Python Pandas - Autocorrelation Plot

Autocorrelation plots are useful tool for analyzing time series data, it determines whether a time series is random or not. This is done by calculating the autocorrelations for data values at different time lags. The plot also provides horizontal lines for 95% and 99% confidence levels, with the dashed line indicating the 99% confidence level.

If the time series is random, the autocorrelation values will be close to zero for all time lags. If it's not random, at least one autocorrelation value will be noticeably different from zero.

Pandas provides a convenient function for autocorrelation plots, in this tutorial will learn how to use the autocorrelation_plot() function to create autocorrelation plots using Pandas.

The autocorrelation_plot() Function

The plotting.autocorrelation_plot() function in the Pandas library is useful for generating the autocorrelation plots for time series data. This function returns a Matplotlib axis object containing the autocorrelation plot.

Syntax

Following is the syntax of the autocorrelation_plot() function −

pandas.plotting.autocorrelation_plot(series, ax=None, **kwargs)

Where,

• series: The Pandas Series containing the time series data.

• ax: Optional, the Matplotlib axis to plot on.

• kwargs: : Additional options for customizing Matplotlib's plot.

Example: Basic Autocorrelation plot

Here is the basic example of plotting the Autocorrelation plot in Pandas using the plotting.autocorrelation_plot() function.

import numpy as np
import pandas as pd
from pandas.plotting import autocorrelation_plot
import matplotlib.pyplot as plt

# Generate a sample time series
values = np.linspace(-5 * np.pi, 5 * np.pi, num=1000)
ts = pd.Series(0.7 * np.random.rand(1000) + 0.3 * np.sin(values))

# Plot the autocorrelation
plt.figure(figsize=(7, 4))
plt.title('Autocorrelation plot')
autocorrelation_plot(ts)
plt.show()

On executing the above code, you will get the following plot −

Example: Autocorrelation Plot for Date-Indexed Data

Here is another example of using the plotting.autocorrelation_plot() function for plotting the autocorrelation plot for a date-indexed time series.

import numpy as np
import pandas as pd
from pandas.plotting import autocorrelation_plot
import matplotlib.pyplot as plt

# Create a date range and sample data
date_range = pd.date_range(start='2024-01-01', end='2024-12-31')
values = np.arange(len(date_range))
df = pd.DataFrame(values, index=date_range, columns=["Values"])

# Generate autocorrelation plot

plt.figure(figsize=(7, 4))
autocorrelation_plot(df["Values"])
plt.title("Autocorrelation for Date-Indexed Data")
plt.show()

Following is the output of the above code −

Example: Multiple Autocorrelation Plots by Category

We can plot autocorrelation plots for multiple groups in a DataFrame. Following is the example −

import pandas as pd
import matplotlib.pyplot as plt
from pandas.plotting import autocorrelation_plot

# Create DataFrame
df = pd.DataFrame({
    'category': ['save','save','save','save','save','check','check','check','check','check','run','run','run','run','run'],
    'value': [1.2,1.3,1.5,1.7,1.8, 10,13,17,20,25, 7,8,8.5,9,9.3]
})

# Get unique categories
categories = df['category'].unique()

# Create a figure with subplots
fig, axes = plt.subplots(len(categories), figsize=(7, 4))

# Iterate through each category and plot its autocorrelation
for ax, cat in zip(axes, categories):
    data = df[df['category'] == cat]['value']
    autocorrelation_plot(data.diff().iloc[1:], ax=ax)
    ax.set_title(f"Autocorrelation for Category: {cat}")

# Adjust layout for better visualization
plt.tight_layout()
plt.show()

Following is the output of the above code −