Autoregressive Conditional Heteroskedasticity (ARCH)

(Question)

Squared Residuals Regression

	Coefficient	Standard Error	p-value
Intercept	3.00	0.577	0.01
Lagged residual  squared	0.28	0.185	0.31

From the data provided above, for a 5% level of significance, one should conclude that his or her AR(1) model exhibits:

A. no autocorrelation.
B. no autoregressive conditional heteroskedasticity (ARCH).
C. no multicollinearity.

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Answer: B

Autoregressive conditional heteroskedasticity refers to an autoregressive equation which the variance of the errors terms is heteroskedastic. (i.e., error variance is not constant.) The presence of ARCH is tested with the following regression:
e_t² = β₁ + β₂ * e_t-1² + v_t

which serves as a proxy for:

var(e_t) = β₁ + β₂ * var(e_t-1) + v_t

The exhibit above indicates that the slope estimate in the ARCH equation is not significant (the t-statistic for the slope estimate of the ARCH equation is not significant.) Therefore, the squared error does not depend on its lagged value (i.e., if the slope value is zero, then the error variance equals the constant β₁, which indicates no conditional heteroskedasticity in the AR model). ARCH is not present.