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Modern Time Series Analysis with R Practical forecasting and impact estimation with tidy, reproducible workflows (Dr. Yeasmin Khandakar, Dr. Roman Ahmed)(Z-Library)

Author Dr. Yeasmin Khandakar, Dr. Roman Ahmed

data
Language English

From the experience across industries, it has been realized that the challenge is not the availability of resources or tools. The challenges are two-fold: (i) a gap in translating business problems into a time-series context, (ii) awareness of time-series-based techniques that could solve business problems with less complexity and cost. This book explores the full evolution of modern forecasting, from classical statistical methods to machine/deep learning. It tackles high dimensional challenges such as hierarchical forecasting and multiple time series methods to ensure consistency across complex business structures. Beyond forecasting, the book investigates the “why” and “when” of data shifts by estimating causal impact. It discusses time-series based methodologies to analyze business intervention data where traditional A/B testing is not applicable. Readers will learn how to identify critical turning points through changepoint analysis and anomaly detection. Ultimately, the book will equip you with the rigorous methodology and technical command necessary to transform volatile temporal data into a cornerstone of evidence-based decision-making.

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Things you will learn: • Understand core concepts and components of time series data • Wrangle data and create specialized visualizations for time series data • Extract features from a large collection of time series data • Apply appropriate adjustments, transformations, and decomposition • A wide collection of forecasting models for univariate time series • Forecast multiple time series presented in hierarchical and grouped structures • Conduct causal impact estimation using interrupted time series analysis for business initiatives • Detect anomalies, structural changes, and perform imputation for missing values Modern Time Series Analysis with R is a comprehensive, hands-on guide to mastering the art of time series analysis using the R programming language. Writt en by leading experts in applied statistics and econometrics, this book helps data scientists, analysts, and developers bridge the gap between traditional statistical theory and practical business applications. Starting with the foundations of R and tidyverse, you’ll explore the core components of time series data, data wrangling, and visualization techniques. The chapters then guide you through key modeling approaches, ranging from classical methods like ARIMA and exponential smoothing to advanced computational techniques, such as machine learning, deep learning, and ensemble forecasting. Beyond forecasting, you’ll discover how time series can be applied to causal inference, anomaly detection, change point analysis, and multiple time series modeling. Practical examples and reproducible code will empower you to assess business problems, choose optimal solutions, and communicate results eff ectively to the stakeholders. By the end of this book, you’ll be confi dent in applying modern time series methods to real- world data, delivering actionable insights for strategic decision-making in business, fi nance, technology, and beyond. Modern Time Series Analysis with R www.packt.com Get a free PDF of this book packt.link/free-ebook/9781805124306 D r. Y e a sm in K h a n d a k a r D r. R o m a n A h m e d M o d e rn T im e S e rie s A n a lysis w ith R
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Modern Time Series Analysis with R Practical forecasting and impact estimation with tidy, reproducible workflows Dr. Yeasmin Khandakar Dr. Roman Ahmed
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Modern Time Series Analysis with R Copyright © 2026 Packt Publishing All rights reserved. No part of this book may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, without the prior written permission of the publisher, except in the case of brief quotations embedded in critical articles or reviews. Every effort has been made in the preparation of this book to ensure the accuracy of the information presented. However, the information contained in this book is sold without warranty, either express or implied. Neither the authors, nor Packt Publishing or its dealers and distributors, will be held liable for any damage caused or alleged to have been caused directly or indirectly by this book. Packt Publishing has endeavored to provide trademark information about all of the companies and products mentioned in this book by the appropriate use of capitals. However, Packt Publishing cannot guarantee the accuracy of this information. Portfolio Director: Sunith Shetty Relationship Lead: Nilesh Kowadkar Project Manager: Shashank Desai Content Engineer: Gowri Rekha Technical Editor: Seemanjay Ameriya Copy Editor: Safis Editing Indexer: Pratik Shirodkar Proofreader: Gowri Rekha Production Designer: Salma Patel Growth Lead: Merlyn M Shelley First published: February 2026 Production reference: 050226 Published by Packt Publishing Ltd. Grosvenor House 11 St Paul's Square Birmingham B3 1RB, UK. ISBN 978-1-80512-401-6 www.packtpub.com
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We would like to dedicate this book to our parents and Mahdiya and Safiyya.
