# Higher power than 2 for white noise time series?

Let $$\{Yt\}$$ given by $$Y_{t} = Z_{t}$$

With $$Z_{t} \sim{N}(0,\sigma^{2})$$

What are $$E[Y_t^{3}]$$ and $$E[Y_t^{4}]$$?

## 1 Answer

Since $$Y_t=Z_t$$ are normal random variables, you can use the moments defined here. That is

$$E[Y_t^3]=0, \ \ \ \ \ \ E[Y_t^4]=3\sigma^4$$