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Book Cover
Author Casals, Jose (Banker), author.

Title State-space methods for time series analysis : theory, applications and software / Jose Casals, Alfredo Garcia-Hiernaux, Miguel Jerez, Sonia Sotoca, A. Alexandre Trindade.

Published Boca Raton Chapman & Hall/CRC, 2016.


Location Call No. Status
Physical description xxvii, 269 pages : illustrations (black and white) ; 24 cm.
Series Chapman & Hall/CRC monographs on statistics & applied probability ; 149.
Chapman & Hall/CRC monographs on statistics & applied probability ; 149.
Notes Formerly CIP. Uk.
Bibliography Includes bibliographical references (pages 247-260) and indexes.
Contents Machine generated contents note: 2.1.The multiple error model -- 2.1.1.Model formulation -- 2.1.2.Similar transformations -- 2.1.3.Properties of the State-Space model -- 2.2.Single error models -- 2.2.1.Model formulation -- 2.2.2.State estimation in the SEM -- 2.2.3.Obtaining the SEM equivalent to a MEM -- 2.2.4.Obtaining the SEM equivalent to a general linear process -- 3.1.Model decomposition -- 3.1.1.Deterministic and stochastic subsystems -- 3.1.2.Implied univariate models -- 3.1.3.Block-diagonal forms -- 3.2.Model combination -- 3.2.1.Endogeneization of stochastic inputs -- 3.2.2.Colored errors -- 3.3.Change of variables in the output -- 3.3.1.Observation errors -- 3.3.2.Missing values and aggregated data -- 3.3.3.Temporal aggregation -- 3.4.Uses of these transformations -- 4.1.The conditional moments of a State-Space model -- 4.2.The Kalman Filter -- 4.3.Decomposition of the smoothed moments -- 4.4.Smoothing for a general State-Space model --
Contents note continued: 4.5.Smoothing for fixed-coefficients and single-error models -- 4.6.Uncertainty of the smoothed estimates in a SEM -- 4.7.Examples -- 4.7.1.Recursive Least Squares -- 4.7.2.Cleaning the Wolf sunspot series -- 4.7.3.Extracting the Hodrick-Prescott trend -- 5.1.Maximum likelihood estimation -- 5.1.1.Problem statement -- 5.1.2.Prediction error decomposition -- 5.1.3.Initialization of the Kalman filter in the stationary case -- 5.2.The likelihood for a nonstationary model -- 5.2.1.Diffuse likelihood -- 5.2.2.Minimally conditioned likelihood -- 5.2.3.Likelihood computation for a fixed-parameter SEM -- 5.2.4.Initialization of the Kalman filter in the nonstationary case -- 5.3.The likelihood for a model with inputs -- 5.3.1.Models with deterministic inputs -- 5.3.2.Models with stochastic inputs -- 5.4.Examples -- 5.4.1.Models for the Airline Passenger series -- 5.4.2.Modeling the series of Housing Starts and Sales --
Contents note continued: 6.1.Regression with time-varying parameters -- 6.1.1.SS formulation -- 6.1.2.Maximum likelihood estimation -- 6.2.Periodic models -- 6.2.1.All the seasons have the same dynamic structure -- 6.2.2.The s models do not have the same dynamic structure -- 6.2.3.Stationarity and invertibility -- 6.2.4.Maximum likelihood estimation -- 6.3.The likelihood of models with GARCH errors -- 6.4.Examples -- 6.4.1.A time-varying CAPM regression -- 6.4.2.A periodic model for West German Consumption -- 6.4.3.A model with vector-GARCH errors for two exchange rate series -- 7.1.Theoretical foundations -- 7.1.1.Subspace structure and notation -- 7.1.2.Assumptions, projections and model reduction -- 7.1.3.Estimating the system matrices -- 7.2.System order estimation -- 7.2.1.Preliminary data analysis methods -- 7.2.2.Model comparison methods -- 7.3.Constrained estimation -- 7.3.1.State sequence structure -- 7.3.2.Subspace-based likelihood --
Contents note continued: 7.4.Multiplicative seasonal models -- 7.5.Examples -- 7.5.1.Univariate models -- 7.5.2.A multivariate model for the interest rates -- 8.1.Input and error-related components -- 8.1.1.The deterministic and stochastic subsystems -- 8.1.2.Enforcing minimality -- 8.2.Estimation of the deterministic components -- 8.2.1.Estimating the total effect of the inputs -- 8.2.2.Estimating the individual effect of each input -- 8.3.Decomposition of the stochastic component -- 8.3.1.Characterization of the structural components -- 8.3.2.Estimation of the structural components -- 8.4.Structure of the method -- 8.5.Examples -- 8.5.1.Comparing different methods with simulated data -- 8.5.2.Common features in wheat prices -- 8.5.3.The effect of advertising on sales -- 9.1.Notation and previous results -- 9.2.Obtaining the VARMAX form of a State-Space model -- 9.2.1.From State-Space to standard VARMAX -- 9.2.2.From State-Space to canonical VARMAX --