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Foreword I have had the privilege of knowing Dr. Yeasmin Khandakar and Dr. Roman Ahmed for more than 20 years, during which time I have witnessed their remarkable contributions in implementing time series and forecasting methods across many organizations. They have also both substantially influenced the field of forecasting; Yeasmin as coauthor of the Hyndman- Khandakar algorithm, which underpins almost all automatic ARIMA modeling software; Roman as coauthor of the first forecast reconciliation method, now a standard approach in hierarchical and grouped time series forecasting. What distinguishes Yeasmin and Roman from many academics and practitioners in this field is their wealth of hands-on experience across diverse business contexts. Between them, they have navigated the challenges of forecasting and time series analysis in retail, finance, telecommunications, technology, and transport sectors. This breadth of experience has given them unique insights into the practical realities that forecasting practitioners face daily: messy data, tight deadlines, stakeholder expectations, and the need to balance statistical rigor with business pragmatism. Modern Time Series Analysis with R is a synthesis of their combined expertise. They understand that practitioners often struggle with knowing which approach to apply to a given business problem, how to prepare data appropriately, and how to communicate results effectively to non-technical stakeholders. The book’s structure reflects this practical orientation. It begins with accessible foundations in R programming before progressing through data wrangling, visualization, and a wide spectrum of forecasting techniques, from simple methods to more advanced machine learning approaches. Importantly, the authors don’t just explain how to implement these methods; they provide crucial guidance on when and why to use each approach, drawing on their extensive experience to help readers avoid common pitfalls. Novice forecasters often underappreciate the importance of data preparation, data visualization, and exploratory data analysis before launching into fitting the latest model. This book addresses these critical steps thoroughly, ensuring readers develop a solid understanding of their data before moving on to model building. For business professionals who find themselves needing to deal with time series analysis and forecasting problems, this book will prove a valuable resource. Whether you’re an analyst preparing monthly forecasts for board meetings, a data scientist building production
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forecasting pipelines, or a manager seeking to understand the capabilities and limitations of different approaches, you will find practical guidance tailored to your needs. The emphasis on reproducible workflows, clear code examples, and real-world context makes this book a great reference for anyone applying time series analysis in business settings. Rob J Hyndman Professor of Statistics Department of Econometrics and Business Statistics Monash University
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Contributors About the authors Dr. Yeasmin Khandakar is a data scientist with over 15 years of experience across diverse sectors, including FinTech (Portland House Group), MedTech (Optalert), retail (Coles, Officeworks) and transport (Transurban). She has a PhD from Monash University and is the co-author of the paper Automatic time series forecasting: the forecast package for R, which has generated over 5,900+ citations. Dr. Khandakar specializes in solving strategic business challenges by integrating advanced statistical methods with machine learning and deep learning, and robust time-series techniques. Dr. Roman Ahmed is an experienced statistician with a PhD specializing in time-series forecasting. He has more than two decades of experience across the corporate and academic sectors. With a career including prominent technical leadership at Optus, Xero, and ANZ Bank, he excels at applying high-impact forecasting, econometric, and machine learning solutions to business strategy. Roman has published methodological and applied research in top-tier journals and has presented work at prestigious conferences. His expertise lies in translating sophisticated methodological research into scalable, real-world tools, particularly within the R ecosystem. The authors would like to thank the technical reviewer, whose constructive suggestions and diligent oversight were instrumental in refining the manuscript into its final form. We extend our acknowledgement to the editorial team at Packt for coordinating such a thorough review process. The authors extend deep gratitude to everyone from Packt who was involved in various stages of the book. We would like to mention a few names: Tejashwini R (for highlighting the potential of this book), Farheen Fathima (for supporting the initial phase in the manuscript development), Hemangi Lotlikar (for being patient while the authors were taking time for content development), and Gowri Rekha (for serving as the diligent catalyst needed to reach the finish line). The authors wish to acknowledge those colleagues and peers who have sought to integrate time-series analysis into their workflow but found themselves hindered by the continuous learning and implementation challenges. We will consider this book a success if it helps them navigate these obstacles and appreciate the elegance and utility of time-series analysis in their professional lives.
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Yeasmin wishes to express gratitude to her employer, Transurban, for their support and flexibility that were instrumental during the initial development of the manuscript. Finally, both authors extend their deepest gratitude to their respective families for their unwavering support. This journey was long and often required the suspension of cherished routines, disrupted weekends, and sacrificed holiday plans. Without their patience and encouragement, this work would not have come to fruition.
