Time Series for Data Science: Analysis and Forecasting
- Length: 506 pages
- Edition: 1
- Language: English
- Publisher: Chapman and Hall/CRC
- Publication Date: 2022-08-01
- ISBN-10: 036753794X
- ISBN-13: 9780367537944
- Sales Rank: #550929 (See Top 100 Books)
Data Science students and practitioners want to find a forecast that “works” and don’t want to be constrained to a single forecasting strategy, Practical Time Series Analysis for Data Science discusses techniques of ensemble modelling for combining information from several strategies. Covering time series regression models, exponential smoothing, Holt-Winters forecasting, and Neural Networks. It places a particular emphasis on classical ARMA and ARIMA models that is often lacking from other textbooks on the subject.
Practical Time Series Analysis for Data Science is an accessible guide that doesn’t require a background in calculus to be engaging but does not shy away from deeper explanations of the techniques discussed.
Features:
Provides a thorough coverage and comparison of a wide array of time series models and methods: Exponential Smoothing, Holt Winters, ARMA and ARIMA, deep learning models including RNNs, LSTMs, GRUs, and ensemble models composed of combinations of these models. Introduces the factor table representation of ARMA and ARIMA models. This representation is not available in any other book at this level and is extremely useful in both practice and pedagogy. Uses real world examples that can be readily found via web links from sources such as the US Bureau of Statistics, Department of Transportation and the World Bank. There is an accompanying R package that is easy to use and requires little or no previous R experience. The package implements the wide variety of models and methods presented in the book and has tremendous pedagogical use.
Cover Half Title Series Page Title Page Copyright Page Dedication Table of Contents Preface Acknowledgments Authors 1 Working with Data Collected Over Time 1.1 Introduction 1.2 Time Series Datasets 1.2.1 Cyclic Data 1.2.2 Trends 1.3 The Programming Language R 1.3.1 The tswge Time Series Package 1.3.2 Base R 1.3.3 Plotting Time Series Data in R 1.3.4 The ts Object 1.3.5 The plotts.wge Function in tswge 1.3.6 Loading Time Series Data into R 1.3.7 Accessing Time Series Data 1.4 Dealing with Messy Data 1.4.1 Preparing Time Series Data for Analysis: Cleaning, Wrangling, and Imputation 1.5 Concluding Remarks Appendix 1A tswge Datasets INTRODUCED IN this Chapter Problems 2 Exploring Time Series Data 2.1 Understanding and Visualizing Data 2.1.1 Smoothing Time Series Data 2.1.2 Decomposing Seasonal Data 2.1.3 Seasonal Adjustment 2.2 Forecasting 2.2.1 Predictive Moving Average Smoother 2.2.2 Exponential Smoothing 2.2.3 Holt-Winters Forecasting 2.2.4 Assessing the Accuracy of Forecasts 2.3 Concluding Remarks Appendix 2A tswge functions TSWGE DATASETS INTRODUCED IN CHAPTER 2 3 Statistical Basics for Time Series Analysis 3.1 Statistics Basics 3.1.1 Univariate Data 3.1.2 Multivariate Data 3.1.3 Independent vs Dependent Data 3.2 Time Series and Realizations 3.2.1 Multiple Realizations 3.2.2 The Effect of Realization Length 3.3 Stationary Time Series 3.3.1 Plotting the Autocorrelations of a Stationary Process 3.3.2 Estimating the Parameters of a Stationary Process 3.4 Concluding Remarks Appendix 3A Appendix 3B TSWGE FUNCTION BASE R COMMANDS Problems 4 The Frequency Domain 4.1 Trigonometric Review and Terminology 4.2 The Spectral Density 4.2.1 Euler’s Formula 4.2.2 Definition and Properties of the Spectrum and Spectral Density 4.2.3 Estimating the Spectral Density 4.3 Smoothing and Filtering 4.3.1 Types of Filters 4.3.2 The Butterworth Filter 4.4 Concluding Remarks Appendix 4A tswge functions Problems 5 ARMA Models 5.1 The Autoregressive Model 5.1.1 The AR(1) Model 5.1.2 The AR(2) Model 5.1.3 The AR(p) Models 5.1.4 Linear Filters, the General Linear Process, and AR(p) Models 5.2 Autoregressive-Moving Average (ARMA) Models 5.2.1 Moving Average Models 5.2.2 ARMA(p,q) Models 5.3 Concluding