E-raamat: Parameter Estimation and Hypothesis Testing in Spectral Analysis of Stationary Time Series

I Properties of Maximum Likelihood Function for a Gaussian Time Series.-
1. General Expression for the log Likelihood.-
2. Asymptotic Expression for
the Principal Part 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. Whittles 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 $$\mathop \theta \limits^ \sim $$
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 White
Noise.-
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 Nice 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 Asymptotically
DifferentiableExperiments).-
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.