Basic data analysis for time series with R

• Main Author: Derryberry, DeWayne R
• Format: eBook Book
• Language: English
• Published: Hoboken, N.J WILEY 2014; Wiley; John Wiley & Sons, Incorporated; Wiley-Blackwell; John Wiley & Sons, Inc
• Edition: 1
• Subjects: Data processing; Mathematics; Probability & Statistics; R (Computer program language); Time-series analysis
• ISBN: 1118422546; 1118593375; 9781118593370; 9781118422540; 1118593367; 9781118593363
• DOI: 10.1002/9781118593233

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 spac...

Table of Contents:

• Basic data analysis for time series with R -- Contents -- Preface -- Acknowledgments -- Part I: Basic Correlation Structures -- 1. R Basics -- 2. Review of Regression and More About R -- 3. The Modeling Approach Taken in this Book and Some Examples of Typical Serially Correlated Data -- 4. Some Comments on Assumptions -- 5. The Autocorrelation Function And AR(1), AR(2) Models -- 6. The Moving Average Models MA(1) And MA(2) -- Part II: Analysis of Periodic Data and Model Selection -- 7. Review of Transcendental Functions and Complex Numbers -- 8. The Power Spectrum and the Periodogram -- 9. Smoothers, The Bias-Variance Tradeoff, and the Smoothed Periodogram -- 10. A Regression Model for Periodic Data -- 11. Model Selection and Cross-Validation -- 12. Fitting Fourier series -- 13. Adjusting for AR(1) Correlation in Complex Models -- Part III: Complex Temporal Structures -- 14. The backshift operator, the impulse response function, and general ARMA models -- 15. The Yule–Walker Equations and the Partial Autocorrelation Function -- 16. Modeling philosophy and Complete Examples -- Part IV: Some Detailed and Complete Examples -- 17. Wolfs sunspot number data -- 18. An Analysis of Some Prostate and Breast Cancer Data -- 19. Christopher Tennant/Ben Crosby Watershed Data -- 20. Vostok Ice Core Data -- Appendix A: Using Datamarket -- Appendix B: AIC Is Press! -- Appendix C: A 15-minute Tutorial on Nonlinear Optimization -- References -- Index -- EULA.
• 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 Autocorrelation -- 5.2.1 Stationarity -- 5.2.2 A Note About Conditions -- 5.2.3 Properties of Autocovariance -- 5.2.4 White Noise -- 5.2.5 Estimation of the Autocovariance and Autocorrelation -- 5.3 The acf() Function in R -- 5.3.1 Background -- 5.3.2 The Basic Code for Estimating the Autocovariance -- 5.4 The First Alternative to White Noise: Autoregressive Errors-AR(1), AR(2) -- 5.4.1 Definition of the AR(1) and AR(2) Models -- 5.4.2 Some Preliminary Facts -- 5.4.3 The AR(1) Model Autocorrelation and Autocovariance -- 5.4.4 Using Correlation and Scatterplots to Illustrate the AR(1) Model -- 5.4.5 The AR(2) Model Autocorrelation and Autocovariance -- 5.4.6 Simulating Data for AR(m) Models -- 5.4.7 Examples of Stable and Unstable AR(1) Models -- 5.4.8 Examples of Stable and Unstable AR(2) Models -- Exercises -- 6 The Moving Average Models MA(1) And MA(2) -- 6.1 The Moving Average Model -- 6.2 The Autocorrelation for MA(1) Models -- 6.3 A Duality Between MA(l) And AR(m) Models -- 6.4 The Autocorrelation for MA(2) Models -- 6.5 Simulated Examples of the MA(1) Model -- 6.6 Simulated Examples of the MA(2) Model -- 6.7 AR(m) and MA(l) model acf() Plots -- Exercises -- PART II Analysis of Periodic Data and Model Selection -- 7 Review of Transcendental Functions and Complex Numbers -- 7.1 Background -- 7.2 Complex Arithmetic -- 7.2.1 The Number i -- 7.2.2 Complex Conjugates -- 7.2.3 The Magnitude of a Complex Number -- 7.3 Some Important Series -- 7.3.1 The Geometric and Some Transcendental Series -- 7.3.2 A Rationale for Eulers Formula -- 7.4 Useful Facts About Periodic Transcendental Functions -- Exercises -- 8 The Power Spectrum and the Periodogram -- 8.1 Introduction
