Introduction to Forecasting with ARIMA in R
ARIMA models are a popular and flexible class of forecasting model that utilize historical information to make predictions. In this tutorial, we walk through an example of examining time series for demand at a bikesharing service, fitting an ARIMA model, and creating a basic forecast.
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Prerequisites: Previous knowledge of forecasting is not required, but the reader should be familiar with basic data analysis and statistics (e.g., averages, correlation). To follow the example, the reader should also be familiar with R syntax. R packages needed: forecast
, tseries
, ggplot2.
The sample dataset can be downloaded here.
Introduction to Time Series Forecasting
This tutorial will provide a stepbystep guide for fitting an ARIMA model using R. ARIMA models are a popular and flexible class of forecasting model that utilize historical information to make predictions. This type of model is a basic forecasting technique that can be used as a foundation for more complex models. In this tutorial, we walk through an example of examining time series for demand at a bikesharing service, fitting an ARIMA model, and creating a basic forecast. We also provide a checklist for basic ARIMA modeling to be used as a loose guide.
Business Uses
Time series analysis can be used in a multitude of business applications for forecasting a quantity into the future and explaining its historical patterns. Here are just a few examples of possible use cases:
 Explaining seasonal patterns in sales
 Predicting the expected number of incoming or churning customers
 Estimating the effect of a newly launched product on number of sold units
 Detecting unusual events and estimating the magnitude of their effect
Objectives
At the end of this tutorial, the reader can expect to learn how to:
 Plot, examine, and prepare series for modeling
 Extract the seasonality component from the time series
 Test for stationarity and apply appropriate transformations
 Choose the order of an ARIMA model
 Forecast the series
Readers can use the following ARIMA cheat sheet as an outline of this tutorial and general guidance when fitting these types of models:
 Examine your data
 Plot the data and examine its patterns and irregularities
 Clean up any outliers or missing values if needed
tsclean()
is a convenient method for outlier removal and inputing missing values Take a logarithm of a series to help stabilize a strong growth trend
 Decompose your data
 Does the series appear to have trends or seasonality?
 Use
decompose()
orstl()
to examine and possibly remove components of the series
 Stationarity
 Is the series stationary?
 Use
adf.test()
, ACF, PACF plots to determine order of differencing needed
 Autocorrelations and choosing model order
 Choose order of the ARIMA by examining ACF and PACF plots
 Fit an ARIMA model
 Evaluate and iterate
 Check residuals, which should haven no patterns and be normally distributed
 If there are visible patterns or bias, plot ACF/PACF. Are any additional order parameters needed?
 Refit model if needed. Compare model errors and fit criteria such as AIC or BIC.
 Calculate forecast using the chosen model
A Short Introduction to ARIMA
ARIMA stands for autoregressive integrated moving average and is specified by these three order parameters: (p, d, q).
The process of fitting an ARIMA model is sometimes referred to as the BoxJenkins method.
An auto regressive (AR(p)) component is referring to the use of past values in the regression equation for the series Y. The autoregressive parameter p specifies the number of lags used in the model. For example, AR(2) or, equivalently, ARIMA(2,0,0), is represented as
where φ_{1}, φ_{2} are parameters for the model.
The d represents the degree of differencing in the integrated (I(d)) component. Differencing a series involves simply subtracting its current and previous values d times. Often, differencing is used to stabilize the series when the stationarity assumption is not met, which we will discuss below.
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Introduction to Forecasting with ARIMA with R.
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