Calculates the mean squared error (MSE) between the forecast and the eventual outcomes.
Syntax
MSE(X, F)
 X
 is the eventual outcome time series sample data (a onedimensional array of cells (e.g. row or column).
 F
 is the forecast time series data (a onedimensional array of cells (e.g. row or column).
Remarks
 The time series is homogeneous or equally spaced.
 The time series X and F must be of identical size
 The time series X or F may include observations with missing values (e.g. #N/A or blank).
 Observations with missing values in Y or F are excluded from the MSE calculation.
 The mean squared error (MSE) is defined as follows:
$${\displaystyle {\mathrm{MSE}=\frac{1}{N}\times\sum_{t=1}^N \left(y_t f_t \right )^2 = \frac{\mathrm{SSE}}{N}}}$$
Where:
 $y_t$ is the actual outcome value at time t.
 $f_t$ is the forecast value at time t.
 $\mathrm{SSE}$ is the sum of squared errors.
 The MSE provides a quadratic loss function as it squares and subsequently averages the various errors, which gives considerably more weight to large errors (outliers) than smaller ones
 MSE is most useful when concerned about large errors than smaller ones.
 The MSE equation is similar to the statistical measure of variance ($\sigma^2$), which allows us to measure the uncertainty around our most likely forecast  $f_T$. In other words, the MSE can be viewed as the variance of the forecast error.
 The main drawback of MSE is the scale dependency. If the forecast task includes objects with different sales or magnitudes then the MSE measure cannot be applied.
 The MSE function is available starting with version 1.65 HAMMOCK.
Examples
Example 1:


Formula  Description (Result) 

=MSE($B$3:$B$21,$C$3:$C$21)  MSE (0.065795) 
Files Examples
Related Links
References
 R.J. Hyndman, A.B. Koehler, "Another look at measures of forecast accuracy", International Journal of Forecasting, 22 (2006), pp. 679688
 James Douglas Hamilton; Time Series Analysis; Princeton University Press; 1st edition(Jan 11, 1994), ISBN: 691042896
 Tsay, Ruey S.; Analysis of Financial Time Series; John Wiley & SONS; 2nd edition(Aug 30, 2005), ISBN: 0471690740
 D. S.G. Pollock; Handbook of Time Series Analysis, Signal Processing, and Dynamics; Academic Press; Har/Cdr edition(Nov 17, 1999), ISBN: 125609906
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