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WorldCat.org

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.

This dis  cussion allows one to get results on the asymptotic distribution of finite para  meter estimates that are broader than those usually given in the literature in Chapter IV.

Stationary sequences and random fields