RMSD - Root Mean Squared Deviations

1. The RMSD is also known as root mean squared error (RMSE).
2. The RMSD compares differences between two data sets, neither of which is accepted as the "standard or actual."
3. The time series is homogeneous or equally spaced.
4. The two time-series must be identical in size.
5. The root mean squared errors (deviations) function is defined as follows:
   $$\mathrm{RMSD}=\mathrm{RMSE}=\sqrt{\frac{\mathrm{SSE}}{N}}=\sqrt{\frac{\sum_{i=1}^N (x_i - \hat x_i)^2}{N}}$$
   Where:
   
   • $\{x_i\}$ is the actual observations time series
   • $\{\hat x_i\}$ is the estimated or forecasted time series
   • $N$ is the number of non-missing data points
6. The normalized root-mean deviation (or errors) function is defined as follows:
   $$\mathrm{NRMSD}=\frac{\mathrm{RMSD}}{x_{\mathrm{max}}-x_{\mathrm{min}}} $$
   Where:
   
   • $x_{\mathrm{max}}$ is the maximum value in the first time series
   • $x_{\mathrm{min}}$ is the minimum value in the first time series
7. The coefficient of variation of the RMSD $\mathrm{CV_{RMSD}}$ is defined as follows:
   $$\mathrm{CV(RMSD)}=\frac{\mathrm{RMSD}}{\bar x}$$
   Where:
   
   • $\bar x$ is the mean of the first (observed) time series

Example 1:

Files Examples

Related Links

• Wikipedia - Root-mean squared error

References

• Hamilton, J .D.; Time Series Analysis, Princeton University Press (1994), ISBN 0-691-04289-6
• Tsay, Ruey S.; Analysis of Financial Time Series John Wiley & SONS. (2005), ISBN 0-471-690740