Contents note continued: 9.3.Practical applications and examples -- 9.3.1.The VARMAX form of some common State-Space models -- 9.3.2.Identifiability and conditioning of the estimates -- 9.3.3.Fitting an errors-in-variables model to Wolf's sunspot series -- 9.3.4."Bottom-up" modeling of quarterly US GDP trend -- 10.1.The effect of aggregation on an SS model -- 10.1.1.The high-frequency model in stacked form -- 10.1.2.Aggregation relationships -- 10.1.3.Relationships between the models for high, low, and mixed-frequency data -- 10.1.4.The effect of aggregation on predictive accuracy -- 10.2.Observability in the aggregated model -- 10.2.1.Unobservable modes -- 10.2.2.Observability and fixed-interval smoothing -- 10.2.3.An algorithm to aggregate a linear model: theory and examples -- 10.3.Specification of the high-frequency model -- 10.3.1.Enforcing approximate consistency -- 10.3.2."Bottom-up" determination of the quarterly model -- 10.4.Empirical example -- 10.4.1.Annual model --
Contents note continued: 10.4.2.Decomposition of the quarterly indicator -- 10.4.3.Specification and estimation of the quarterly model -- 10.4.4.Diagnostics -- 10.4.5.Forecast accuracy and non-conformable samples -- 10.4.6.Comparison with alternative methods -- 11.1.Model formulation -- 11.2.The Kalman Filter -- 11.2.1.Case of uncorrelated state and observational errors -- 11.2.2.Case of correlated state and observational errors -- 11.3.The linear mixed model in SS form -- 11.4.Maximum likelihood estimation -- 11.5.Missing data modifications -- 11.5.1.Missingness in responses only -- 11.5.2.Missingness in both responses and covariates: method 1 -- 11.5.3.Missingness in both responses and covariates: method 2 -- 11.6.Real data examples -- 11.6.1.A LMM for the mare ovarian follicles data -- 11.6.2.Smoothing and prediction of missing values for the beluga whales data -- A.Some results in numerical algebra and linear systems -- A.1.QR Decomposition -- A.2.Schur decomposition --
Contents note continued: A.3.The Hessenberg Form -- A.4.SVD Decomposition -- A.5.Canonical Correlations -- A.6.Algebraic Lyapunov and Sylvester equations -- A.7.Numerical solution of a Sylvester equation -- A.8.Block-diagonalization of a matrix -- A.9.Reduced rank least squares -- A.10.Riccati equations -- A.10.1.Definition -- A.10.2.Solving the ARE in the general case -- A.10.3.Solving the ARE for GARCH models -- A.11.Kalman filter -- B.Asymptotic properties of maximum likelihood estimates -- B.1.Preliminaries -- B.2.Basic likelihood results for the State-Space model -- B.2.1.The information matrix -- B.2.2.Regularity conditions -- B.2.3.Choice of estimation method -- B.3.The State-Space model with cross-sectional extension -- C.Software (E4) -- C.1.Models supported in E4 -- C.1.1.State-Space model -- C.1.2.The THD format -- C.1.3.Basic models -- C.1.3.1.Mathematical definition -- C.1.3.2.Definition in THD format -- C.1.4.Models with GARCH errors --
Contents note continued: C.1.4.1.Mathematical definition of the GARCH process -- C.1.4.2.Defining a model with GARCH errors in THD format -- C.1.5.Nested models -- C.2.Overview of computational procedures -- C.2.1.Standard procedures for time series analysis -- C.2.2.Signal extraction methods -- C.2.3.Likelihood and model estimation -- C.3.Who can benefit from E4? -- D.Downloading E4 and the examples in this book -- D.1.The e website -- D.2.Downloading and installing E4 -- D.3.Downloading the code for the examples in this book.
Other formats Also published electronically.
Other author Garcia-Hiernaux, Alfredo, author.
Jerez, Miguel, author.
Sotoca, Sonia, author.
Trindade, A. Alexandre, author.
Subject State-space methods.
Time-series analysis.
ISBN 9781482219593 (hbk.) £63.99
9781498787352 (ePub ebook) () £63.99
9781482219609 (PDF ebook) () £63.99