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In statistics, the mean signed difference (MSD), also known as mean signed error (MSE), is a sample statistic that summarises how well an estimator matches the quantity that it is supposed to estimate. It is one of a number of statistics that can be used to assess an estimation procedure, and it would often be used in conjunction with a sample version of the mean square error.
The mean signed difference is derived from a set of n pairs, , where is an estimate of the parameter in a case where it is known that . In many applications, all the quantities will share a common value. When applied to forecasting in a time series analysis context, a forecasting procedure might be evaluated using the mean signed difference, with being the predicted value of a series at a given lead time and being the value of the series eventually observed for that time-point. The mean signed difference is defined to be
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