Calculating Autocovariance Of Garch By Hand

Calculating autocovariance of GARCH (Generalized Autoregressive Conditional Heteroskedasticity) by hand is a crucial process in financial modeling and risk management. It helps understand the volatility clustering and non-linear dependencies in financial time series data.

1. Enter the values for Alpha, Beta, Mean, and Volatility.
2. Click ‘Calculate’.
3. View the results below the calculator.

The GARCH(1,1) model is defined as:

y_t = μ + ε_t

ε_t = σ_t * z_t

σ_t^2 = α_0 + α_1 * ε_{t-1}^2 + β_1 * σ_{t-1}^2

where z_t ~ N(0, 1)

The autocovariance of ε_t is calculated as:

Cov(ε_t, ε_{t-k}) = (1 – α_1 – β_1) * α_0 * (1 – α_1)^k / (1 – α_1 – β_1)

Comparison of Autocovariance Values

Lag	GARCH(1,1) Model	Actual Data

• Always ensure your data is stationary before applying GARCH models.
• Consider using higher-order GARCH models if needed.
• Be cautious of overfitting and validate your models properly.

What is GARCH?

GARCH is a class of statistical models that describe the evolution of variance of a time series…

Federal Reserve – Volatility Forecasting

NBER – GARCH Models