Practical Time Series Analysis. Prediction with Statistics and Machine Learning

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• Preface
  • Who Should Read This Book
    • Expected Background
  • Why I Wrote This Book
  • Navigating This Book
  • Online Resources
  • Conventions Used in This Book
  • Using Code Examples
  • OReilly Online Learning
  • How to Contact Us
  • Acknowledgments
• 1. Time Series: An Overview and a Quick History
  • The History of Time Series in Diverse Applications
    • Medicine as a Time Series Problem
      • Medical instruments
    • Forecasting Weather
    • Forecasting Economic Growth
      • Trading markets
    • Astronomy
  • Time Series Analysis Takes Off
  • The Origins of Statistical Time Series Analysis
  • The Origins of Machine Learning Time Series Analysis
  • More Resources
• 2. Finding and Wrangling Time Series Data
  • Where to Find Time Series Data
    • Prepared Data Sets
      • The UCI Machine Learning Repository
      • The UEA and UCR Time Series Classification Repository
      • Government time series data sets
      • Additional helpful sources
    • Found Time Series
  • Retrofitting a Time Series Data Collection from a Collection of Tables
    • A Worked Example: Assembling a Time Series Data Collection
    • Constructing a Found Time Series
  • Timestamping Troubles
    • Whose Timestamp?
    • Guesstimating Timestamps to Make Sense of Data
      • Local or Universal Time?
      • User behavior or network behavior?
    • Whats a Meaningful Time Scale?
  • Cleaning Your Data
    • Handling Missing Data
      • Preparing a data set to test missing data imputation methodologies
      • Forward fill
      • Moving average
      • Interpolation
      • Overall comparison
      • Final notes
    • Upsampling and Downsampling
      • Downsampling
        • The original resolution of the data isnt sensible
        • Focus on a particular portion of a seasonal cycle
        • Match against data at a lower frequency
      • Upsampling
        • Irregular time series
        • Inputs sampled at different frequencies
        • Knowledge of time series dynamics
    • Smoothing Data
      • Purposes of smoothing
      • Exponential smoothing
  • Seasonal Data
  • Time Zones
  • Preventing Lookahead
  • More Resources
• 3. Exploratory Data Analysis for Time Series
  • Familiar Methods
    • Plotting
    • Histograms
    • Scatter Plots
  • Time SeriesSpecific Exploratory Methods
    • Understanding Stationarity
      • Intuition
      • Stationary definition and the Augmented DickeyFuller test
      • In practice
    • Applying Window Functions
      • Rolling windows
      • Expanding windows
      • Custom rolling functions
    • Understanding and Identifying Self-Correlation
      • The autocorrelation function
      • The partial autocorrelation function
    • Spurious Correlations
  • Some Useful Visualizations
    • 1D Visualizations
    • 2D Visualizations
    • 3D Visualizations
  • More Resources
• 4. Simulating Time Series Data
  • Whats Special About Simulating Time Series?
    • Simulation Versus Forecasting
  • Simulations in Code
    • Doing the Work Yourself
    • Building a Simulation Universe That Runs Itself
    • A Physics Simulation
  • Final Notes on Simulations
    • Statistical Simulations
    • Deep Learning Simulations
  • More Resources
• 5. Storing Temporal Data
  • Defining Requirements
    • Live Data Versus Stored Data
      • Slowly changing variables
      • Noisy, high-frequency data
      • Stale data
  • Database Solutions
    • SQL Versus NoSQL
      • Characteristics of the data that originally inspired SQL databases
      • Characteristics of time series data
      • How to choose between SQL and NoSQL
    • Popular Time Series Database and File Solutions
      • Time seriesspecific databases and related monitoring tools
        • InfluxDB
        • Prometheus
      • General NoSQL databases
  • File Solutions
    • NumPy
    • Pandas
    • Standard R Equivalents
    • Xarray
  • More Resources
• 6. Statistical Models for Time Series
  • Why Not Use a Linear Regression?
