Book Image

Hands-On Time Series Analysis with R

By : Rami Krispin
Book Image

Hands-On Time Series Analysis with R

By: Rami Krispin

Overview of this book

Time-series analysis is the art of extracting meaningful insights from, and revealing patterns in, time-series data using statistical and data visualization approaches. These insights and patterns can then be utilized to explore past events and forecast future values in the series. This book explores the basics of time-series analysis with R and lays the foundation you need to build forecasting models. You will learn how to preprocess raw time-series data and clean and manipulate data with packages such as stats, lubridate, xts, and zoo. You will analyze data using both descriptive statistics and rich data visualization tools in R including the TSstudio, plotly, and ggplot2 packages. The book then delves into traditional forecasting models such as time-series linear regression, exponential smoothing (Holt, Holt-Winter, and more) and Auto-Regressive Integrated Moving Average (ARIMA) models with the stats and forecast packages. You'll also work on advanced time-series regression models with machine learning algorithms such as random forest and Gradient Boosting Machine using the h2o package. By the end of this book, you will have developed the skills necessary for exploring your data, identifying patterns, and building a forecasting model using various traditional and machine learning methods.

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Table of Contents (14 chapters)
Preface
Preface
Who this book is for
What this book covers
To get the most out of this book
Get in touch
Free Chapter
1
Introduction to Time Series Analysis and R
Introduction to Time Series Analysis and R
Technical requirements
Time series data
Historical background of time series analysis
Time series analysis
Getting started with R
A brief introduction to R
Working and manipulating data
Summary
2
Working with Date and Time Objects
Working with Date and Time Objects
Technical requirements
The date and time formats
Date and time objects in R
Creating a date or time index
Manipulation of date and time with the lubridate package
Summary
3
The Time Series Object
The Time Series Object
Technical requirement
The Natural Gas Consumption dataset
The attributes of the ts class
Data manipulation of ts objects
Visualizing ts and mts objects
Summary
4
Working with zoo and xts Objects
Working with zoo and xts Objects
Technical requirement
The zoo class
The xts class
Manipulating the zoo and xts objects
Plotting zoo and xts objects
xts, zoo, or ts – which one to use?
Summary
5
Decomposition of Time Series Data
Decomposition of Time Series Data
Technical requirement
The moving average function
The time series components
The additive versus the multiplicative model
The decomposition of time series
Seasonal adjustment
Summary
6
Seasonality Analysis
Seasonality Analysis
Technical requirement
Seasonality types
Seasonal analysis with descriptive statistics
Structural tools for seasonal analysis
Summary
7
Correlation Analysis
Correlation Analysis
Technical requirement
Correlation between two variables
Lags analysis
The autocorrelation function
The partial autocorrelation function
Lag plots
Causality analysis
Summary
8
Forecasting Strategies
Forecasting Strategies
Technical requirement
The forecasting workflow
Training approaches
Finalizing the forecast
Handling forecast uncertainty
Summary
9
Forecasting with Linear Regression
Forecasting with Linear Regression
Technical requirement
The linear regression
Forecasting with linear regression
Forecasting a series with multiseasonality components – a case study
Summary
10
Forecasting with Exponential Smoothing Models
Forecasting with Exponential Smoothing Models
Technical requirement
Forecasting with moving average models
Forecasting with exponential smoothing
Summary
11
Forecasting with ARIMA Models
Forecasting with ARIMA Models
Technical requirement
The stationary process
The AR process
The moving average process
The ARMA model
Forecasting AR, MA, and ARMA models
The ARIMA model
The seasonal ARIMA model
The auto.arima function
Linear regression with ARIMA errors
Summary
12
Forecasting with Machine Learning Models
Forecasting with Machine Learning Models
Technical requirement
Why and when should we use machine learning?
Why h2o?
Forecasting monthly vehicle sales in the US – a case study
Summary
13
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The ARMA model

Up until now, we have seen how the applications of AR and MA are processed separately. However, in some cases, combining the two allows us to handle more complex time series data. The ARMA model is a combination of the AR(p) and MA(q) processes and can be written as follows:

The following terms are used in the preceding equation:

  • ARMA(p,q) defines an ARMA process with a p-order AR process and q-order moving average process
  • Yt represents the series itself
  • c represents a constant (or drift)
  • p defines the number of lags to regress against Yt
  • is the coefficient of the i lag of the series
  • Yt-1 is the i lag of the series
  • q defines the number of past error terms to be used in the equation
  • is the corresponding coefficient of
  • are white noise error terms
  • represents the error term, which is white noise

For instance, an ARMA(3,2) model is defined by the following equation...

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