book

Basic Data Analysis for Time Series with R

Name: Basic Data Analysis for Time Series with R
Author: DeWayne Derryberry
ISBN: 9781118422540

by DeWayne Derryberry

July 2014

Intermediate to advanced

320 pages

8h 11m

English

Wiley

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PREFACE
What This Book is AboutMotivationRequired BackgroundA Couple of Odd Features
ACKNOWLEDGMENTS
PART I BASIC CORRELATION STRUCTURES
1 R Basics
1.1 Getting Started1.2 Special R Conventions1.3 Common Structures1.4 Common Functions1.5 Time Series Functions1.6 Importing DataExercises
2 Review of Regression and More About R
2.1 Goals of This Chapter2.2 The Simple(ST) Regression Model2.3 Simulating The Data From A Model and Estimating The Model Parameters in R2.4 Basic Inference for the Model2.5 Residuals Analysis—What Can go Wrong…2.6 Matrix Manipulation in RExercises
3 The Modeling Approach Taken in this Book and Some Examples of Typical Serially Correlated Data
3.1 Signal and Noise3.2 Time Series Data3.3 Simple Regression in the Framework3.4 Real Data and Simulated Data3.5 The Diversity of Time Series Data3.6 Getting Data Into RExercises
4 Some Comments on Assumptions
4.1 Introduction4.2 The Normality Assumption4.3 Equal Variance4.4 Independence4.5 Power of Logarithmic Transformations Illustrated4.6 SummaryExercises
5 The Autocorrelation Function And AR(1), AR(2) Models
5.1 Standard Models—What are the Alternatives to WHITE NOISE?5.2 Autocovariance and Autocorrelation5.3 The acf() Function in R5.4 The First Alternative to White Noise: Autoregressive Errors—AR(1), AR(2)Exercises
6 The Moving Average Models MA(1) And MA(2)
6.1 The Moving Average Model6.2 The Autocorrelation for MA(1) Models6.3 A Duality Between MA(l) And AR(m) Models6.4 The Autocorrelation for MA(2) Models6.5 Simulated Examples of the MA(1) Model6.6 Simulated Examples of the MA(2) Model6.7 AR(m) and MA(l) model acf() PlotsExercises
PART II ANALYSIS OF PERIODIC DATA AND MODEL SELECTION

7 Review of Transcendental Functions and Complex Numbers
7.1 Background7.2 Complex Arithmetic7.3 Some Important Series7.4 Useful Facts About Periodic Transcendental FunctionsExercises
8 The Power Spectrum and the Periodogram
8.1 Introduction8.2 A Definition and a Simplified Form for p(f)8.3 Inverting p(f) to Recover the Ck Values8.4 The Power Spectrum for Some Familiar Models8.5 The Periodogram, a Closer Look8.6 The Function SPEC.PGRAM() in RExercises
9 Smoothers, The Bias-Variance Tradeoff, and the Smoothed Periodogram
9.1 Why is Smoothing Required?9.2 Smoothing, Bias, and Variance9.3 Smoothers Used in R9.4 Smoothing the Periodogram for a Series With a Known and Unknown Period9.5 SummaryExercises
10 A Regression Model for Periodic Data
10.1 The Model10.2 An Example: The NYC Temperature Data10.3 Complications 1: CO2 Data10.4 Complications 2: Sunspot Numbers10.5 Complications 3: Accidental Deaths10.6 SummaryExercises
11 Model Selection and Cross-Validation
11.1 Background11.2 Hypothesis tests in simple regression11.3 A more general setting for likelihood ratio tests11.4 A subtlety different situation11.5 Information criteria11.6 Cross-validation (Data splitting): NYC temperatures11.7 SummaryExercises
12 Fitting Fourier series
12.1 Introduction: more complex periodic models12.2 More complex periodic behavior: Accidental deaths12.3 The Boise river flow data12.4 Where do we go from here?Exercises
13 Adjusting for AR(1) Correlation in Complex Models
13.1 Introduction13.2 The Two-Sample t-Test—UNCUT and Patch-Cut Forest13.3 The Second Sleuth Case—Global Warming, A Simple Regression13.4 The Semmelweis Intervention13.5 The NYC Temperatures (Adjusted)13.6 The Boise River Flow Data: Model Selection With Filtering13.7 Implications of AR(1) Adjustments and the “Skip” Method13.8 SummaryExercises
PART III COMPLEX TEMPORAL STRUCTURES
14 The backshift operator, the impulse response function, and general ARMA models
14.1 The general ARMA model14.2 The backshift (shift, lag) operator14.3 The impulse response operator – intuition14.4 Impulse response operator, g(B)—computation14.5 Interpretation and utility of the impulse response functionExercises
15 The Yule–Walker Equations and the Partial Autocorrelation Function
15.1 Background15.2 Autocovariance of an ARMA(m,l) Model15.3 AR(m) and the Yule–Walker Equations15.4 The Partial Autocorrelation Plot15.5 The Spectrum For Arma Processes15.6 SummaryExercises
16 Modeling philosophy and Complete Examples
16.1 Modeling overview16.2 A complex periodic model—Monthly river flows, Furnas 1931–197816.3 A modeling example—trend and periodicity: CO2 levels at Mauna Lau16.4 Modeling periodicity with a possible intervention—two examples16.5 Periodic models: monthly, weekly, and daily averages16.6 SummaryExercises
PART IV SOME DETAILED AND COMPLETE EXAMPLES
17 Wolf's sunspot number data
17.1 Background17.2 Unknown period ⇒ nonlinear model17.3 The function nls() IN R17.4 Determining the period17.5 Instability in the mean, amplitude, and period17.6 Data splitting for prediction17.7 SummaryExercises
18 An Analysis of Some Prostate and Breast Cancer Data
18.1 Background18.2 The First Data Set18.3 The Second Data SetExercises
19 Christopher Tennant/Ben Crosby Watershed Data
19.1 Background and Question19.2 Looking at the Data and Fitting Fourier Series19.3 Averaging Data19.4 ResultsExercises
20 Vostok Ice Core Data
20.1 Source of the Data20.2 Background20.3 Alignment20.4 A NaÏve Analysis20.5 A Related Simulation20.6 An AR(1) Model for Irregular Spacing20.7 SummaryExercises
Appendix A Using Datamarket
A.1 OverviewA.2 Loading a Time Series in DatamarketA.3 Respecting Datamarket Licensing Agreements
Appendix B AIC is PRESS!
B.1 IntroductionB.2 PressB.3 Connection to Akaike's resultB.4 Normalization and R2B.5 An exampleB.6 Conclusion and further comments
Appendix C A 15-Minute Tutorial on Nonlinear Optimization
C.1 IntroductionC.2 Newton's method for one-dimensional nonlinear optimizationC.3 A sequence of directions, step sizes, and a stopping ruleC.4 What could go wrong?C.5 Generalizing the optimization problemC.6 What could go wrong—revisitedC.7 What can be done?
REFERENCES
INDEX
End User License Agreement

Overview

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

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