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About the reviewers Rohit Choudhary holds a master’s degree in management science from the University of Texas at Dallas and has over a decade of experience in statistics, forecasting, and data analytics. He has worked across diverse domains, translating complex data into actionable business insights and driving data-informed decision-making. Rohit specializes in predictive modeling, performance measurement, and analytical strategy, with a strong passion for applying advanced analytics to solve real-world business problems. He continues to explore innovative approaches in data science and business intelligence. Rahul Singh is a data science manager at Adobe, where he works at the intersection of product data, customer behavior, and data science to solve complex business problems. His experience spans customer value measurement, in-product personalization, applied machine learning, LLM-enabled systems, and understanding how users and AI agents interact through conversational and agentic traffic data. He regularly speaks and writes about how the data science field is evolving with the rise of AI agents and how people and technology can work together to support better decision-making. He also serves as an AI advisor to Zindi, supporting efforts to grow the data science ecosystem across Africa.
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Table of Contents Preface xxi Free benefits with your book .......................................................................... xxviii Part 1: Setting the Scene: R 1 Chapter 1: R, Rstudio, and R packages 3 1.1 Introduction to the R ecosystem ....................................................................... 4 1.1.1 What is R? • 4 1.1.2 What is RStudio? • 4 1.1.3 What are R packages? • 5 1.2 Downloading R and RStudio ............................................................................ 6 1.3 Installing R and RStudio with admin access ...................................................... 6 1.3.1 Windows • 6 1.3.2 macOS • 7 1.3.3 Linux • 8 1.3.3.1 Ubuntu • 8 1.3.3.2 Debian • 9 1.4 Installation in a custom location ..................................................................... 11 1.5 Installing R packages ...................................................................................... 12 1.5.1 Package installation via the RStudio menu • 12 1.5.2 Package installation via R console • 13 1.5.3 R package pathways • 15 1.5.4 Installing R packages in development • 16 1.6 Loading installed packages ............................................................................. 17 1.7 Updating software and packages ..................................................................... 17 1.7.1 Checking and updating R packages • 18 1.7.2 Checking and updating R and RStudio • 18
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1.8 How to choose R packages .............................................................................. 19 1.9 RStudio for productive programming ............................................................. 20 1.9.1 Do configure global and project level options • 20 1.9.2 Do set up a working directory • 21 1.9.3 Do start with an RStudio project • 21 1.9.4 Do not preserve the workspace between sessions • 21 1.10 The tidyverse package collection .................................................................. 22 Summary ........................................................................................................... 24 Further reading .................................................................................................. 24 Get this book’s PDF version and more ................................................................. 25 Chapter 2: Objects and Functions in R 27 Technical requirements ...................................................................................... 28 2.1 Objects and their names ................................................................................ 29 2.2 Object types ................................................................................................... 31 2.3 Data types ...................................................................................................... 31 2.4 Atomic vectors .............................................................................................. 32 2.4.1 Double • 33 2.4.2 Integer • 34 2.4.3 Logical • 34 2.4.4 Character • 35 2.5 Lists .............................................................................................................. 36 2.5.1 Matrix • 38 2.5.2 Array • 40 2.6 Coercion ........................................................................................................ 41 2.7 S3 atomic vectors .......................................................................................... 42 2.7.1 Factors • 43 2.7.2 Dates • 45 2.7.3 Date-times • 46 2.7.4 Duration • 47 2.8 S3 lists .......................................................................................................... 48 2.8.1 Data frames • 48 Table of Contents x
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2.8.2 Tibbles • 51 2.9 Missing values .............................................................................................. 55 2.10 Time Series Specific Objects ......................................................................... 57 2.10.1 ts • 57 2.10.2 tsibble • 58 2.11 Functions in R ............................................................................................... 61 2.12 Comparisons ............................................................................................... 63 2.13 Conditions ................................................................................................... 64 2.14 Conditional execution ................................................................................. 65 2.15 Iterations .................................................................................................... 68 2.15.1 The apply family • 69 2.15.2 The map family • 73 Summary ........................................................................................................... 75 Further reading .................................................................................................. 75 Join our community on Discord .......................................................................... 76 Chapter 3: Data Input/Output in R 77 Technical requirements ...................................................................................... 78 3.1 General structure of input/output functions ................................................... 79 3.2 Saving and loading files generated by R .......................................................... 80 3.3 Data files from R packages ............................................................................. 81 3.4 Importing external files ................................................................................. 82 3.4.1 The readr package • 82 3.4.2 The readxl package • 85 3.4.3 The fst package • 87 3.4.4 Import data via RStudio’s menu • 88 3.5 Importing data from relational databases ...................................................... 89 3.5.1 Connecting to databases • 89 3.5.2 Credential security • 92 3.5.2.1 Pre-configuring credentials during ODBC set-up • 92 3.5.2.2 The keyring package • 92 3.5.2.3 The config package • 93 xi Table of Contents
