Having trouble understanding sources of hetroscedasticity

[Rabolisk]

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

Y_t=B₁+B₂x_2t+B₃x_3t+...+B_kX_kt+$\gamma$$\varpi+$ε$^{}_{t}$


Y_t=B₁+B₂x_2t+B₃x_3t+...+B_kx_kt+ε$^{*}_{t}$

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

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

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

 

[viraltux]

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

Y_t=B₁+B₂x_2t+B₃x_3t+...+B_kX_kt+$\gamma$$\varpi+$ε$^{}_{t}$


Y_t=B₁+B₂x_2t+B₃x_3t+...+B_kx_kt+ε$^{*}_{t}$

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

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

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

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).