ARCH-LM Test

The ARCH-LM test, proposed by Engle, checks whether squared residuals depend on their own past values, indicating time-varying conditional variance (ARCH effects).

ARCH-LM 검정은 Engle 이 제안한 방법으로, 제곱 잔차가 자신의 과거 값에 의존하는지(조건부 이분산, ARCH 효과)를 검정한다.

Do my daily returns show volatility clustering that needs a GARCH model?

일별 수익률에 변동성 군집이 있어 GARCH 모형이 필요한지 알고 싶어요.

The test regresses squared mean-model residuals on q of their own lags and compares the number of observations times R² with a chi-square distribution on q degrees of freedom. A significant result means large shocks tend to follow large shocks.

When to use ARCH-LM Test

• You are deciding whether a GARCH-type model is needed.
• You want to check residuals of an ARIMA or regression model for heteroskedasticity over time.
• The data are financial returns or other high-frequency series.

When to use something else

• Heteroskedasticity depends on regressors rather than on time; use the Breusch-Pagan or White test.
• You already need the volatility estimates themselves; fit GARCH and EGARCH Volatility Models directly.

Assumptions and requirements

• The mean model is correctly specified.
• Residuals have finite fourth moments.
• Lag order q is chosen in advance.

What the analysis reports

• LM statistic, degrees of freedom and p-value
• F-version of the test
• Mean model used for the residuals

How to report it

Engle's ARCH-LM test with [value] lags gave LM = [value], χ²([value]), p = [value].

Related methods

• GARCH and EGARCH Volatility Models
• ARIMA Model

Run ARCH-LM Test on Quorant