Author | Azencott, Robert. author |
---|---|
Title | Series of Irregular Observations [electronic resource] : Forecasting and Model Building / by Robert Azencott, Didier Dacunha-Castelle |
Imprint | New York, NY : Springer New York, 1986 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-4912-2 |
Descript | VIII, 236 p. online resource |
I Discrete Time Random Processes -- 1. Random Variables and Probability Spaces -- 2. Random Vectors -- 3. Random Processes -- 4. Second-Order Process -- II Gaussian Processes -- 1. The Use (and Misuse) of Gaussian Models -- 2. Fourier Transform: A Few Basic Facts -- 3. Gaussian Random Vectors -- 4. Gaussian Processes -- III Stationary Processes -- 1. Stationarity and Model Building -- 2. Strict Stationarity and Second-Order Stationarity -- 3. Construction of Strictly Stationary Processes -- 4. Ergodicity -- 5. Second-Order Stationarity: Processes with Countable Spectrum -- IV Forecasting and Stationarity -- 1. Linear and Nonlinear Forecasting -- 2. Regular Processes and Singular Processes -- 3. Regular Stationary Processes and Innovation -- 4. Prediction Based on a Finite Number of Observations -- 5. Complements on Isometries -- V Random Fields and Stochastic Integrals -- 1. Random Measures with Finite Support -- 2. Uncorrected Random Fields -- 3. Stochastic Integrals -- VI Spectral Representation of Stationary Processes -- 1. Processes with Finite Spectrum -- 2. Spectral Measures -- 3. Spectral Decomposition -- VII Linear Filters -- 1. Often Used Linear Filters -- 2. Multiplication of a Random Field by a Function -- 3. Response Functions and Linear Filters -- 4. Applications to Linear Representations -- 5. Characterization of Linear Filters as Operators -- VIII ARMA Processes and Processes with Rational Spectrum -- 1. ARMA Processes -- 2. Regular and Singular Parts of an ARMA Process -- 3. Construction of ARMA Processes -- 4. Processes with Rational Spectrum -- 5. Innovation for Processes with Rational Spectrum -- IX Nonstationary ARMA Processes and Forecasting -- 1. Nonstationary ARMA Models -- 2. Linear Forecasting and Processes with Rational Spectrum -- 3. Time Inversion and Estimation of Past Observations -- 4. Forecasting and Nonstationary ARMA Processes -- X Empirical Estimators and Periodograms -- 1. Empirical Estimation -- 2. Periodograms -- 3. Asymptotic Normality and Periodogram -- 4. Asymptotic Normality of Empirical Estimators -- 5. The Toeplitz Asymptotic Homomorphism -- XI Empirical Estimation of the Parameters for ARMA Processes with Rational Spectrum -- 1. Empirical Estimation and Efficient Estimation -- 2. Computation of the ak and Yule-Walker Equations -- 3. Computation of the bl and of ?2 -- 4. Empirical Estimation of the Parameters When p, q are Known -- 5. Characterization of p and q -- 6. Empirical Estimation of d for an ARIMA (p,d,q) Model -- 7. Empirical Estimation of (p,q) -- 8. Complement: A Direct Method of Computation for the bk -- 9. The ARMA Models with Seasonal Effects -- 10. A Technical Result: Characterization of Minimal Recursive Identities -- 11. Empirical Estimation and Identification -- XII Effecient Estimation for the Parameters of a Process with Rational Spectrum -- 1. Maximum Likelihood -- 2. The Box-Jenkins Method to Compute (รฃ, b) -- 3. Computation of the Information Matrix -- 4. Convergence of the Backforecasting Algorithm -- XIII Asymptotic Maximum Likelihood -- 1. Approximate Log-Likelihood -- 2. Kullback Information -- 3. Convergence of Maximum Likelihood Estimators -- 4. Asymptotic Normality and Efficiency -- XIV Identification and Compensated Likelihood -- 1. Identification -- 2. Parametrization -- 3. Compensated Likelihood -- 4. Mathematical Study of Compensated Likelihood -- 5. Noninjective Parametrization -- 6. Almost Sure Bounds for the Maximal Log-Likelihood -- 7. Law of the Interated Logarithm for the Periodogram -- XV A Few Problems not Studied Here -- 1. Tests of Fit for ARMA Models -- 2. Nonlinearity