Forecast variance and forecast error variance

There is sometimes confusion between “forecast variance” and “forecast error variance”. In fact, they are the same thing.

Suppose we have a probabilistic forecast with estimated mean $\hat{\mu}_{T+h|T}$ and estimated variance $\hat{V}_{T+h|T}$ . That is, our estimated distribution of the future observation $y_{T+h}$ , based on the data <img src=“https://latex.codecogs.com/ …