#### 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 moving average process

In some cases, the forecasting model is unable to capture all the series patterns, and therefore some information is left over in model residuals (or forecasting error) . The goal of the moving average process is to capture patterns in the residuals, if they exist, by modeling the relationship between Yt, the error term, t, and the past q error terms of the models (for example, ). The structure of the MA process is fairly similar to the ones of the AR. The following equation defines an MA process with a q order:

The following terms are used in the preceding equation:

• MA(q) is the notation for an MA process with q-order
• represents the mean of the series
• are white noise error terms
• is the corresponding coefficient of
• q defines the number of past error terms to be used in the equation
Like the AR process, the MA equation holds only if the...