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
- 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 GRMSE calculation.
- The geometric root mean squared error (GRMSE) is defined as follows:
$${\displaystyle{\mathrm{GRMSE}= \sqrt[2N]{\prod_{t=1}^{N}e_t^2}=\sqrt[2N]{\prod_{t=1}^{N}(y_t-f_t)^2}}}$$ - The GRMSE is more robust than RMSE and less affected by outliers.
- The main drawback is the scale dependency. If the forecast task includes objects with different scales or magnitudes then GRMSE measure could not applied.
- The GRMSE function is available starting with version 1.65 HAMMOCK.
Examples
Example 1:
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| Formula | Description (Result) |
|---|---|
| =GRMSE($B$3:$B$21,$C$3:$C$21) | GRMSE (0.099035) |
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. 679-688
- 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: 0-471-690740
- 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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