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2017 | Buch

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Time Series Analysis and Its Applications

With R Examples

verfasst von: Robert H. Shumway, David S. Stoffer

Verlag: Springer International Publishing

Buchreihe : Springer Texts in Statistics

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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Über dieses Buch

The fourth edition of this popular graduate textbook, like its predecessors, presents a balanced and comprehensive treatment of both time and frequency domain methods with accompanying theory. Numerous examples using nontrivial data illustrate solutions to problems such as discovering natural and anthropogenic climate change, evaluating pain perception experiments using functional magnetic resonance imaging, and monitoring a nuclear test ban treaty.

The book is designed as a textbook for graduate level students in the physical, biological, and social sciences and as a graduate level text in statistics. Some parts may also serve as an undergraduate introductory course. Theory and methodology are separated to allow presentations on different levels. In addition to coverage of classical methods of time series regression, ARIMA models, spectral analysis and state-space models, the text includes modern developments including categorical time series analysis, multivariate spectral methods and long memory series.

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Inhaltsverzeichnis

Frontmatter

Chapter 1. Characteristics of Time Series

Abstract

The analysis of experimental data that have been observed at different points in time leads to new and unique problems in statistical modeling and inference. The obvious correlation introduced by the sampling of adjacent points in time can severely restrict the applicability of the many conventional statistical methods traditionally dependent on the assumption that these adjacent observations are independent and identically distributed. The systematic approach by which one goes about answering the mathematical and statistical questions posed by these time correlations is commonly referred to as time series analysis.

Robert H. Shumway, David S. Stoffer

Chapter 2. Time Series Regression and Exploratory Data Analysis

Abstract

In this chapter we introduce classical multiple linear regression in a time series context, model selection, exploratory data analysis for preprocessing nonstationary time series (for example trend removal), the concept of differencing and the backshift operator, variance stabilization, and nonparametric smoothing of time series.

Robert H. Shumway, David S. Stoffer

Chapter 3. ARIMA Models

Abstract

Classical regression is often insufficient for explaining all of the interesting dynamics of a time series. For example, the ACF of the residuals of the simple linear regression fit to the price of chicken data (see Example 2.4) reveals additional structure in the data that regression did not capture. Instead, the introduction of correlation that may be generated through lagged linear relations leads to proposing the autoregressive (AR) and autoregressive moving average (ARMA) models that were presented in Whittle [209]. Adding nonstationary models to the mix leads to the autoregressive integrated moving average (ARIMA) model popularized in the landmark work by Box and Jenkins [30]. The Box–Jenkins method for identifying ARIMA models is given in this chapter along with techniques for parameter estimation and forecasting for these models. A partial theoretical justification of the use of ARMA models is discussed in Sect. B.4.

Robert H. Shumway, David S. Stoffer

Chapter 4. Spectral Analysis and Filtering

Abstract

In this chapter, we focus on the frequency domain approach to time series analysis. We argue that the concept of regularity of a series can best be expressed in terms of periodic variations of the underlying phenomenon that produced the series. Many of the examples in Sect. 1.1 are time series that are driven by periodic components. For example, the speech recording in Fig. 1.3 contains a complicated mixture of frequencies related to the opening and closing of the glottis. The monthly SOI displayed in Fig. 1.5 contains two periodicities, a seasonal periodic component of 12 months and an El Niño component of about three to seven years. Of fundamental interest is the return period of the El Niño phenomenon, which can have profound effects on local climate.

Robert H. Shumway, David S. Stoffer

Chapter 5. Additional Time Domain Topics

Abstract

In this chapter, we present material that may be considered special or advanced topics in the time domain. Chapter 6 is devoted to one of the most useful and interesting time domain topics, state-space models. Consequently, we do not cover state-space models or related topics—of which there are many—in this chapter. This chapter contains sections of independent topics that may be read in any order. Most of the sections depend on a basic knowledge of ARMA models, forecasting and estimation, which is the material that is covered in Chap. 3. A few sections, for example the section on long memory models, require some knowledge of spectral analysis and related topics covered in Chap. 4. In addition to long memory, we discuss unit root testing, GARCH models, threshold models, lagged regression or transfer functions, and selected topics in multivariate ARMAX models.

Robert H. Shumway, David S. Stoffer

Chapter 6. State Space Models

Abstract

A very general model that subsumes a whole class of special cases of interest in much the same way that linear regression does is the state-space model or the dynamic linear model, which was introduced in Kalman [112] and Kalman and Bucy [113]. The model arose in the space tracking setting, where the state equation defines the motion equations for the position or state of a spacecraft with location xt and the data yt reflect information that can be observed from a tracking device such as velocity and azimuth. Although introduced as a method primarily for use in aerospace-related research, the model has been applied to modeling data from economics (Harrison and Stevens [90]; Harvey and Pierse [92]; Harvey and Todd [91]; Kitagawa and Gersch [119], Shumway and Stoffer [181]), medicine (Jones [108]) and the soil sciences (Shumway [183], §3.4.5). An excellent treatment of time series analysis based on the state space model is the text by Durbin and Koopman [55]. A modern treatment of nonlinear state space models can be found in Douc, Moulines and Stoffer [53].

Robert H. Shumway, David S. Stoffer

Chapter 7. Statistical Methods in the Frequency Domain

Abstract

In previous chapters, we sawmany applied time series problems that involved relating series to each other or to evaluating the effects of treatments or design parameters that arise when time-varying phenomena are subjected to periodic stimuli. In many cases, the nature of the physical or biological phenomena under study are best described by their Fourier components rather than by the difference equations involved in ARIMA or state-space models. The fundamental tools we use in studying periodic phenomena are the discrete Fourier transforms (DFTs) of the processes and their statistical properties. Hence, in Sect. 7.2, we review the properties of the DFT of a multivariate time series and discuss various approximations to the likelihood function based on the large-sample properties and the properties of the complex multivariate normal distribution. This enables extension of the classical techniques such as ANOVA and principal component analysis to the multivariate time series case, which is the focus of this chapter.

Robert H. Shumway, David S. Stoffer

Backmatter

Titel: Time Series Analysis and Its Applications
verfasst von: Robert H. Shumway
David S. Stoffer
Copyright-Jahr: 2017
Verlag: Springer International Publishing
Electronic ISBN: 978-3-319-52452-8
Print ISBN: 978-3-319-52451-1
DOI: https://doi.org/10.1007/978-3-319-52452-8

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