Algorithmic Trading & Indicators Advanced

GARCH(1,1) Volatility Forecasting Model in Python (arch library)

Fit a Generalized Autoregressive Conditional Heteroskedasticity GARCH(1,1) model in Python to forecast future market volatility clustering.

#pandas#numpy#arch

Problem Statement

Financial returns exhibit volatility clustering (periods of high volatility follow high volatility). GARCH(1,1) models time-varying variance far more accurately than standard rolling standard deviation.

Formula / Core Logic

sigma_t^2 = omega + alpha * epsilon_{t-1}^2 + beta * sigma_{t-1}^2

Installation

pip install pandas numpy arch

garch-volatility-forecasting-model-python.py

import pandas as pd
import numpy as np
from arch import arch_model
\.def fit_garch_volatility(returns_series):
    scaled_returns = returns_series.dropna() * 100.0
    model = arch_model(scaled_returns, vol='GARCH', p=1, q=1, mean='Constant', dist='normal')
    results = model.fit(disp='off')
    forecasts = results.forecast(horizon=5)
    conditional_vol = np.sqrt(results.conditional_volatility / 100.0)
    return results, forecasts.variance.iloc[-1].values

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Frequently Asked Questions

Q: Why scale returns by multiplying by 100 before fitting GARCH?

Optimization algorithms converge much faster and avoid numerical underflow when return variances are scaled closer to integer magnitude.