Applied Time Series Analysis with R

Wayne A. Woodward, Henry L. Gray, Alan C. Elliott

• Publisher: CRC Press
• Year: 2017
• Print ISBN: 9781032097220
• eBook ISBN: 9781498734318
• Edition: 2
• Topic: Mathematics
• Subtopic: Probability & Statistics
• Index: Mathematics

Virtually any random process developing chronologically can be viewed as a time series. In economics closing prices of stocks, the cost of money, the jobless rate, and retail sales are just a few examples of many. Developed from course notes and extensively classroom-tested, Applied Time Series Analysis with R, Second Edition includes examples across a variety of fields, develops theory, and provides an R-based software package to aid in addressing time series problems in a broad spectrum of fields. The material is organized in an optimal format for graduate students in statistics as well as in the natural and social sciences to learn to use and understand the tools of applied time series analysis.

Features

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• Gives readers the ability to actually solve significant real-world problems

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• Addresses many types of nonstationary time series and cutting-edge methodologies

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• Promotes understanding of the data and associated models rather than viewing it as the output of a "black box"

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• Provides the R package tswge available on CRAN which contains functions and over 100 real and simulated data sets to accompany the book. Extensive help regarding the use of tswge functions is provided in appendices and on an associated website.

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• Over 150 exercises and extensive support for instructors

The second edition includes additional real-data examples, uses R-based code that helps students easily analyze data, generate realizations from models, and explore the associated characteristics. It also adds discussion of new advances in the analysis of long memory data and data with time-varying frequencies (TVF).

1

Stationary Time Series

In basic statistical analysis, attention is usually focused on data samples, X₁, X₂, …, X_n, where the X_is are independent and identically distributed random variables. In a typical introductory course in univariate mathematical statistics, the case in which samples are not independent but are in fact correlated is not generally covered. However, when data are sampled at neighboring points in time, it is very likely that such observations will be correlated. Such time-dependent sampling schemes are very common. Examples include the following:

• Daily Dow Jones stock market closes over a given period

• Monthly unemployment data for the United States

• Annual global temperature data for the past 100 years

• Monthly incidence rate of influenza

• Average number of sunspots observed each year since 1749

• West Texas monthly intermediate crude oil prices

• Average monthly temperatures for Pennsylvania

Note that in each of these cases, an observed data value is (probably) not independent of nearby observations. That is, the data are correlated and are therefore not appropriately analyzed using univariate statistical methods based on independence. Nevertheless, these types of data are abundant in fields such as economics, biology, medicine, and the physical and engineering sciences, where there is interest in understanding the mechanisms underlying these data, producing forecasts of future behavior, and drawing conclusions from the data. Time series analysis is the study of these types of data, and in this book we will introduce you to the extensive collection of tools and models for using the inherent correlation structure in such data sets to assist in their analysis and interpretation.

As examples, in Figure 1.1a we show monthly West Texas intermediate crude oil prices from January 2000 to October 2009, and in Figure 1.1b we show the average monthly temperatures in degrees Fahrenheit for Pennsylvania from January 1990 to December 2004. In both cases, the monthly data are certainly correlated. In the case of the oil process, it seems that prices for a given month are positively correlated with the prices for nearby (past and future) months. In the case of Pennsylvania temperatures, there is a clear 12 month (annual) pattern as would be expected because of the natural ...

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Table of Contents
• Preface for Second Edition
• Acknowledgments
• 1 Stationary Time Series
• 2 Linear Filters
• 3 ARMA Time Series Models
• 4 Other Stationary Time Series Models
• 5 Nonstationary Time Series Models
• 6 Forecasting
• 7 Parameter Estimation
• 8 Model Identification
• 9 Model Building
• 10 Vector-Valued (Multivariate) Time Series
• 11 Long-Memory Processes
• 12 Wavelets
• 13 G-Stationary Processes
• References
• Index