MSE - Mean Squared Error

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 MSE calculation.
5. 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.
6. 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
7. MSE is most useful when concerned about large errors than smaller ones.
8. 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.
9. 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.
10. The MSE function is available starting with version 1.65 HAMMOCK.

Example 1:

Files Examples

Related Links

• Wikipedia - Mean squared error

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