| Description |
1 online resource |
| Contents |
Machine generated contents note: 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[2014]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[2014]New York City Temperatures, -- 3.6.3. The Diskette and the read.table() Function[2014]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, -- 5. The Autocorrelation Function And AR(1), AR(2) Models -- 5.1. Standard Models[2014]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[2014]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, -- 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 Euler's Formula, -- 7.4. Useful Facts About Periodic Transcendental Functions, -- Exercises, -- 8. The Power Spectrum and the Periodogram -- 8.1. Introduction, -- 8.2. A Definition and a Simplified Form for p(f), -- 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 Naive Code for a Periodogram, -- 8.5.3. An Example[2014]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, |
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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, -- 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[2014]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[2014]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[2014]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[2014]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, -- 13.7.2. Impact of Serial Correlation on p-Values, -- 13.7.3. The "skip" Method, -- 13.8. Summary, -- Exercises, -- 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[2014]Intuition, -- 14.4. Impulse Response Operator, g(B)[2014]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[2014]Walker Equations and the Partial Autocorrelation Function -- 15.1. Background, -- 15.2. Autocovariance of an ARMA(m, /) Model, -- 15.2.1. A Preliminary Result, -- 15.2.2. The Autocovariance Function for ARMA(m, /) Models, -- 15.3. AR(m) and the Yule[2014]Walker Equations, -- 15.3.1. The Equations, -- 15.3.2. The R Function aryw() with an AR(3) Example, -- 15.3.3. Information Criteria-Based Model Selection Using aryw(), -- 15.4. The Partial Autocorrelation Plot, -- 15.4.1. A Sequence of Hypothesis Tests, -- 15.4.2. The pacf() Function[2014]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, |
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Note continued: 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[2014]Monthly River Flows, Fumas 1931-1978, -- 16.2.1. The Data, -- 16.2.2. A Saturated Model, -- 16.2.3. Building an AR(m) Filtering Matrix, -- 16.2.4. Model Selection, -- 16.2.5. Predictions and Prediction Intervals for an AR(3) Model, -- 16.2.6. Data Splitting, -- 16.2.7. Model Selection Based on a Validation Set, -- 16.3. A Modeling Example[2014]Trend and Periodicity: CO2 Levels at Mauna Lau, -- 16.3.1. The Saturated Model and Filter, -- 16.3.2. Model Selection, -- 16.3.3. How Well Does the Model Fit the Data?, -- 16.4. Modeling Periodicity with a Possible Intervention[2014]Two Examples, -- 16.4.1. The General Structure, -- 16.4.2. Directory Assistance, -- 16.4.3. Ozone Levels in Los Angeles, -- 14.5. Interpretation and Utility of the Impulse Response Function, -- Exercises, -- 15. The Yule[2014]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, /) Models, -- 15.3. AR(m) and the Yule[2014]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[2014]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[2014]Monthly River Flows, Fumas 1931-1978, -- 16.2.1. The Data, -- 16.2.2. A Saturated Model, -- 16.2.3. Building an AR(m) Filtering Matrix, -- 16.2.4. Model Selection, -- 16.2.5. Predictions and Prediction Intervals for an AR(3) Model, -- 16.2.6. Data Splitting, -- 16.2.7. Model Selection Based on a Validation Set, -- 16.3. A Modeling Example[2014]Trend and Periodicity: CO2 Levels at Mauna Lau, -- 16.3.1. The Saturated Model and Filter, -- 16.3.2. Model Selection, -- 16.3.3. How Well Does the Model Fit the Data?, -- 16.4. Modeling Periodicity with a Possible Intervention[2014]Two Examples, -- 16.4.1. The General Structure, -- 16.4.2. Directory Assistance, -- 16.4.3. Ozone Levels in Los Angeles, -- 16.5. Periodic Models: Monthly, Weekly, and Daily Averages, -- 16.6. Summary, -- Exercises, -- 17. Wolf's Sunspot Number Data -- 17.1. Background, -- 17.2. Unknown Period -> Nonlinear Model, -- 17.3. The Function nls() in R, -- 17.4. Determining the Period, -- 17.5. Instability in the Mean, Amplitude, and Period, -- 17.6. Data Splitting