Time Series in the Time Domain

Amsterdam

1990

490 S.

zahlr. Lit. Ang.

Bandaufführung

0 444 8762(falsch)9 4

12309

68828

One of the successful parametric models is the classical autoregressive scheme, going back to the pioneering work of G.U. Yule, early in this century. The model is a difference equation with constant coefficients, and much of the classical work is done if the roots of its characteristic equation are interior to the unit circle. If the roots are of unit modulus, the analysis presents many difficulties. The advances made in recent years in this area are described in W. Fuller's article. An important development in the time domain area is the work of R. Kalman. It led to the emphasis on a formalization of rational transfer function systems as defined by an underlying state vector generated in a Markovian manner and observed subject to noise. This representation is connected with a rich structure theory whose understanding is central in the subject. It is surveyed in the article by M. Deistler. The structure ans analysis of several classes of nonstationary time series that are not of autoregressive type but for which the ideas of Fourier analysis extend is given in the article by M.M. Rao; and the filtering and smoothing problems are discussed by D.K. Chang. Related results on what may be termed "asymptotically stationary" and allied time series have been surveyed in C.S.K. Bahagavan's paper. The papers by L. Ljung, P. Young and G.C. Tiao relate to the estimation problems in the dynamical modelling systems. Here Young's paper deals with the on-line (real time) calculations. One of the uses of these models has been to analyze the consequences of an intervention (such as the introduction of exhaust emission laws) and another to consider the outlier detection problems. These are discussed by Tiao and T. Ozaki. Though rational transfer function models are parametric, it is seldom the case that the model set contains the truth and the problem may better be viewed as one of selecting a structure from an infinite set in some asymptotically optimal manner. This point ov view is explored by R. Shibata. Though least squares techniques, applied to the prediction errors, have dominated, there is a need to modify these to obtain estimators less influenced by discrepant observations. This is treated by Tiao and, in an extensive discussion, by R.D. Martin and V.J. Yohai. The model selection and unequally spaced data are natural problems in this area confronting the experimenter, and these are discussed by R.H. Jones. Since the time points may sometimes be under control of the experimenter, their optimal choice must be considered. This problem is treated by S. Cambanis. The modelling in the papers referred to above has been essentially linear. Ozaki presents an approach to the difficult problem of nonlinear modelling. The autoregressive models may have time varying parameters, and this is considered by D.F. Nicholls and A.R. Pagan. Their paper has special reference to econometric data as does also the paper by H. Theil and D. G. Fiebig who treat the problem where the regressor vectors in a multivariate System may be of a dimension higher than the number of time points for observation. The final two papers on applications by M. A. Cameron, P. J. Thomson and P. de Souza complement the areas covered by the preceding ones. These are designed to show two special applications, namely in signal attenuation estimation and speech recognition. Thus several aspects of the time domain analysis and the current trends are described in the diflferent chapters of this volume. So they will be of interest not only to the research workers in the area of f time series, but also to data analysts who use these techniques in their work.