Spectral Analysis and Time Series (Probability & Mathematical Statistics Monograph)

 
9780125649216: Spectral Analysis and Time Series (Probability & Mathematical Statistics Monograph)

A principal feature of this book is the substantial care and attention devoted to explaining the basic ideas of the subject. Whenever a new theoretical concept is introduced it is carefully explained by reference to practical examples drawn mainly from the physical sciences. Subjects covered include: spectral analysis which is closely intertwined with the "time domain" approach, elementary notions of Hilbert Space Theory, basic probability theory, and practical analysis of time series data. The inclusion of material on "kalman filtering", state-space filtering", "non-linear models" and continuous time" models completes the impressive list of unique and detailed features which will give this book a prominent position among related literature. The first section-Volume 1-deals with single (univariate) series, while the second-Volume 2-treats the analysis of several (multivariate) series and the problems of prediction, forecasting and control.

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Electric signals, stress and vibration records, seismographic traces and economic index stress all exhibit irregular patterns of vibration over time, and one of the main objectives of time series analysis is to describe the statistical properties of these irregularities by means of mathematical models. Such models can provide considerable insight into the basic structure of the series and form one of the major tools used for forecasting future behaviour on the basis of past values.

A principal feature of this book is the substantial care and attention devoted to explaining the basic ideas of the subject. Whenever a new theoretical concept is introduced it is carefully explained by reference to practical examples drawn mainly from the physical sciences. Subjects covered include: spectral analysis which is closely intertwined with the "time domain" approach, elementary notions of Hilbert Space Theory, basic probability theory, and practical analysis of time series data. The inclusion of material on "kalman filtering", state-space filtering", "non-linear models" and continuous time" models completes the impressive list of unique and detailed features which will give this book a prominent position among related literature. The first section-Volume 1-deals with single (univariate) series, while the second-Volume 2-treats the analysis of several (multivariate) series and the problems of prediction, forecasting and control.

The reader is assumed to have knowledge of mathematics to at least first degree standard, although an advanced level of statistical knowledge is not necessary, as the book contains its own treatment of relevant topics in probability theory and statistical inference. The book will appeal to professional mathematical statisticians, in particular, and will also provide physicists, oceanographers, economists, and electrical engineers with a compact account of this subject.

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