for Prediction, -- 17.6.1. The Approach, -- 17.6.2. Step 1-Fitting One Step Ahead, -- 17.6.3. The AR Correction, -- 17.6.4. Putting it All Together, -- 17.6.5. Model Selection, -- 17.6.6. Predictions Two Steps Ahead, -- 17.7. Summary, -- Exercises, -- 18. An Analysis of Some Prostate and Breast Cancer Data -- 18.1. Background, -- 18.2. The First Data Set, -- 18.3. The Second Data Set, -- 18.3.1. Background and Questions, -- 18.3.2. Outline of the Statistical Analysis, -- 18.3.3. Looking at the Data, -- 18.3.4. Examining the Residuals for AR(m) Structure, -- 18.3.5. Regression Analysis with Filtered Data, -- Exercises, -- 19. Christopher Tennant/Ben Crosby Watershed Data -- 19.1. Background and Question, -- 19.2. Looking at the Data and Fitting Fourier Series, -- 19.2.1. The Structure of the Data, -- 19.2.2. Fourier Series Fits to the Data, -- 19.2.3. Connecting Patterns in Data to Physical Processes, -- 19.3. Averaging Data, -- 19.4. Results, -- Exercises, -- 20. Vostok Ice Core Data -- 20.1. Source of the Data, -- 20.2. Background, -- 20.3. Alignment, -- 20.3.1. Need for Alignment, and Possible Issues Resulting from Alignment, -- 20.3.2. Is the Pattern in the Temperature Data Maintained?, -- 20.3.3. Are the Dates Closely Matched?, -- 20.3.4. Are the Times Equally Spaced?, -- 20.4. A Naïve Analysis, -- 20.4.1. A Saturated Model, -- 20.4.2. Model Selection, -- 20.4.3. The Association Between CO2 and Temperature Change, -- 20.5. A Related Simulation, -- 20.5.1. The Model and the Question of Interest, -- 20.5.2. Simulation Code in R, -- 20.5.3. A Model Using all of the Simulated Data, -- 20.5.4. A Model Using a Sample of 283 from the Simulated Data, -- 20.6. An AR(1) Model for Irregular Spacing, -- 20.6.1. Motivation, -- 20.6.2. Method, -- 20.6.3. Results, -- 20.6.4. Sensitivity Analysis, -- 20.6.5. A Final Analysis, Well Not Quite, -- 20.7. Summary, -- Exercises, -- A.1. Overview, -- A.2. Loading a Time Series in Datamarket, -- A.3. Respecting Datamarket Licensing Agreements, -- B.1. Introduction, -- B.2. PRESS, -- B.3. Connection to Akaike's Result, -- B.4. Normalization and R2, -- B.5. An example, -- B.6. Conclusion and Further Comments, -- C.1. Introduction, -- C.2. Newton's Method for One-Dimensional Nonlinear Optimization, -- C.3. A Sequence of Directions, Step Sizes, and a Stopping Rule, -- C.4. What Could Go Wrong?, -- C.5. Generalizing the Optimization Problem, -- C.6. What Could Go Wrong[2014]Revisited, -- C.7. What Can be Done? |
| Summary |
"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 |
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"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 |
| Bibliography |
Includes bibliographical references and index |
| Notes |
Copyright © John Wiley & Sons |
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Print version record and CIP data provided by publisher |
| Subject |
Time-series analysis -- Data processing
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R (Computer program language)
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MATHEMATICS -- Probability & Statistics -- General.
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R (Computer program language)
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Time-series analysis -- Data processing
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Anàlisi de sèries temporals.
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Processament de dades.
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R (Llenguatge de programació)
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| Genre/Form |
Llibres electrònics.
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| Form |
Electronic book
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| LC no. |
2014007300 |
| ISBN |
9781118593370 |
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1118593375 |
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9781118593363 |
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1118593367 |
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9781118593233 |
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1118593235 |
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1118422546 |
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9781118422540 |
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9781322007595 |
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1322007594 |
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