The Augmented Dickey-Fuller (ADF) test is a statistical test used to determine whether a unit root is present in a time series dataset. A unit root represents that a time series is non-stationary, meaning its mean and variance change over time.

R code is always interesting.

Let me show you an example code on how you can perform an ADF test, using a built-in dataset (AirPassengers dataset).

# Load required libraries
library(tseries)  # For ADF test
library(forecast) # For loading AirPassengers dataset

# Load dataset
data("AirPassengers")

# Inspect the dataset
head(AirPassengers)

# Check if the time series is stationary
adf.test(AirPassengers)

The code is simple, I’ll explain it.

1. The tseries library contains the adf.test() function. This function performs the Augmented Dickey-Fuller test. The forecast library is used to load the AirPassengers dataset.
2. Now load the AirPassengers dataset, which is a built-in dataset in R containing the monthly totals of international airline passengers from 1949 to 1960.
3. It’s always good to inspect the dataset to understand its structure and content. You can use head() to view the first few rows of the dataset.
4. The adf.test() function performs the actual ADF test on the time series data. It returns the test statistic and p-value.

The code generates the following output:

Augmented Dickey-Fuller Test

data:  AirPassengers
Dickey-Fuller = -1.7306, Lag order = 9, p-value = 0.4133
alternative hypothesis: stationary

Let’s spend some more time to understand the output.

• The test statistic value (-1.7306 in this case).
• The number of lags used in the regression model (9 in this case).
• The p-value associated with the test statistic. In this case, it’s 0.4133.

This ADF test indicates whether the alternative hypothesis is “stationary” or “explosive”. Since the p-value is greater than the significance level of 0.05 (commonly used), we fail to reject the null hypothesis, suggesting that the time series is likely non-stationary.

You can apply the same kind of ADF test for any other dataset.