• 12.2.1 Fourier Series Structure -- 12.2.2 R Code for Fitting Large Fourier Series -- 12.2.3 Model Selection with AIC -- 12.2.4 Model Selection with Likelihood Ratio Tests -- 12.2.5 Data Splitting -- 12.2.6 Accidental Deaths-Some Comment on Periodic Data -- 12.3 The Boise river flow data -- 12.3.1 The Data -- 12.3.2 Model Selection with AIC -- 12.3.3 Data Splitting -- 12.3.4 The Residuals -- 12.4 Where do we go from here? -- EXERCISES -- 13 Adjusting for AR(1) Correlation in Complex Models -- 13.1 Introduction -- 13.2 The Two-Sample t-Test-UNCUT and Patch-Cut Forest -- 13.2.1 The Sleuth Data and the Question of Interest -- 13.2.2 A Simple Adjustment for t-Tests When the Residuals Are AR(1) -- 13.2.3 A Simulation Example -- 13.2.4 Analysis of the Sleuth Data -- 13.3 The Second Sleuth Case-Global Warming, A Simple Regression -- 13.3.1 The Data and the Question -- 13.3.2 Filtering to Produce (Quasi-)Independent Observations -- 13.3.3 Simulated Example-Regression -- 13.3.4 Analysis of the Regression Case -- 13.3.5 The Filtering Approach for the Logging Case -- 13.3.6 A Few Comments on Filtering -- 13.4 The Semmelweis Intervention -- 13.4.1 The Data -- 13.4.2 Why Serial Correlation? -- 13.4.3 How This Data Differs from the Patch/Uncut Case -- 13.4.4 Filtered Analysis -- 13.4.5 Transformations and Inference -- 13.5 The NYC Temperatures (Adjusted) -- 13.5.1 The Data and Prediction Intervals -- 13.5.2 The AR(1) Prediction Model -- 13.5.3 A Simulation to Evaluate These Formulas -- 13.5.4 Application to NYC Data -- 13.6 The Boise River Flow Data: Model Selection With Filtering -- 13.6.1 The Revised Model Selection Problem -- 13.6.2 Comments on R2 and R2pred -- 13.6.3 Model Selection After Filtering with a Matrix -- 13.7 Implications of AR(1) Adjustments and the "Skip" Method -- 13.7.1 Adjustments for AR(1) Autocorrelation
• 8.2 A Definition and a Simplified Form for -- 8.3 Inverting p(f) to Recover the Ck Values -- 8.4 The Power Spectrum for Some Familiar Models -- 8.4.1 White Noise -- 8.4.2 The Spectrum for AR(1) Models -- 8.4.3 The Spectrum for AR(2) Models -- 8.5 The Periodogram, a Closer Look -- 8.5.1 Why is the Periodogram Useful? -- 8.5.2 Some Naïve Code for a Periodogram -- 8.5.3 An Example-The Sunspot Data -- 8.6 The Function SPEC.PGRAM() in R -- Exercises -- 9 Smoothers, The Bias-Variance Tradeoff, and the Smoothed Periodogram -- 9.1 Why is Smoothing Required? -- 9.2 Smoothing, Bias, and Variance -- 9.3 Smoothers Used in R -- 9.3.1 The R Function Lowess() -- 9.3.2 The R Function Smooth.Spline() -- 9.3.3 Kernel Smoothers in Spec.Pgram() -- 9.4 Smoothing the Periodogram for a Series With a Known and Unknown Period -- 9.4.1 Period Known -- 9.4.2 Period Unknown -- 9.5 Summary -- Exercises -- 10 A Regression Model for Periodic Data -- 10.1 The Model -- 10.2 An Example: The NYC Temperature Data -- 10.2.1 Fitting a Periodic Function -- 10.2.2 An Outlier -- 10.2.3 Refitting the Model with the Outlier Corrected -- 10.3 Complications 1: CO2 Data -- 10.4 Complications 2: Sunspot Numbers -- 10.5 Complications 3: Accidental Deaths -- 10.6 Summary -- Exercises -- 11 Model Selection and Cross-Validation -- 11.1 Background -- 11.2 Hypothesis tests in simple regression -- 11.3 A more general setting for likelihood ratio tests -- 11.4 A subtlety different situation -- 11.5 Information criteria -- 11.6 Cross-validation (Data splitting): NYC temperatures -- 11.6.1 Explained Variation, R2 -- 11.6.2 Data Splitting -- 11.6.3 Leave-One-Out Cross-Validation -- 11.6.4 AIC as Leave-One-Out Cross-Validation -- 11.7 Summary -- Exercises -- 12 Fitting Fourier series -- 12.1 Introduction: more complex periodic models -- 12.2 More complex periodic behavior: Accidental deaths
