Stationary Sequences and Random Fields

1. Front Matter

   Pages 1-10

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2. Stationary Processes

   • Murray Rosenblatt

   Pages 11-27

3. Prediction and Moments

   • Murray Rosenblatt

   Pages 29-52

4. Quadratic Forms, Limit Theorems and Mixing Conditions

   • Murray Rosenblatt

   Pages 53-81

5. Estimation of Parameters of Finite Parameter Models

   • Murray Rosenblatt

   Pages 83-124

6. Spectral Density Estimates

   • Murray Rosenblatt

   Pages 125-161

7. Cumulant Spectral Estimates

   • Murray Rosenblatt

   Pages 163-190

8. Density and Regression Estimates

   • Murray Rosenblatt

   Pages 191-203

9. Non-Gaussian Linear Processes

   • Murray Rosenblatt

   Pages 205-238

10. Back Matter

    Pages 239-258

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This book has a dual purpose. One of these is to present material which selec­ tively will be appropriate for a quarter or semester course in time series analysis and which will cover both the finite parameter and spectral approach. The second object is the presentation of topics of current research interest and some open questions. I mention these now. In particular, there is a discussion in Chapter III of the types of limit theorems that will imply asymptotic nor­ mality for covariance estimates and smoothings of the periodogram. 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. A derivation of the asymptotic distribution for spectral (second order) estimates is given under an assumption of strong mixing in Chapter V. A discussion of higher order cumulant spectra and their large sample properties under appropriate moment conditions follows in Chapter VI. Probability density, conditional probability density and regression estimates are considered in Chapter VII under conditions of short range dependence. Chapter VIII deals with a number of topics. At first estimates for the structure function of a large class of non-Gaussian linear processes are constructed. One can determine much more about this structure or transfer function in the non-Gaussian case than one can for Gaussian processes. In particular, one can determine almost all the phase information.

• Banach Space
• Hilbert space
• Likelihood
• Maximum
• Time series
• Variance
• differential equation

• Department of Mathematics, University of California, San Diego, La Jolla, USA

  Murray Rosenblatt

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