Author | Rosenblatt, Murray. author |
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Title | Stationary Sequences and Random Fields [electronic resource] / by Murray Rosenblatt |
Imprint | Boston, MA : Birkhรคuser Boston, 1985 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-5156-9 |
Descript | 258 p. 2 illus. online resource |
I Stationary Processes -- 1. General Discussion -- 2. Positive Definite Functions -- 3. Fourier Representation of a Weakly Stationary Process -- Problems -- Notes -- II Prediction and Moments -- 1. Prediction -- 2. Moments and Cumulants -- 3. Autoregressive and Moving Average Processes -- 4. Non-Gaussian Linear Processes -- 5. The Kalman-Bucy Filter -- Problems -- Notes -- III Quadratic Forms, Limit Theorems and Mixing Conditions -- 1. Introduction -- 2. Quadratic Forms -- 3. A Limit Theorem -- 4. Summability of Cumulants -- 5. Long-range Dependence -- 6. Strong Mixing and Random Fields -- Problems -- Notes -- IV Estimation of Parameters of Finite Parameter Models -- 1. Maximum Likelihood Estimates -- 2. The Newton-Raphson Procedure and Gaussian ARMA Schemes -- 3. Asymptotic Properties of Some Finite Parameter Estimates -- 4. Sample Computations Using Monte Carlo Simulation -- 5. Estimating the Order of a Model -- 6. Finite Parameter Stationary Random Fields -- Problems -- V Spectral Density Estimates -- 1. The Periodogram -- 2. Bias and Variance of Spectral Density Estimates -- 3. Asymptotic Distribution of Spectral Density Estimates -- 4. Prewhitening and Tapering -- 5. Spectral Density Estimates Using Blocks -- 6. A Lower Bound for the Precision of Spectral Density Estimates -- 7. Turbulence and the Kolmogorov Spectrum -- 8. Spectral Density Estimates for Random Fields -- Problems -- Notes -- VI Cumulant Spectral Estimates -- 1. Introduction -- 2. The Discrete Fourier Transform and Fast Fourier Transform -- 3. Vector-Valued Processes -- 4. Smoothed Periodograms -- 5. Aliasing and Discretely Sampled Time Series -- Notes -- VII Density and Regression Estimates -- 1. Introduction. The Case of Independent Observations -- 2. Density and Regression Estimates for Stationary Sequences -- Notes -- VIII Non-Gaussian Linear Processes -- 1. Estimates of Phase, Coefficients, and Deconvolution for Non-Gaussian -- Linear Processes -- 2. Random Fields -- 3. Non-Gaussian Linear Random Fields -- Notes -- 1. Monotone Functions and Measures -- 2. Hilbert Space -- 3. Banach Space -- 4. Banach Algebras and Homomorphisms -- Postscript -- Author Index