#### 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.
Preface
Free Chapter
Introduction to Time Series Analysis and R
Working with Date and Time Objects
The Time Series Object
Working with zoo and xts Objects
Decomposition of Time Series Data
Seasonality Analysis
Correlation Analysis
Forecasting Strategies
Forecasting with Linear Regression
Forecasting with Exponential Smoothing Models
Forecasting with ARIMA Models
Forecasting with Machine Learning Models
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# The AR process

The AR process defines the current value of the series, Yt, as a linear combination of the previous p lags of the series, and can be formalized with the following equation:

Following are the terms used in the preceding equation:

• AR(p) is the notation for an AR process with p-order
• 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 (here, must be between -1 and 1, otherwise, the series would be trending up or down and therefore cannot be stationary over time)
• Yt-i is the i lag of the series
• t represents the error term, which is white noise
An AR process can be used on time series data if, and only if, the series is stationary. Therefore, before applying an AR process on a series, you will have to verify that the series is stationary. Otherwise, you will have to apply some...