Remarks Appendix 5AtswgeFunctions Appendix 5B Stationarity Conditions of an AR(1) Problem Set 6 ARMA Fitting and Forecasting 6.1 Fitting ARMA Models to Data 6.1.1 Estimating the Parameters of an ARMA(p,q) Model 6.1.2 ARMA Model Identification 6.2 Forecasting Using an ARMA(p,q) Model 6.2.1 ARMA Forecasting Setting, Notation, and Strategy 6.2.2 Forecasting Using an AR(p) Model 6.2.3 Basic Formula for Forecasting Using an ARMA(p,q) Model 6.2.4 Eventual Forecast Functions 6.2.5 Probability Limits for ARMA Forecasts 6.2.6 Assessing Forecast Performance 6.3 Concluding Remarks Appendix 6A tswge functions Problems 7 ARIMA and Seasonal Models 7.1 ARIMA(p, d, q) Models 7.1.1 Properties of the ARIMA(p,d,q) Model 7.1.2 Model Identification and Parameter Estimation of ARIMA(p,d,q) Models 7.1.3 Forecasting with ARIMA Models 7.2 Seasonal Models 7.2.1 Properties of Seasonal Models 7.2.2 Fitting Seasonal Models to Data 7.2.3 Forecasting Using Seasonal Models 7.3 ARCH and GARCH Models 7.3.1 ARCH(1) Model 7.3.2 The ARCH(p) and GARCH(p,q) Processes 7.3.3 Assessing the Appropriateness of an ARCH/GARCH Fit to a Set of Data 7.3.4 Fitting ARCH/GARCH Models to Simulated Data 7.3.5 Modeling Daily Rates of Return Data 7.4 Concluding Remarks Appendix 7A tswge functions Appendix 7B Problems 8 Time Series Regression 8.1 Line+Noise Models 8.1.1 Testing for Linear Trend 8.1.2 Fitting Line+Noise Models to Data 8.1.3 Forecasting Using Line+Noise Models 8.2 Cosine Signal+Noise Models 8.2.1 Fitting a Cosine Signal+Noise Model to Data 8.2.2 Forecasting Using Cosine Signal+Noise Models 8.2.3 Deciding Whether to Fit a Cosine Signal+Noise Model to a Set of Data 8.3 Concluding Remarks Appendix 8Atswge functions Exercises 9 Model Assessment 9.1 Residual Analysis 9.1.1 Checking Residuals for White Noise 9.1.2 Checking the Residuals for Normality 9.2 CASE STUDY 1: Modeling the Global Temperature Data 9.2.1 A Stationary Model 9.2.2 A Correlation-Based Model with a Unit Root 9.2.3 Line+Noise Models for the Global Temperature Data 9.3 CASE STUDY 2: Comparing Models for the Sunspot Data 9.3.1 Selecting the Models for Comparison 9.3.2 Do the Models Whiten the Residuals? 9.3.3 Do Realizations and Their Characteristics Behave Like the Data? 9.3.4 Do Forecasts Reflect What Is Known about the Physical Setting? 9.4 Comprehensive Analysis of Time Series Data: A Summary 9.5 Concluding Remarks Appendix 9A tswge Function Base R Function Problems 10 Multivariate Time Series 10.1 Introduction 10.2 Multiple Regression with Correlated Errors 10.2.1 Notation for Multiple Regression with Correlated Errors 10.2.2 Fitting Multiple Regression Models to Time Series Data 10.2.3 Cross Correlation 10.3 Vector Autoregressive (VAR) models 10.3.1 Forecasting with VAR(p) Models 10.4 Relationship between MLR and VAR models 10.5 A Comprehensive and Final Example: Los Angeles Cardiac Mortality 10.5.1 Applying the VAR(p) to the Cardiac Mortality Data 10.5.2 The Seasonal VAR(p) Model 10.5.3 Forecasting the Future 10.6 Conclusion Appendix 10ABASE R FUNCTIONS CRAN package dpylr CRAN package vars tswge Datasets Introduced in this Chapter Appendix 10B Relationship between MLR with Correlated Errors and VAR Three Important Points Should Be Considered: Problems 11 Deep Neural Network-Based Time Series Models 11.1 Introduction 11.2 The Perceptron 11.3 The Extended Perceptron for Univariate Time Series Data 11.3.1 A Neural Network Similar to the AR(1) 11.3.2 A Neural Network Similar to AR(p): Adding More Lags 11.3.3 A Deeper Neural Network: Adding a Hidden Layer 11.4 The Extended Perceptron for Multivariate Time Series Data 11.4.1 Forecasting Melanoma Using Sunspots 11.4.2 Forecasting Cardiac Mortality Using Temperature and Particulates 11.5 An “Ensemble” Model 11.5.1 Final Forecasts for the Next Fifty-Two Weeks 11.5.2 Final Forecasts for the Next Three Years (Longer Term Forecasts) 11.6 Concluding Remarks Appendix 11A tswge function Appendix 11B Chapter 11 Problems Mini Research Project References Index
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