Financial Time Series Analysis: Volatility and Dependencies

Module: Fintech AI | Difficulty: Advanced

GARCH(1,1)

Realized Volatility

Volatility Forecasting

Volatility Regimes

| Regime | Volatility | Trading Strategy | |--------|-----------|-----------------| | Low | <15% | Carry, momentum | | Medium | 15-25% | Balanced | | High | >25% | Defensive, vol selling |

import numpy as np
from arch import arch_model

class VolatilityModeler:
    def __init__(self, returns):
        self.returns = returns
    def garch_fit(self):
        model = arch_model(self.returns * 100, vol='Garch', p=1, q=1)
        return model.fit(disp='off')
    def realized_volatility(self, intraday_returns):
        return np.sqrt(np.sum(intraday_returns**2))
    def forecast_volatility(self, model, horizon=5):
        return model.forecast(horizon=horizon).variance.values[-1]

Research Insight: Volatility modeling is crucial for risk management and derivatives pricing. GARCH models capture volatility clustering but underestimate tail risk. Realized volatility using high-frequency data provides more accurate estimates. Volatility forecasting improves portfolio optimization and hedging.