GARCH and EGARCH Volatility Models

GARCH and EGARCH models are time-series models in which the conditional variance of a series depends on past squared shocks and past variances, with EGARCH allowing asymmetric responses to positive and negative shocks.

GARCH·EGARCH 모형은 시계열의 조건부 분산이 과거 충격의 제곱과 과거 분산에 의해 결정되도록 한 시계열 모형이며, EGARCH는 양(+)과 음(-)의 충격에 대한 비대칭 반응을 허용한다.

How do I model changing volatility in a financial time series?

금융 시계열에서 변하는 변동성은 어떻게 모형화하나요?

GARCH models describe volatility clustering by letting today's conditional variance depend on recent shocks and recent variance, and EGARCH models the log variance so negative shocks can raise volatility more than positive ones. They fit high-frequency return series such as daily stock, exchange-rate, or commodity returns.

When to use GARCH and EGARCH Volatility Models

• Daily or weekly asset returns showing volatility clustering
• Forecasting conditional variance or value at risk
• Testing whether bad news increases volatility more than good news (leverage effect)

When to use something else

• The series shows no ARCH effects in squared residuals: a mean model such as ARIMA is sufficient
• Volatility of several assets must be modeled jointly: use multivariate GARCH such as DCC

Assumptions and requirements

• The return series is stationary
• ARCH effects are present (e.g., Engle's ARCH-LM test)
• A suitable error distribution (normal, Student t, or skewed t)
• Stationarity conditions on GARCH parameters (e.g., alpha + beta < 1 in GARCH(1,1))

What the analysis reports

• Mean and variance equation coefficients with standard errors
• Persistence (alpha + beta) and asymmetry parameter for EGARCH
• Log-likelihood, AIC, BIC
• Ljung-Box tests on standardized and squared standardized residuals
• Plot of conditional volatility

How to report it

A GARCH(1,1) model showed high volatility persistence, α + β = [value]; in the EGARCH model the asymmetry term was [value] (p = [value]).

Related methods

• ARIMA Model
• ARCH-LM Test
• Multivariate GARCH (DCC)

Run GARCH and EGARCH Volatility Models on Quorant