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Answer: one lag of the squared residuals, and test whether the slope coefficient is statistically different from 0.
## Explanation To test for **ARCH(1)** effects in the residuals: **Correct procedure:** 1. Estimate the squared residuals from the AR(2) model 2. Regress these squared residuals on: - A constant term - **One lag of the squared residuals** (for ARCH(1) testing) 3. Test whether the **slope coefficient is statistically different from 0** **Why this works:** - ARCH(1) means the conditional variance depends on the previous period's squared error - If the slope coefficient is significantly different from zero, it indicates ARCH effects - Testing against 1 would be incorrect - we're testing for the presence of ARCH, not specific parameter values This is the standard Engle's ARCH test procedure for detecting autoregressive conditional heteroskedasticity.
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An analyst estimates an AR(2) model for the monthly sales of a company and calculates the squared residuals from this regression. To test for the presence of ARCH(1) in the residuals, the analyst should regress the squared residuals on a constant and:
A
a time trend, and test whether the time trend coefficient is statistically different from 0.
B
one lag of the squared residuals, and test whether the slope coefficient is statistically different from 0.
C
one lag of the squared residuals, and test whether the slope coefficient is statistically different from 1.