How do I call a forecast that is both accurate and precise? How do I call a forecast (more precisely, a forecasting rule) that is both accurate and precise?
Is there a word that expresses both properties combined?
I do not mean the forecasting rule is perfect, i.e. it does not have to produce forecasts that always perfectly coincide with their respective targets, but its accuracy is good (low bias) and its precision too (low variance).
 A: When I first studied statistics, it was actually an econometrics module and from what I remember (it was a while ago) a great deal of emphasis was placed on estimators that were BLUE. Best Linear Unbiased Predictor, arising from the Gauss-Markov Theorem in the context of linear regression models.
So if you are dealing with a linear model, maybe BLUE can apply to you ? If not, then BUE.
I suppose that, to be BLUE or BUE, although they would be unbiased, they are not necessarily precise, because Best just means lowest variance - so there could be several very imprecise estimators, but one of them will be best. To get over this hurdle, there could need to be some (presumably subjective) choice as to the hurdle for what level of precision is desired.
With that in mind, perhaps it is useful for your case ?
Edit: There doesn't seem to be a word which simultaneously means both (unless we can create one into existence in this thread perhaps !) so to avoid the problem of comparison by using Best, another alternative is simply Precise and Unbiased. 
A: How about "correct"? 
Correct = free from error. Therefore free from bias-error, i.e accurate, and free from variance-error, i.e. precise.
A: My guess would be 'consistent forecast'. As you said:

How do I call a forecast (more precisely, a forecasting rule) that is both accurate and precise?

Quoting Wikipedia on consistency: Use of the terms consistency and consistent in statistics is restricted to cases where essentially the same procedure can be applied to any number of data items. I am taking procedure and rule to be synonymous in this case. 
And some more: A consistent estimator is one for which, when the estimate is considered as a random variable indexed by the number n of items in the data set, as n increases the estimates converge to the value that the estimator is designed to estimate.
So if the estimate converges to the value the forecasting rule is designed to estimate then it can be called accurate  and given the same information the forecasting rule must give precise forecasts.
