Author | Aoki, Masanao. author |
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Title | State Space Modeling of Time Series [electronic resource] / by Masanao Aoki |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 1987 |
Connect to | http://dx.doi.org/10.1007/978-3-642-96985-0 |
Descript | XI, 315 p. online resource |
1 Introduction -- 2 The Notion of State -- 3 Representation of Time Series -- 3.1 Time Domain Representation -- 3.2 Frequency Domain Representation -- 4 State Space and ARMA Representation -- 4.1 State Space Models -- 4.2 Unit Roots -- 4.3 Conversion to State Space Representation -- 5 Properties of State Space Models -- 5.1 Observability -- 5.2 Covariance and Impulse Response Matrices -- 5.3 The Hankel Matrix -- 5.4 System Parameters and Innovation Models -- 5.5 Singular Value Decomposition -- 5.6 Balanced Realization of State Space Model -- 5.7 Hankel Norm of a Transfer Function -- 5.8 Singular Value Decomposition in the z-Domain -- 6 Innovation Processes -- 6.1 Cholesky Decomposition and Innovations -- 6.2 Orthogonal Projections -- 7 Kalman Filters -- 7.1 Innovation Models -- 7.2 Kalman Filters -- 7.3 Causal Invertibility and Innovation -- 7.4 Likelihood Functions and Identification -- 7.5 A Non-Iterative Algorithm for Riccati Equations -- 7.6 Forecasting Equations -- 8 State Vectors and Optimality Measures -- 8.1 State Vectors -- 8.2 Optimality Measures -- 9 Compution of System Matrices -- 9.1 System Matrices -- 9.2 Balanced Models for Scalar Time Series -- 9.3 Prediction Error Analysis -- 9.4 Non-Stationary Models -- 9.5 Rescaling and Other Transformation of Variables -- 9.6 Dynamic Multipliers -- 9.7 Numerical Examples -- 10 Approximate Models and Error Analysis -- 10.1 Structural Sensitivity -- 10.2 Error Norms -- 10.3 Error Propagation -- 10.4 Some Statistical Aspects -- 11 Numerical Examples -- 11.1 Chemical Process Yields -- 11.2 IBM Stock Prices -- 11.3 Canadian GNP and Money Data -- 11.4 Germany -- 11.5 United Kingdom -- 11.6 Combined Models for the United Kingdom and Germany -- 11.7 Japan -- 11.8 Japan-US Interactions -- 11.9 The United States of America -- 11.10 Comparison with VAR Models -- Appendices -- A.1 Differences Equations -- First Order Stable Equations -- First Order Unstable Equations -- Second Order Equations -- State Space Method -- A.2 Geometry of Weakly Stationary Stochastic Sequences -- A.3 The z-Transform -- A. 4 Discrete and Continuous Time System Correspondences -- A.5 Calculation of the Inverse -- A. 6 Some Useful Relations for Matrix Quadratic Forms -- A.7 Spectral Decomposition Representation -- A. 8 Computation of Sample Covariance Matrices -- A.9 Vector Autoregressive Models -- A. 10 Properties of Symplectic Matrices -- A. 11 Common Factors in ARMA Models -- A. 12 Singular Value Decomposition Theorem -- A. 13 Hankel Matrices -- A. 14 Spectrum and Factorization -- A. 15 Intertemporal Optimization by Dynamic Programming -- A. 16 Solution of Scalar Riccati Equations -- A. 17 Time Series from Intertemporal Optimization -- A. 18 Time Series from Rational Expectations Models -- A. 19 Data Sources -- References