#### 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 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...