$($a$)$ Name one feature of return data that can be reproduced using a standard GARCH $(1,1)$ process.

$[$Do not write more than one line of text.$]$

$(3$ points$)$

$($b$)$ Name and describe one feature of return data that cannot be reproduced using a standard

GARCH$(1,1)$ process. Why is it unable to capture such a phenomenon?

$[$Do not write more than three lines of text.$]$

$(7$points$)$

Based on daily return data for company ABC over the last $10$ years, you obtain the following parameter

estimates for an ARMA$(0,0)-$GARCH $(1,1)$ model: $=0\mathrm{.}0010,{}_0=0\mathrm{.}000020,{}_1=0\mathrm{.}15,$ and $=0\mathrm{.}75.$

Suppose

diamond ABC's unconditional daily standard deviation is $1\%,$

diamond the forecast you made yesterday for ABC's standard deviation was $2\%,$ and

diamond ABC's unexpected return observed today is $3\%.$

What is your forecast for tomorrow's standard deviation?

$(10$ points$)$