: Typically an AR, MA, or ARMA model that captures the average behavior of the series. Variance Equation : Defines the conditional variance ( σt2sigma sub t squared
import pandas as pd import numpy as np from arch import arch_model import matplotlib.pyplot as plt arch models
Consider daily returns of Tesla stock:
ARCH and GARCH models are indispensable tools for analyzing financial time series. By allowing variance to change over time, they provide superior forecasts for risk management, option pricing, and portfolio optimization. While the basic GARCH(1,1) model is robust for many datasets, practitioners should consider asymmetric extensions (GJR, EGARCH) when analyzing equity markets prone to asymmetric reactions to news. : Typically an AR, MA, or ARMA model