.2.3 A convenient representation 105 -- 5.3 Exact initial state smoothing 106 -- 5.3.1 Smoothed mean of state vector 106 -- 5.3.2 Smoothed variance of state vector 107 -- 5.4 Exact initial disturbance smoothing 109 -- 5.5 Exact initial simulation smoothing 110 -- 5.6".
catalog tableOfContents "Spline smoothing 61 -- 3.11.1 Spline smoothing in discrete time 61 -- 3.11.2 Spline smoothing in continuous time 62 -- 4 Filtering, smoothing and forecasting 64 -- 4.2 Filtering 65 -- 4.2.1 Derivation of Kalman filter 65 -- 4.2.2 Kalman filter recursion 67 -- 4.2.3 Steady state 68 -- 4.2.4 State estimation errors and forecast errors 68 -- 4.3 State smoothing 70 -- 4.3.1 Smoothed state vector 70 -- 4.3.2 Smoothed state variance matrix 72 -- 4.3.3 State smoothing recursion 73 -- 4.4 Disturbance smoothing 73 -- 4.4.1 Smoothed disturbances 73 -- 4.4.2 Fast state smoothing 75 -- 4.4.3 Smoothed disturbance variance matrices 75 -- 4.4.4 Disturbance smoothing recursion 76 -- 4.5 Covariance matrices of smoothed estimators 77 -- 4.6 Weight functions 81 -- 4.6.2 Filtering weights 81 -- 4.6.3 Smoothing weights 82 -- 4.7 Simulation smoothing 83 -- 4.7.1".
catalog title "Time series analysis by state space methods / J. Durbin and S.J. Koopman.".
catalog type "text".