• Intro -- Basic Data Analysis for Time Series with R -- Contents -- Preface -- What This Book is About -- Motivation -- Required Background -- A Couple of Odd Features -- Acknowledgments -- PART I Basic Correlation Structures -- 1 R Basics -- 1.1 Getting Started -- 1.2 Special R Conventions -- 1.3 Common Structures -- 1.4 Common Functions -- 1.5 Time Series Functions -- 1.6 Importing Data -- Exercises -- 2 Review of Regression and More About R -- 2.1 Goals of This Chapter -- 2.2 The Simple(ST) Regression Model -- 2.2.1 Ordinary Least Squares -- 2.2.2 Properties of OLS Estimates -- 2.2.3 Matrix Representation of the Problem -- 2.3 Simulating The Data From A Model and Estimating The Model Parameters in R -- 2.3.1 Simulating Data -- 2.3.2 Estimating the Model Parameters in R -- 2.4 Basic Inference for the Model -- 2.5 Residuals Analysis-What Can go Wrong… -- 2.6 Matrix Manipulation in R -- 2.6.1 Introduction -- 2.6.2 OLS the Hard Way -- 2.6.3 Some Other Matrix Commands -- Exercises -- 3 The Modeling Approach Taken in this Book and Some Examples of Typical Serially Correlated Data -- 3.1 Signal and Noise -- 3.2 Time Series Data -- 3.3 Simple Regression in the Framework -- 3.4 Real Data and Simulated Data -- 3.5 The Diversity of Time Series Data -- 3.6 Getting Data Into R -- 3.6.1 Overview -- 3.6.2 The Diskette and the scan() and ts() Functions-New York City Temperatures -- 3.6.3 The Diskette and the read.table() Function-The Semmelweis Data -- 3.6.4 Cut and Paste Data to a Text Editor -- Exercises -- 4 Some Comments on Assumptions -- 4.1 Introduction -- 4.2 The Normality Assumption -- 4.2.1 Right Skew -- 4.2.2 Left Skew -- 4.2.3 Heavy Tails -- 4.3 Equal Variance -- 4.3.1 Two-Sample t-Test -- 4.3.2 Regression -- 4.4 Independence -- 4.5 Power of Logarithmic Transformations Illustrated -- 4.6 Summary -- Exercises
• 13.7.2 Impact of Serial Correlation on p-Values -- 13.7.3 The "skip" Method -- 13.8 Summary -- Exercises -- PART III Complex Temporal Structures -- 14 The backshift operator, the impulse response function, and general ARMA models -- 14.1 The general ARMA model -- 14.1.1 The Mathematical Formulation -- 14.1.2 The arima.sim() Function in R Revisited -- 14.1.3 Examples of ARMA(m,l) Models -- 14.2 The backshift (shift, lag) operator -- 14.2.1 Definition of B -- 14.2.2 The Stationary Conditions for a General AR(m) Model -- 14.2.3 ARMA(m,l) Models and the Backshift Operator -- 14.2.4 More Examples of ARMA(m,l) Models -- 14.3 The impulse response operator - intuition -- 14.4 Impulse response operator, g(B)-computation -- 14.4.1 Definition of g(B) -- 14.4.2 Computing the Coefficients, -- 14.4.3 Plotting an Impulse Response Function -- 14.5 Interpretation and utility of the impulse response function -- Exercises -- 15 The Yule-Walker Equations and the Partial Autocorrelation Function -- 15.1 Background -- 15.2 Autocovariance of an ARMA(m,l) Model -- 15.2.1 A Preliminary Result -- 15.2.2 The Autocovariance Function for ARMA(m,l) Models -- 15.3 AR(m) and the Yule-Walker Equations -- 15.3.1 The Equations -- 15.3.2 The R Function ar.yw() with an AR(3) Example -- 15.3.3 Information Criteria-Based Model Selection Using ar.yw() -- 15.4 The Partial Autocorrelation Plot -- 15.4.1 A Sequence of Hypothesis Tests -- 15.4.2 The pacf() Function-Hypothesis Tests Presented in a Plot -- 15.5 The Spectrum For Arma Processes -- 15.6 Summary -- Exercises -- 16 Modeling philosophy and Complete Examples -- 16.1 Modeling overview -- 16.1.1 The Algorithm -- 16.1.2 The Underlying Assumption -- 16.1.3 An Example Using an AR(m) Filter to Model MA(3) -- 16.1.4 Generalizing the "Skip" Method -- 16.2 A complex periodic model-Monthly river flows, Furnas 1931-1978 -- 16.2.1 The Data
• 16.2.2 A Saturated Model