#### 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 partial autocorrelation function

One of the downsides of the autocorrelation function is that it does not remove the effect of lags 1 up to k-1 on the series when calculating the correlation of the series with the k lag. The partial autocorrelation function (PACF), the sister function of the ACF, provides a solution for this by computing the conditional correlation of the series with the k lag given the relationship of the 1, 2, ..., and k-1 lags with the series. In other words, the PACF provides an estimation for the direct correlation of the series with the k lag after removing the correlation of the k lag with the previous lags. The pacf function from the stats package provides an estimation for the PACF values for a given input. Let's review the PACF output for the first 60 lags of the USgas dataset:

`pacf(USgas, lag.max = 60) `

We will get the following plot:

Both...