Basic data analysis for time series with R / DeWayne R. Derryberry, Department of Mathematics and Statistics, Idaho State University, Voise, ID.

Includes bibliographical references and index.

"This book emphasizes the collaborative analysis of data that is used to collect increments of time or space. Written at a readily accessible level, but with the necessary theory in mind, the author uses frequency- and time-domain and trigonometric regression as themes throughout the book. The content includes modern topics such as wavelets, Fourier series, and Akaike's Information Criterion (AIC), which is not typical of current-day "classics." Applications to a variety of scientific fields are showcased. Exercise sets are well crafted with the express intent of supporting pedagogy through recognition and repetition. R subroutines are employed as the software and graphics tool of choice. Brevity is a key component to the retention of the subject matter. The book presumes knowledge of linear algebra, probability, data analysis, and basic computer programming"-- Provided by publisher.

"This book emphasizes the collaborative analysis of data that is used to collect increments of time or space. Written at a readily accessible level, but with the necessary theory in mind, the author uses frequency- and time-domain and trigonometric regression as themes throughout the book"-- Provided by publisher.

Machine generated contents note: Part I -- Basic correlation structures Chapter 0 -- R basics 0.1 Getting started 0.2 Special R conventions 0.3 Common structures 0.4 Common functions 0.5 Time series functions 0.6 Importing data Chapter 1 -- Review of regression and more about R 1.1 Goals of this chapter 1.2 The simple(st) regression model 1.3 Simulating the data from a model and estimating the model parameters in R 1.4 Basic inference for the model 1.5 Residuals analysis -- What can go wrong ... 1.6 Matrix manipulation in R Chapter 2 -- The modeling approach taken in this book and some examples of typical serially correlated data 2.1 Signal and noise 2.2 Time series data 2.3 Simple regression in the framework 2.4 Real data and simulated data 2.5 The diversity of time series data 2.6 Getting data into R Chapter 3 -- Some comments on assumptions 3.1 Introduction 3.2 The normality assumption 3.3 Equal variance 3.4 Independence 3.5 Power of logarithmic transformations illustrated 3.6 Summary Chapter 4 -- The autocorrelation function and AR(1), AR(2) models 4.1 Standard models -- What are the alternatives to white noise? 4.2 Autocovariance and autocorrelation 4.3 The acf() function in R 4.4 The first alternative to white noise: Autoregressive errors -- AR(1), AR(2) Chapter 5 -- The moving average models MA(1) and MA(2) 5.1 The moving average model 5.2 The autocorrelation for MA(1) models 5.3 A duality between MA(l) and AR(m) models 5.4 The autocorrelation for MA(2) models 5.5 Simulated examples of the MA(1) model 5.5 Simulated examples of the MA(2) model 5.6 AR(m) and MA(l) model acf() plots Part II -- Analysis of periodic data and model selection Chapter 6 -- Review of transcendental functions and complex numbers 6.1 Background 6.2 Complex arithmetic 6.3 Some important series 6.4 Useful facts about periodic transcendental functions Chapter 7 -- The power spectrum and the periodogram 7.1 Introduction 7.2 A definition and a simplified form for p(f) 7.3 Inverting p(f) to recover the Ck values 7.4 The power spectrum for some familiar models 7.5 The periodogram, a closer look 7.6 The function spec.pgram() in R Chapter 8 -- Smoothers, the bias-variance tradeoff, and the smoothed periodogram 8.1 Why is smoothing required? 8.2 Smoothing, bias, and variance 8.3 Smoothers used in R 8.4 Smoothing the periodogram for a series with a known period or unknown period. 8.5 Summary Chapter 9 -- A regression model for periodic data. 9.1 The model 9.2 An example: the NYC temperature data 9.2 Complications 1: CO2 data 9.3 Complications 2: Sunspots 9.4 Complications 3: Accidental Deaths 9.5 Summary Chapter 10 -- Basic model selection and cross validation. 10.1 Background 10.2 Hypothesis tests in simple regression 10.3 A more general setting for likelihood ratio tests 10.4 A subtlety different situation 10.5 Information criteria 10.6 Cross validation (Data splitting): NYC temperatures 10.7 Summary Chapter 11 -- Fitting some Fourier series 11.1 Introduction: more complex periodic models 11.2 More complex periodic behavior: Accidental deaths 11.3 The Boise river flow data 11.4 Where do we go from here? Chapter 12 -- Adjusting for AR(1) correlation in complex models 12.1 Introduction 12.2 The two sample t-test -- Uncut and patch cut forest 12.3 The second Sleuth case -- Global warming, a simple regression 12.4 The Semmelweis intervention 12.5 The NYC temperatures (adjusted) 12.6 The Boise river flow data: model selection with filtering 12.7 Implications of AR(1) adjustments and the "skip" method 12.8 Summary Part III -- Complex temporal structures Chapter 13 -- The backshift operator, the impulse response function, and general ARMA models 13.1 The general ARMA model 13.2 The backshift (shift, lag) operator 13.3 The impulse response operator -- intuition 13.4 Impulse response operator, g(B) -- computation 13.5 Interpretation and utility of the impulse response function Chapter 14 -- The Yule-Walker equations and the partial autocorrelation function. 14.1 Background 14.2 Autocovariance of an ARMA(m, l) model 14.3 AR(m) and the Yule-Walker equations 14.4 The partial autocorrelation plot 14.5 The spectrum for ARMA processes 14.6 Summary Chapter 15 -- Modeling philosophy and complete examples 15.1 Modeling overview 15.2 A complex periodic model -- Monthly river flows, Furnas 1931-1978 15.3 A modeling example -- trend and periodicity: CO2 levels at Mauna Lau 15.4 Modeling periodicity with a possible intervention -- two examples 15.5 Periodic models: monthly, weekly, and daily averages 15.6 Summary Part IV -- Some detailed and complete examples Chapter 16 -- the Wolf sunspot number data 16.1 Background 16.2 Unknown period => nonlinear model 16.3 The function nls() in R 16.4 Determining the period 16.5 Instability in the mean, amplitude, and period 16.6 Data splitting for prediction 16.7 Summary Chapter 17 -- Analysis of prostate and breast cancer data 17.1 Background 17.2 The first data set 17.3 The second data set Chapter 18 -- Christopher Tennant/Ben Crosby watershed data 18.1 Background and question 18.2 Looking at the data and fitting Fourier series 18.3 Averaging data 18.4 Results Chapter 19 -- Vostok ice core data 19.1 Source of the data 19.2 Background 19.3 Alignment 19.4 A naïve analysis 19.5 A related simulation 19.6 An AR(1) model for irregular spacing 19.7 Summary Appendices Appendix 1 -- Using Data Market A1.1 Overview A1.2 Loading a time series in DataMarket A1.3 Respecting DataMarket licensing agreements Appendix 2 -- AIC is PRESS A2.1 Introduction A2.2 PRESS A2.3 Connection to Akaike's result A2.4 Normalization and R2 A2.5 An example A2.6 Conclusion and further comments Appendix 3 -- A 15 minute tutorial on optimization and nonlinear regression A3.1 Introduction A3.2 Newton's method for one dimensional nonlinear optimization A3.3 A direction, a step size, and a stopping rule A3.4 What could go wrong? A3.5 Generalizing the optimization problem A3.6 What could go wrong revisited A3.7 What can be done?

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