Question $6$

$($b$)$ What is the unconditional variance var$(t)?$ Consider the ARCH model for stock returns $($DLOG$($STOCK$))$

shown in Table $4$ below. Use the estimates of the variance equation to estimate the unconditional variance for

this model.

$($c$)$ Explain how to test for ARCH effects.

Table $4$: Arch Model

Dependent Variable: DLOG$($STOCK$)$

Method: ML ARCH $-$ Normal distribution $($BFGS $/$ Marquardt steps$)$

Date: $11/10/21$ Time: $11$:$45$

Sample: $1948$Q$12016$Q$2$

Included observations: $274$

Convergence achieved after $10$ iterations

Coefficient covariance computed using outer product of gradients

Presample variance: backcast $($ parameter $=0\mathrm{.}7)$

GARCH$=C(2)+C(3{)}^{***}$RESID$(-1{)}^{{?}^{{?}^{?}}}2$