# Having trouble understanding sources of hetroscedasticity

1. May 13, 2012

### Rabolisk

Hey. Iam trying to understand how specification of the equation can lead to hetroscedasticity. This is stright out of my notes.

Yt=B1+B2x2t+B3x3t+......+BkXkt+$\gamma$$\varpi+$ε$^{}_{t}$

Yt=B1+B2x2t+B3x3t+......+Bkxkt+ε$^{*}_{t}$

where
ε$^{*}_{t}$ = εt + $\gamma$$\varpi$t

Since Var(εt) = $\sigma$$^{2}_{ε}+$$\gamma$$^{}_{t}$var($\varpi$t)

I dont understand the variance part. I know that the variance of any epsilon is $\sigma$2, but why does the γt go outside the variance operator? I know it's a constant so why isn't it γ2?

2. May 14, 2012

### viraltux

If γ is a constant the it's a typo and γ should be squared when outside the variance.

This seems a time series, so one to way to introduce heterocedasticity in this model is by increasing γt over time, I am assuming ϖ is a random variable with the same behavior over time (it's not clear in your formulation since sometimes they both have the t subscript at the end but not in the beginning).