Calculates the geometric mean squared error (GMSE) between the forecast and the eventual outcomes.
Syntax
GMSE(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 GMSE calculation.
 The geometric mean squared error (MSE) is defined as follows:
$${\displaystyle{\mathrm{GMSE}= \sqrt[N]{\prod_{t=1}^{N}e_t^2}=\sqrt[N]{\prod_{t=1}^{N}(y_tf_t)^2}}}$$  The GMSE is more robust to outliers than MSE.
 In general, the biggest advantage of the geometric mean is that the mean absolute of two methods or models can be compared by computing their geometric means. If one geometric mean is 10 and the other is 12, it can be inferred that the mean absolute error of the second methods are 20% higher than those of the first.
 The main drawback is the scale dependency. If the forecast task includes objects with different scales or magnitudes then GMSE measure could not applied.
 The GMSE function is available starting with version 1.65 HAMMOCK.
Examples
Example 1:


Formula  Description (Result) 

=GMSE($B$3:$B$21,$C$3:$C$21)  GMSE (0.009808) 
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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