Parameter Estimation and Hypothesis Testing in Spectral Analysis of Stationary Time Series

1. Front Matter

   Pages i-vi

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2. Introduction

   • K. Dzhaparidze

   Pages 1-34

3. Properties of Maximum Likelihood Function for a Gaussian Time Series

   • K. Dzhaparidze

   Pages 35-101

4. Estimation of Parameters by Means of P. Whittle’s Method

   • K. Dzhaparidze

   Pages 102-197

5. Simplified Estimators Possessing “Nice” Asymptotic Properties

   • K. Dzhaparidze

   Pages 198-235

6. Testing Hypotheses on Spectrum Parameters of a Gaussian Time Series

   • K. Dzhaparidze

   Pages 236-272

7. Goodness-of-Fit Tests for Testing the Hypothesis About the Spectrum of Linear Processes

   • K. Dzhaparidze

   Pages 273-305

8. Back Matter

   Pages 306-324

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. . ) (under the assumption that the spectral density exists). For this reason, a vast amount of periodical and monographic literature is devoted to the nonparametric statistical problem of estimating the function tJ( T) and especially that of leA) (see, for example, the books [4,21,22,26,56,77,137,139,140,]). However, the empirical value t;; of the spectral density I obtained by applying a certain statistical procedure to the observed values of the variables Xl' . . . , X , usually depends in n a complicated manner on the cyclic frequency). . This fact often presents difficulties in applying the obtained estimate t;; of the function I to the solution of specific problems rela ted to the process X . Theref ore, in practice, the t obtained values of the estimator t;; (or an estimator of the covariance function tJ~( T» are almost always "smoothed," i. e. , are approximated by values of a certain sufficiently simple function 1 = 1

• Analysis
• Estimator
• Gaussian distribution
• Likelihood
• Series
• Time
• Time series
• best fit

• Mathematisch Centrum, Amsterdam, The Netherlands

  K. Dzhaparidze

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