# GRMSE – Geometric Root Mean Square Error

Calculates the geometric mean root square error (GRMSE) between the forecast and the eventual outcomes.

## Syntax

GRMSE(X, F)
X
is the eventual outcome time series sample data (a one-dimensional array of cells e.g. row or column).
F
is the forecast time series data (a one-dimensional array of cells e.g. row or column).

## Remarks

1. The time series is homogeneous or equally spaced.
2. The time series X and F must be of identical size
3. The time series X or F may include observations with missing values (e.g. #N/A or blank).
4. Observations with missing values in Y or F are excluded from the GRMSE calculation.
5. The geometric root mean squared error (GRMSE) is defined as follows:

$${\displaystyle{\mathrm{GRMSE}= \sqrt[2N]{\prod_{t=1}^{N}e_t^2}=\sqrt[2N]{\prod_{t=1}^{N}(y_t-f_t)^2}}}$$
6. The GRMSE is more robust than RMSE and less affected by outliers.
7. The main drawback is the scale dependency. If the forecast task includes objects with different scales or magnitudes then GRMSE measure could not applied.
8. The GRMSE function is available starting with version 1.65 HAMMOCK.

## Examples

Example 1:

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A B C
Date Data Forecast
2008-01-01 -2.9 -2.95
2008-02-01 -2.83 -2.7
2008-03-01 -0.95 -1.00
2008-04-01 -0.88 -0.68
2008-05-01 1.21 1.50
2008-06-01 -1.67 -1.00
2008-07-01 0.83 0.90
2008-08-01 -0.27 -0.37
2008-09-01 1.36 1.26
2008-10-01 -0.34 -0.54
2008-11-01 0.48 0.58
2008-12-01 -2.83 -2.13
2009-01-01 -0.95 -0.75
2009-02-01 -0.88 -0.89
2009-03-01 1.21 1.25
2009-04-01 -1.67 -1.65
2009-05-01 -2.99 -3.20
2009-06-01 1.24 1.29
2009-07-01 0.64 0.60

Formula Description (Result)
=GRMSE($B$3:$B$21,$C$3:$C$21) GRMSE (0.099035)