#### 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
Other Books You May Enjoy

# Linear regression with ARIMA errors

In Chapter 9, Forecasting with Linear Regression, we saw that with some simple steps, we can utilize a linear regression model as a time series forecasting model. Recall that a general form of the linear regression model can be represented by the following equation:

One of the main assumptions of the linear regression model is that the error term of the series, , is the white noise series (for example, there is no correlation between the residuals and their lags). However, when working with time series data, this assumption is eased as, typically, the model predictors do not explain all the variations of the series, and some patterns are left on the model residuals. An example of the failure of this assumption can be seen while fitting a linear regression model to forecast the AirPassenger series.

...