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3.5.2.4 The RStudio API • 93 3.6 Using SQL from R .......................................................................................... 93 3.6.1 Inline SQL query • 94 3.6.2 SQL query from a file • 95 3.6.3 SQL translations via dplyr • 95 3.6.4 Parameterized query using glue_sql() • 96 3.7 Data governance ........................................................................................... 98 Summary ......................................................................................................... 100 Further reading ................................................................................................ 100 Get this book’s PDF version and more ................................................................ 101 Part 2: The Main Character: Time Series 103 Chapter 4: Time Series Characteristics 105 4.1 What is a time series? .................................................................................. 106 4.2 Distinction of time series from other time-indexed data ................................ 107 4.3 How to classify time-indexed data to apply suitable analytics ....................... 108 4.4 Components of a time series ........................................................................ 109 4.4.1 Trend • 109 4.4.2 Seasonality • 110 4.4.3 Cyclical • 111 4.4.4 Random errors or remainders • 112 4.5 Combining time series components .............................................................. 113 4.6 Stationarity ................................................................................................. 114 4.7 Autocorrelation ............................................................................................ 115 4.8 Types of time series ..................................................................................... 116 Summary .......................................................................................................... 118 Join our community on Discord ......................................................................... 118 Chapter 5: Time Series Data Wrangling and Visualization 119 Technical requirements .................................................................................... 120 5.1 Parsing date-time variables .......................................................................... 121 Table of Contents xii
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5.2 Setting components of date-time .................................................................. 123 5.3 When to transform data into time series object? ............................................ 125 5.4 Wrangling functions .................................................................................... 126 5.5 Visualization functions ................................................................................ 129 5.6 Time plots ................................................................................................... 130 5.7 Seasonal plots .............................................................................................. 136 5.7.1 Seasonal subseries plots • 139 5.8 Visualizing relationships among time series ................................................. 141 5.8.1 Scatter plots • 141 5.8.2 Lag plots • 143 5.9 Interactive plots ........................................................................................... 146 Summary .......................................................................................................... 146 Get this book’s PDF version and more ................................................................ 147 Chapter 6: Business Applications of Time Series Analysis 149 Technical requirements ..................................................................................... 150 6.1 Time series characteristics level problem domains ........................................ 151 6.1.1 Trend (trend-cycle) analysis • 152 6.1.2 Seasonality analysis • 156 6.1.3 Outlier/anomaly detection • 159 6.2 Inference and attribution problem domains ................................................ 160 6.3 Impact measurement problem domains ........................................................ 161 6.4 Forecasting problem domains ...................................................................... 162 Summary .......................................................................................................... 163 Further reading ................................................................................................. 164 Join our community on Discord ......................................................................... 164 Part 3: The Makeover: Adjusting the Appearance 165 Chapter 7: Time Series Adjustments, Transformations, and Decomposition 167 Technical requirements .................................................................................... 168 xiii Table of Contents
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7.1 Summary of differences: Adjustments, transformations and decompositions . 169 7.2 Rationales for time series adjustments and transformations .......................... 170 7.3 Time series adjustments ............................................................................... 171 7.3.1 Calendar adjustments • 173 7.3.2 Population adjustments • 174 7.3.3 Base adjustments • 176 7.4 Time series transformations ......................................................................... 179 7.4.1 Logarithmic transformation • 179 7.4.2 Box-Cox transformation • 180 7.5 Decomposition plots .................................................................................... 183 7.6 Decomposition using MAs ............................................................................ 187 7.6.1 MA smoothing of data with trends • 188 7.6.2 MA smoothing of data with seasonality • 189 7.7 Trend and seasonal decomposition with the classical method ....................... 190 7.8 Model based decomposition methods ........................................................... 193 7.9 STL decomposition ....................................................................................... 194 7.9.1 Summary of decomposition techniques • 196 Summary .......................................................................................................... 197 Further reading ................................................................................................ 198 Get this book’s PDF version and more ................................................................ 