New Directions in Time Series Analysis: Part IIDavid Brillinger, Peter Caines, John Geweke, Emanuel Parzen, Murray Rosenblatt, Murad S. Taqqu This IMA Volume in Mathematics and its Applications NEW DIRECTIONS IN TIME SERIES ANALYSIS, PART II is based on the proceedings of the IMA summer program "New Directions in Time Series Analysis. " We are grateful to David Brillinger, Peter Caines, John Geweke, Emanuel Parzen, Murray Rosenblatt, and Murad Taqqu for organizing the program and we hope that the remarkable excitement and enthusiasm of the participants in this interdisciplinary effort are communicated to the reader. A vner Friedman Willard Miller, Jr. PREFACE Time Series Analysis is truly an interdisciplinary field because development of its theory and methods requires interaction between the diverse disciplines in which it is applied. To harness its great potential, strong interaction must be encouraged among the diverse community of statisticians and other scientists whose research involves the analysis of time series data. This was the goal of the IMA Workshop on "New Directions in Time Series Analysis. " The workshop was held July 2-July 27, 1990 and was organized by a committee consisting of Emanuel Parzen (chair), David Brillinger, Murray Rosenblatt, Murad S. Taqqu, John Geweke, and Peter Caines. Constant guidance and encouragement was provided by Avner Friedman, Director of the IMA, and his very helpful and efficient staff. The workshops were organized by weeks. It may be of interest to record the themes that were announced in the IMA newsletter describing the workshop: l. |
Contents
| 1 | |
Autoregressive estimation of the prediction mean squared error | 9 |
Identification of linear systems from noisy data 21 | 21 |
On backcasting in linear time series models | 25 |
Fourier and likelihood analysis in NMR spectroscopy | 41 |
A survey | 43 |
Transferfunction models with nonstationary input | 65 |
A nonparametric approach to nonlinear time | 70 |
Identification of stochastic timevarying parameters | 211 |
Least squares estimation of the linear model with autoregressive errors | 215 |
Convergence of ÅströmWittenmarks selftuning | 225 |
On the closure of several sets of ARMA | 239 |
Weak convergence to selfaffine processes | 254 |
Recursive estimation in ARMAX models | 263 |
Time series statistics and information | 265 |
Fundamental roles of the idea of regression and Wold decomposition | 287 |
State space modeling and conditional mode estimation | 87 |
Asymptotics of predictive stochastic complexity | 93 |
A survey | 111 |
Smoothness priors | 113 |
An extension of quadraturebased methods for solving Euler conditions | 147 |
Selection of time series models and spectrum estimates using | 155 |
Contraction mappings in mixed spectrum estimation | 169 |
On approximate modeling of linear Gaussian processes | 177 |
On bounded and harmonizable solutions of infinite order ARMA systems | 193 |
On the identification and prediction of nonlinear models 195 | 194 |
On adaptive stabilization and ergodic behaviour of systems | 289 |
The convergence of output error recursions | 315 |
Linear models with longrange dependence | 325 |
Predictive deconvolution of chaotic and random processes | 335 |
Posterior analysis of possibly integrated | 341 |
Contrasting aspects of nonlinear time analysis | 357 |
On network structure function computations | 363 |
A nonparametric framework for time series analysis | 371 |
Asymptotic properties of estimates in incorrect ARMA | 374 |
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adaptive control algorithm applications approximation ARMA assume asymptotic autoregressive Bayesian Cauchy index coefficients component compute conditional consider constant convergence covariance defined denotes Econometrics equation equivalent ergodicity error exists finite fractional function Gaussian Gersch given Hankel matrix Hence Hilbert space hyperparameter identification IEEE Trans integral invariant probability measure K₂ kernel Kitagawa least squares Lemma limit theorems linear dynamical models long-range dependence markovian Mathematics matrix maximum likelihood method minimal multivariate noise nonlinear nonstationary observations obtained optimal parameters polynomial prediction probability measure problem proof properties random variables recursive representation RKHS sample satisfies self-similar sequence smoothness priors solution space spectral density stable stationary stationary process Statistics stochastic complexity stochastic process Taqqu Tauchen theory trend unit root values variance vector X₁ zero