Author | Rosenblatt, Murray. author |
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Title | Gaussian and Non-Gaussian Linear Time Series and Random Fields [electronic resource] / by Murray Rosenblatt |
Imprint | New York, NY : Springer New York : Imprint: Springer, 2000 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-1262-1 |
Descript | XIII, 247 p. online resource |
1 Reversibility and Identifiability -- 1.1 Linear Sequences and the Gaussian Property -- 1.2 Reversibility -- 1.3 Identifiability -- 1.4 Minimum and Nonminimum Phase Sequences -- 2 Minimum Phase Estimation -- 2.1 The Minimum Phase Case and the Quasi-Gaussian Likelihood -- 2.2 Consistency -- 2.3 The Asymptotic Distribution -- 3 Homogeneous Gaussian Random Fields -- 3.1 Regular and Singular Fields -- 3.2 An Isometry -- 3.3 L-Fields and L-Markov Fields -- 4 Cumulants, Mixing and Estimation for Gaussian Fields -- 4.1 Moments and Cumulants -- 4.2 Higher Order Spectra -- 4.3 Some Simple Inequalities and Strong Mixing -- 4.4 Strong Mixing for Two-Sided Linear Processes -- 4.5 Mixing and a Central Limit Theorem for Random Fields -- 4.6 Estimation for Stationary Random Fields -- 4.7 Cumulants of Finite Fourier Transforms -- 4.8 Appendix: Two Inequalities -- 5 Prediction for Minimum and Nonminimum Phase Models -- 5.1 Introduction -- 5.2 A First Order Autoregressive Model -- 5.3 Nonminimum Phase Autoregressive Models -- 5.4 A Functional Equation -- 5.5 Entropy -- 5.6 Continuous Time Parameter Processes -- 6 The Fluctuation of the Quasi-Gaussian Likelihood -- 6.1 Initial Remarks -- 6.2 Derivation -- 6.3 The Limiting Process -- 7 Random Fields -- 7.1 Introduction -- 7.2 Markov Fields and Chains -- 7.3 Entropy and a Limit Theorem -- 7.4 Some Illustrations -- 8 Estimation for Possibly Nonminimum Phase Schemes -- 8.1 The Likelihood for Possibly Non-Gaussian Autoregressive Schemes -- 8.2 Asymptotic Normality -- 8.3 Preliminary Comments: Approximate Maximum Likelihood Estimates for Non-Gaussian Nonminimum Phase ARMA Sequences -- 8.4 The Likelihood Function -- 8.5 The Covariance Matrix -- 8.6 Solution of the Approximate Likelihood Equations -- 8.7 Cumulants and Estimation for Autoregressive Schemes -- 8.8 Superefficiency -- Bibliographic Notes -- References -- Notation -- Author Index