Building a GARCH Volatility Model in Python: A Step-by-Step Tutorial with Statistical Analysis (2024)

The Generalized Autoregressive Conditional Heteroscedasticity (GARCH) model is a statistical model that is widely used to analyze and forecast volatility in financial time series data. The model is based on the premise that the variance of the error term in a time series is not constant over time, but rather varies as a function of past error terms.

The GARCH model was first introduced by Robert F. Engle in the early 1980s, and has since become one of the most popular models used in financial econometrics. Engle was awarded the Nobel Prize in Economics in 2003 for his contributions to the development of time series econometrics.

The GARCH model is important because it allows us to better understand the dynamics of financial markets and to make more accurate predictions about future market behavior. By analyzing volatility in financial time series data, we can identify patterns and trends that can inform investment decisions and risk management strategies.

We start by importing the necessary libraries, including numpy, pandas, matplotlib, and arch.

# Import necessary libraries
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import arch

Next, we generate a random time series with 1000 observations using numpy.

# Generate a random time series with 1000…