Author | Dzhaparidze, K. author |
---|---|
Title | Parameter Estimation and Hypothesis Testing in Spectral Analysis of Stationary Time Series [electronic resource] / by K. Dzhaparidze |
Imprint | New York, NY : Springer New York, 1986 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-4842-2 |
Descript | 324 p. online resource |
I Properties of Maximum Likelihood Function for a Gaussian Time Series -- 1. General Expression for the log Likelihood -- 2. Asymptotic Expression for the โPrincipal Partโ of the log Likelihood -- 3. The Asymptotic Differentiability of Gaussian Distributions with Spectral Densities Separated from Zero -- 4. The Asymptotic Differentiability of Gaussian Distributions with Spectral Densities Possessing Fixed Zeros -- Appendix 1 -- Appendix 2 -- Appendix 3. Remarks and Bibliography -- II Estimation of Parameters by Means of P. Whittleโs Method -- 1. Asymptotic Maximum Likelihood Estimators -- 2. Properties of Asymptotic Maximum Likelihood Estimators in the Case of Strictly Positive Spectral Density -- 3. Consistency, Asymptotic Normality, and Asymptotic Efficiency of the Estimator $$\mathop \theta \limitŝ \sim $$ in the Case of Spectral Density Possessing Fixed Zeros -- 4. Examples of Determination of Asymptotic Maximum Likelihood Estimators -- 5. Asymptotic Maximum Likelihood Estimator of the Spectrum of Processes Distorted by โWhite Noiseโ -- 6. Least-Squares Estimation of Parameters of a Spectrum of a Linear Process -- 7. Estimation by Means of the Whittle Method of Spectrum Parameters of General Processes Satisfying the Strong Mixing Condition -- Appendix 1 -- Appendix 2 -- Appendix 3. Remarks and Bibliography -- III Simplified Estimators Possessing โNiceโ Asymptotic Properties -- 1. Asymptotic Properties of Simplified Estimators -- 2. Examples of Preliminary Consistent Estimators -- 3. Examples of Constructing Simplified Estimators -- Appendix 1. Remarks and Bibliography -- IV Testing Hypotheses on Spectrum Parameters of a Gaussian Time Series -- 1. Testing Simple Hypotheses -- 2. Testing Composite Hypotheses (The Case of a Sequence of General โAsymptotically Differentiable Experimentsโ) -- 3. Testing of Composite Hypothesis about a Parameter of a Spectrum of a Gaussian Time Series -- Appendix 1. Remarks and Bibliography -- V Goodness-of-Fit Tests for Testing the Hypothesis about the Spectrum of Linear Processes -- 1. A Class of Goodness-of-Fit Tests for Testing a Simple Hypothesis about the Spectrum of Linear Processes -- 2. X2 Test for Testing a Simple Hypothesis about the Spectrum of a Linear Process -- 3. Goodness-of-Fit Test for Testing Composite Hypotheses about the Spectrum of a Linear Process -- Appendix 1. Remarks and Bibliography