ARMA-GARCH Model in Python

The AutoRegressive Moving Average- Generalized Autoregressive Conditional Heteroskedasticity (ARMA-GARCH) model is a statistical model used to analyze financial data that exhibit volatility clustering, meaning periods of high volatility tend to be followed by periods of high volatility and vice versa.

Python provides several libraries to implement the ARMA-GARCH model, including statsmodels, arch, and pyflux. In this article, we will focus on arch.

Installation

To install arch, you can use pip:

pip install arch

Creating an ARMA-GARCH Model

To create an ARMA-GARCH model using arch, we first need to import the necessary libraries and load data.

import pandas as pd
import arch

data = pd.read_csv('data.csv', index_col='Date', parse_dates=True)

Next, we can create an ARMA-GARCH model by specifying the order of the AR and MA terms and the order of the GARCH terms.

model = arch.arch_model(data['Returns'], mean='ARMA', lags=[1, 2, 3], vol='GARCH', p=1, o=0, q=1, dist='Normal')

In this example, we have specified an ARMA(3) model and a GARCH(1,1) model with a Normal distribution assumption. We can fit the model to the data by calling the .fit() method.

results = model.fit()

We can then summarize the results with the .summary() method.

print(results.summary())

The output will include information such as the log-likelihood, parameter estimates, and significance levels.

Predicting with an ARMA-GARCH Model

Once we have created and fitted an ARMA-GARCH model, we can use it to make predictions. To do so, we call the .forecast() method.

forecast = results.forecast(horizon=5)

This will give us a forecast of the next 5 periods. We can also plot the forecasted values and the actual values.

import matplotlib.pyplot as plt

fig = plt.figure(figsize=(12, 6))
ax = fig.add_subplot(1, 1, 1)

data['Returns'].tail(50).plot(ax=ax, label='Actual')
forecast.mean[-1:].plot(ax=ax, label='Forecast')

plt.legend()
plt.show()

This will plot the last 50 actual values and the forecasted value for the next period.

Conclusion

In this article, we have introduced the ARMA-GARCH model and shown how to implement it in Python using the arch library. We demonstrated how to create a model, fit it to data, and make predictions with it. With this knowledge, you can begin to use ARMA-GARCH models to analyze financial data and make informed decisions based on your predictions.