199 Chapter 8: Time Series Features 201 Technical requirements .................................................................................... 202 8.1 Time series features ..................................................................................... 203 8.2 Statistical summary-based features ............................................................. 205 8.3 Autocorrelation based features .................................................................... 207 8.4 STL-based features ..................................................................................... 209 8.5 Tiling window features ................................................................................ 214 8.6 Sliding window features .............................................................................. 215 8.7 Statistical test-based features ....................................................................... 217 8.8 Other useful features .................................................................................. 220 8.9 Clustering using time series features ........................................................... 222 Table of Contents xiv
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8.9.1 PCA on time series features • 223 8.9.2 Clustering using time series features, UMAP, and K-means • 227 Summary ......................................................................................................... 235 Further reading ................................................................................................ 235 Join our community on Discord ........................................................................ 236 Chapter 9: Time Series Smoothing and Filtering 237 Technical requirements .................................................................................... 238 9.1 Comparison of time series preprocessing techniques .................................... 238 9.2 Exponentially weighted moving average method (EWMA) ............................ 241 9.3 Time series filtering .................................................................................... 244 9.3.1 The Nyquist frequency and sampling considerations • 244 9.4 Linear filtering with moving average (MA) .................................................. 246 9.5 The Hodrick-Prescott filter .......................................................................... 248 9.6 The Kalman filter ......................................................................................... 251 Summary .......................................................................................................... 257 Further reading ................................................................................................. 257 Get this book’s PDF version and more ............................................................... 258 Part 4: The Crystal Ball: Forecasting 259 Chapter 10: Basics of Forecasting 261 Technical requirements .................................................................................... 262 10.1 Notations ................................................................................................... 263 10.2 Forecasting workflow ................................................................................ 264 10.3 fable for forecasting ................................................................................... 265 10.4 Naïve forecasting method .......................................................................... 266 10.5 Seasonal Naïve method .............................................................................. 276 10.6 Forecasting using average ........................................................................... 281 10.7 Time Series Linear Model (TSLM) .............................................................. 284 10.7.1 Scenario analysis • 290 10.8 Evaluating point forecast accuracy ............................................................ 295 xv Table of Contents
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10.9 Time series cross-validation ...................................................................... 299 Summary ......................................................................................................... 302 Further reading ................................................................................................ 302 Join our community on Discord ........................................................................ 303 Chapter 11: Exponential Smoothing 305 Technical requirements .................................................................................... 306 11.1 Forecasting methods versus models ............................................................ 306 11.2 Exponential smoothing forecasting ............................................................ 308 11.3 Simple Exponential Smoothing (SES) .......................................................... 311 11.3.1 Component form of the (N, N) method • 311 11.3.2 SES with additive errors: ETS(A, N, N) • 311 11.3.3 SES with multiplicative errors: ETS(M, N, N) • 317 11.4 Holt’s linear trend method .......................................................................... 318 11.4.1 Component form of Holt’s linear trend method • 318 11.4.2 Holt’s linear trend model with additive errors: ETS(A, A, N) • 319 11.4.3 Holt’s linear trend model with multiplicative errors: ETS(M, A, N) • 321 11.4.4 Additive damped trend method • 323 11.5 Holt-Winters’ trend and seasonality method ............................................... 326 11.5.1 Component form of additive Holt-Winters’ method (A, A) • 326 11.5.2 Component form of multiplicative Holt-Winters’ method (A, M) • 326 11.5.3 Component form of Holt-Winters’ damped method (Ad, A) • 327 11.6 Automated model selection using ETS() ....................................................... 333 Summary .......................................................................................................... 337 Further reading ................................................................................................. 337 Get this book’s PDF version and more ............................................................... 338 Chapter 12: ARIMA Forecasting Models 339 Technical requirements .................................................................................... 340 12.1 Basics of ARIMA models .............................................................................. 341 12.2 Autoregressive model (the AR in ARIMA) .................................................... 342 12.3 Integration (the I in ARIMA) ...................................................................... 346 Table of Contents xvi