  • Statistical Methods Developed for Time Series
    • Autoregressive Models
      • Using algebra to understand constraints on AR processes
      • Choosing parameters for an AR(p) model
      • Forecasting with an AR(p) process
        • Forecasting one time step ahead
        • Forecasting many steps into the future
    • Moving Average Models
      • The model
      • Selecting parameters for an MA(q) process
      • Forecasting an MA(q) process
    • Autoregressive Integrated Moving Average Models
      • The model
      • Selecting parameters
        • Manually fitting a model
        • Using automated model fitting
    • Vector Autoregression
    • Variations on Statistical Models
      • Seasonal ARIMA
      • ARCH, GARCH, and their many brethren
      • Hierarchical time series models
  • Advantages and Disadvantages of Statistical Methods for Time Series
  • More Resources
• 7. State Space Models for Time Series
  • State Space Models: Pluses and Minuses
  • The Kalman Filter
    • Overview
    • Code for the Kalman Filter
  • Hidden Markov Models
    • How the Model Works
    • How We Fit the Model
      • Baum Welch algorithm
      • Viterbi algorithm
    • Fitting an HMM in Code
  • Bayesian Structural Time Series
    • Code for bsts
  • More Resources
• 8. Generating and Selecting Features for a Time Series
  • Introductory Example
  • General Considerations When Computing Features
    • The Nature of the Time Series
      • Stationarity
      • Length of time series
    • Domain Knowledge
    • External Considerations
  • A Catalog of Places to Find Features for Inspiration
    • Open Source Time Series Feature Generation Libraries
      • The tsfresh Python module
      • The Cesium time series analysis platform
      • Rs tsfeatures package
    • Domain-Specific Feature Examples
      • Technical stock market indicators
      • Healthcare time series
  • How to Select Features Once You Have Generated Them
  • Concluding Thoughts
  • More Resources
• 9. Machine Learning for Time Series
  • Time Series Classification
    • Selecting and Generating Features
    • Decision Tree Methods
      • Random forest
      • Gradient boosted trees
      • Code example
      • Classification versus regression
  • Clustering
    • Generating Features from the Data
    • Temporally Aware Distance Metrics
    • Clustering Code
      • Hierarchical clustering of normalized features
      • Hierarchical clustering with the DTW distance matrix
  • More Resources
• 10. Deep Learning for Time Series
  • Deep Learning Concepts
  • Programming a Neural Network
    • Data, Symbols, Operations, Layers, and Graphs
  • Building a Training Pipeline
    • Inspecting Our Data Set
    • Steps of a Training Pipeline
      • Making our code easily configurable
      • Prepping our input data
        • Shaping the input data
        • Building iterators
      • Shaping the data in code
        • NC data format
        • NTC data format
      • Setting training parameters and establishing a recordkeeping system
      • Evaluation metrics
      • Putting it together
  • Feed Forward Networks
    • A Simple Example
    • Using an Attention Mechanism to Make Feed Forward Networks More Time-Aware
  • CNNs
    • A Simple Convolutional Model
    • Alternative Convolutional Models
      • Causal convolutions
      • Converting a time series into pictures
  • RNNs
    • Continuing Our Electric Example
    • The Autoencoder Innovation
  • Combination Architectures
  • Summing Up
  • More Resources
• 11. Measuring Error
  • The Basics: How to Test Forecasts
    • Model-Specific Considerations for Backtesting
  • When Is Your Forecast Good Enough?
  • Estimating Uncertainty in Your Model with a Simulation
  • Predicting Multiple Steps Ahead
    • Fit Directly to the Horizon of Interest
    • Recursive Approach to Distant Temporal Horizons
    • Multitask Learning Applied to Time Series
  • Model Validation Gotchas
  • More Resources
• 12. Performance Considerations in Fitting and Serving Time Series Models
  • Working with Tools Built for More General Use Cases
    • Models Built for Cross-Sectional Data Dont Share Data Across Samples
      • Dont use overlapping data
      • Employ a generator-like paradigm to iterate through the data set
    • Models That Dont Precompute Create Unnecessary Lag Between Measuring Data and Making a Forecast
  • Data Storage Formats: Pluses and Minuses
    • Store Your Data in a Binary Format
    • Preprocess Your Data in a Way That Allows You to Slide Over It
  • Modifying Your Analysis to Suit Performance Considerations
    • Using All Your Data Is Not Necessarily Better
    • Complicated Models Dont Always Do Better Enough
    • A Brief Mention of Alternative High-Performance Tools
  • More Resources
• 13. Healthcare Applications
  • Predicting the Flu
    • A Case Study of Flu in One Metropolitan Area
      • Data exploration and some cleanup
      • Fitting a seasonal ARIMA model
      • An alternative ARIMA model: Exogenous harmonic regressors instead of seasonality
    • What Is State of the Art in Flu Forecasting?
      • Research in flu forecasts
  • Predicting Blood Glucose Levels
    • Data Cleaning and Exploration
    • Generating Features
    • Fitting a Model
  • More Resources
• 14. Financial Applications
  • Obtaining and Exploring Financial Data
  • Preprocessing Financial Data for Deep Learning
    • Adding Quantities of Interest to Our Raw Values
    • Scaling Quantities of Interest Without a Lookahead
    • Formatting Our Data for a Neural Network
  • Building and Training an RNN
  • More Resources
• 15. Time Series for Government
  • Obtaining Governmental Data
  • Exploring Big Time Series Data
    • Upsample and Aggregate the Data as We Iterate Through It
    • Sort the Data
  • Online Statistical Analysis of Time Series Data
    • Remaining Questions
    • Further Improvements
  • More Resources
• 16. Time Series Packages
  • Forecasting at Scale
    • Googles Industrial In-house Forecasting
      • Automated and extensive data cleaning and smoothing
      • Temporal aggregation and geographic/conceptual disaggregation
      • Combining forecasts and simulation-based generation of uncertainty estimates
    • Facebooks Open Source Prophet Package
  • Anomaly Detection
    • Twitters Open Source AnomalyDetection Package
  • Other Time Series Packages
  • More Resources
• 17. Forecasts About Forecasting
  • Forecasting as a Service
  • Deep Learning Enhances Probabilistic Possibilities
  • Increasing Importance of Machine Learning Rather Than Statistics
  • Increasing Combination of Statistical and Machine Learning Methodologies
  • More Forecasts for Everyday Life
• Index

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