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 the GRMSE measure could not be applied.
- The GRMSE function is available starting with version 1.65 HAMMOCK.

## 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.

## Comments

Article is closed for comments.