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12.4 Moving Average model (the MA in ARIMA) .................................................. 352 12.5 General structure of an ARIMA model ......................................................... 356 12.5.1 Non-seasonal ARIMA model • 357 12.5.2 Seasonal ARIMA models • 361 12.6 ARIMA with exogenous variables (ARIMAX) ............................................... 368 12.7 Steps in fitting an ARIMA model .................................................................. 371 12.8 Automatic ARIMA algorithm ....................................................................... 373 12.9 ARIMA and forecast explainability .............................................................. 375 12.9.1 Impact of the constant term on forecasts • 375 12.9.2 Prediction intervals from ARIMA models • 376 12.9.3 Impact of differencing orders on prediction intervals • 376 12.9.4 Impact of AR order on cyclic forecasts • 376 Summary .......................................................................................................... 377 Further reading ................................................................................................. 377 Join our community on Discord ........................................................................ 378 Chapter 13: Advanced Computational Methods for Forecasting 379 Technical requirements ..................................................................................... 381 13.1 Understanding the connection between forecasting and prediction ............. 382 13.2 DL forecasting: Neural network .................................................................. 383 13.2.1 Forecasting using neural networks • 387 13.2.2 Prediction interval for neural networks • 394 13.3 ML forecasting ........................................................................................... 395 13.3.1 Application of ML in forecasting • 396 13.3.2 Quantile regularized regression: A brief summary • 404 13.4 Forecasting as a curve fitting: The Prophet method ..................................... 406 13.4.1 Prophet forecasting • 408 13.5 Forecast ensemble ...................................................................................... 413 Summary .......................................................................................................... 421 Further reading ................................................................................................ 422 Get this book’s PDF version and more ............................................................... 423 xvii Table of Contents
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Chapter 14: Forecasting Models for Multiple Time Series 425 Technical requirements .................................................................................... 426 14.1 The dynamics of multiple interconnected time series .................................. 427 14.2 Vector Autoregression model ..................................................................... 428 14.2.1 Mathematical background of the VAR(1) model • 428 14.2.2 Inspect time series for stationarity • 430 14.2.3 Identifying VAR model orders • 434 14.2.4 Interpretation of VAR model coefficients • 439 14.2.5 Granger causality test for a VAR(1) model • 440 14.2.6 Impulse Response Analysis • 442 14.2.7 Forecasting from a VAR model • 446 14.3 Hierarchical and grouped time series .......................................................... 447 14.3.1 Traditional hierarchical forecasting: top-down, bottom-up, and middle-out approaches • 449 14.3.1.1 Top-down approach • 453 14.3.1.2 Bottom-up approach • 456 14.3.1.3 Middle-out approach • 459 14.3.2 Optimal reconciliation forecast for hierarchical time series using trace minimization • 462 14.3.2.1 Reconciliation problem Setup • 463 14.3.2.2 Optimal reconciliation via trace minimization • 463 14.3.3 Forecast accuracy evaluation • 465 14.4 Machine learning for multiple time series forecasting ................................ 467 Summary ......................................................................................................... 468 Further reading ................................................................................................ 468 Join our community on Discord ........................................................................ 469 Part 5: Plot Twists and Turning Points: Measuring Impact and Detecting Anomalies 471 Chapter 15: Causal Impact Estimation 473 Technical requirements .................................................................................... 474 Table of Contents xviii
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15.1 What is causal inference? ............................................................................. 475 15.2 Causal inference with experimentation ...................................................... 476 15.2.1 Practical challenges of conducting experiments • 477 15.3 Causal inference with observational data ................................................... 478 15.4 Equivalence of hypothesis tests and regression ........................................... 480 15.4.1 Paired sample • 481 15.4.2 Two independent samples • 485 15.5 Interrupted Time Series (ITS) analysis ........................................................ 488 15.6 ITS on stationary time series ...................................................................... 490 15.6.1 Stationary data impact measurement approaches • 494 15.6.2 Durbin-Watson test to identify an AR(1) process • 497 15.6.3 Statistical power analysis in regression • 497 15.7 ITS on time series with a trend ................................................................... 499 15.7.1 Trend data impact measurement approaches • 501 15.8 ITS on time series with autocorrelation ...................................................... 504 15.8.1 AR(1) data impact measurement approaches • 506 15.8.2 Adjustments in the linear model for AR(1) process • 508 15.8.3 ARIMAX for measuring the impact from an AR(1) process • 512 15.9 ITS on time series with AR(1) and trends ..................................................... 515 15.9.1 ARIMAX for measuring the impact from AR(1) data with trends • 517 15.10 Flexibilities of ITS-based inference ............................................................ 521 15.11 Monitoring guardrail metrics in ITS ........................................................... 523 Summary .......................................................................................................... 525 Further reading ................................................................................................. 525 Get this book’s PDF version and more ............................................................... 526 Chapter 16: Changepoint Detection 527 Technical requirements .................................................................................... 528 16.1 What is changepoint detection? .................................................................. 528 16.2 Breaks for Additive Season and Trend .......................................................... 531 16.2.1 BFAST implementation on non-seasonal data • 534 16.2.2 BFAST implementation on a seasonal series • 536 xix Table of Contents
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