Basic Data Analysis for Time Series with R

DeWayne R. Derryberry

• Publisher: Wiley
• Year: 2014
• Print ISBN: 9781118422540
• eBook ISBN: 9781118593363
• Edition: 1
• Topic: Mathematics
• Subtopic: Probability & Statistics
• Index: Mathematics

Presents modern methods to analyzing data with multiple applications in a variety of scientific fields

Written at a readily accessible level, Basic Data Analysis for Time Series with R emphasizes the mathematical importance of collaborative analysis of data used to collect increments of time or space. Balancing a theoretical and practical approach to analyzing data within the context of serial correlation, the book presents a coherent and systematic regression-based approach to model selection. The book illustrates these principles of model selection and model building through the use of information criteria, cross validation, hypothesis tests, and confidence intervals.

Focusing on frequency- and time-domain and trigonometric regression as the primary themes, the book also includes modern topical coverage on Fourier series and Akaike's Information Criterion (AIC). In addition, Basic Data Analysis for Time Series with R also features:

• Real-world examples to provide readers with practical hands-on experience
• Multiple R software subroutines employed with graphical displays
• Numerous exercise sets intended to support readers understanding of the core concepts
• Specific chapters devoted to the analysis of the Wolf sunspot number data and the Vostok ice core data sets

PART I
BASIC CORRELATION STRUCTURES

1
R BASICS

1.1 GETTING STARTED

Programming, writing code, is an integral part of modern data analysis. This book assumes some experience with a programming language. R is simply a high level programming language with several functions that perform specialized statistical analysis. Any R programmer may also write their own functions, but the focus of this book is using functions already in R and writing some basic code using these functions.

In this book, R code is always shaded. Related R output that follows is always underlined or, if extensive, presented in a table. Comments in R code follow the pound sign, #. When R functions are discussed in the text, they will be italicized.

FIGURE 1.1 An example of a plot in R.

Some basic statistical analysis might involve inputting some values and performing some basic statistical analysis. Following the conventions already stated,

# this is a comment x <- c(0.1,1.1,2.3,4.1, 5.6, 8.3) # create a vector of 6 values, these were just made up y <- c(8.7, 6.5, 3.1, 3.3, −1.1, −0.9) #create a second vector plot(x,y,xlab = “this places a label on the x axis”, ylab = “this labels the y axis”) title(“this is a demo”) # either “<-” or “=” can be used for assignments, but “<-” makes more sense. # The reader should be aware that “=” and “<-” are not always interchangeable in R 

(Figure 1.1).

The R code produces the data plotted in Figure 1.1.

[The commands for plots used in the book are simple commands that produce bitmap files that can easily be pasted into any report and resized. The actual graphs produced for the book use the slightly more complex tiff() function for better quality. For more information on better graphs check out help(tiff)].

Naming conventions used in this book:

n	is always the sample size.
y	variants represent response variables.
noise	simulated white noise (independent normal random variables).
error	random error added to models (may not be white noise).
x	variants are independent/explanatory variables.
i	the square root of −1, in other words, we will not use this for any other purpose in this book. We will not use it as a variable or name.
time	usually integers from 1 to n, representing equally spaced time intervals.

A number of simple statistical operations are worth mentioning, using the data simulated for Figure 1.1.

• mean(x) produces the output: 3.583333 which is the mean of the x values.
• sum(x) produces the o...

Table of contents

• Cover
• Titlepage
• Copyright
• PREFACE
• ACKNOWLEDGMENTS
• PART I BASIC CORRELATION STRUCTURES
• PART II ANALYSIS OF PERIODIC DATA AND MODEL SELECTION
• PART III COMPLEX TEMPORAL STRUCTURES
• PART IV SOME DETAILED AND COMPLETE EXAMPLES
• Appendix A Using Datamarket
• Appendix B AIC is PRESS!
• Appendix C A 15-Minute Tutorial on Nonlinear Optimization
• REFERENCES
• INDEX
• End User License Agreement