How to Use SARIMA in Python for Time Series Forecasting

Use the SARIMAX class from the statsmodels library to build SARIMA models in Python. Define seasonal and non-seasonal orders, fit the model on your time series data, and then use it to forecast future values.

Syntax

The SARIMA model in Python is implemented via the SARIMAX class from statsmodels.tsa.statespace.sarimax. You specify the non-seasonal order (p, d, q) and seasonal order (P, D, Q, s), where s is the seasonal period.

Key parts:

• order=(p, d, q): non-seasonal ARIMA parameters
• seasonal_order=(P, D, Q, s): seasonal ARIMA parameters
• fit(): fits the model to data
• forecast(steps): predicts future values

python

from statsmodels.tsa.statespace.sarimax import SARIMAX

model = SARIMAX(data, order=(p, d, q), seasonal_order=(P, D, Q, s))
model_fit = model.fit()
forecast = model_fit.forecast(steps=10)

Example

This example shows how to fit a SARIMA model on monthly airline passenger data and forecast the next 12 months.

python

import pandas as pd
from statsmodels.tsa.statespace.sarimax import SARIMAX
import matplotlib.pyplot as plt

# Load sample data
url = 'https://raw.githubusercontent.com/jbrownlee/Datasets/master/airline-passengers.csv'
data = pd.read_csv(url, parse_dates=['Month'], index_col='Month')

# Define SARIMA model parameters
order = (1, 1, 1)  # non-seasonal
seasonal_order = (1, 1, 1, 12)  # seasonal with yearly period

# Fit SARIMA model
model = SARIMAX(data['Passengers'], order=order, seasonal_order=seasonal_order)
model_fit = model.fit(disp=False)

# Forecast next 12 months
forecast = model_fit.forecast(steps=12)

# Plot
plt.plot(data.index, data['Passengers'], label='Observed')
plt.plot(forecast.index, forecast, label='Forecast', color='red')
plt.legend()
plt.title('SARIMA Forecast of Airline Passengers')
plt.show()

Output

A plot showing observed monthly airline passengers and a red line forecasting the next 12 months with SARIMA.

Common Pitfalls

• Not differencing enough: If your data is not stationary, the model may fail or give poor forecasts. Use d and D to difference data.
• Wrong seasonal period: Make sure s matches your data's seasonality (e.g., 12 for monthly, 4 for quarterly).
• Ignoring model diagnostics: Always check residuals and model summary to ensure good fit.
• Using sklearn instead of statsmodels: SARIMA is not in sklearn, use statsmodels instead.

python

from statsmodels.tsa.statespace.sarimax import SARIMAX

# Wrong: Using sklearn for SARIMA (no SARIMA in sklearn)
# from sklearn.sarima import SARIMA  # This will cause ImportError

# Right: Use statsmodels SARIMAX
model = SARIMAX(data, order=(1,1,1), seasonal_order=(1,1,1,12))
model_fit = model.fit()

Quick Reference

Remember these key SARIMA parameters:

Parameter	Description	Example
p	Order of non-seasonal AR term	1
d	Order of non-seasonal differencing	1
q	Order of non-seasonal MA term	1
P	Order of seasonal AR term	1
D	Order of seasonal differencing	1
Q	Order of seasonal MA term	1
s	Length of seasonal cycle	12 (monthly data)

Key Takeaways

Use statsmodels SARIMAX class to build SARIMA models in Python.

Set both non-seasonal and seasonal orders correctly for your data.

Fit the model with .fit() and predict future points with .forecast().

Check data stationarity and seasonal period before modeling.

SARIMA is not available in sklearn; use statsmodels instead.