# Interpretation of MSE (mean square error) and ME (mean error)

I'd like to produce forecasts by considering different scenarios. I'm using Mean Error (ME), where the error $=$ forecast $-$ demand, and Mean Square Error (MSE) to evaluate the results. For the scenarios that bias (ME) is negative the MSE is very high, how can I interpret these results?

I know that the MSE$=$variance of forecast error + bias$^2$, so for these scenarios, we have a low bias but MSE is high, so it means the variance of forecast error is high.

• "... for the scenarios that ME is negative..." this makes me wonder if you using the mean of the error, or the mean of the absolute value of the error? Because if it's the former, positive and negative errors will cancel out. A set of errors {-100, 100, -100, 100} has a mean error of zero, despite every entry having an absolute error of 100. However the root mean squared error will be 100, as $(-100)^2 = 10000$, i.e. positive and negative values don't cancel. Whether you want errors to cancel will depend on your application. Most applications don't, so use mean squared or mean absolute error – Pat Jun 27 '13 at 8:59