SSE - Sum of Squared Errors

Calculates the sum of the squared errors of the prediction function.

Syntax

SSE (X, Y)

X

is the original (eventual outcomes) time series sample data (a one-dimensional array of cells (e.g., rows or columns)).

Y

is the forecasted time series data (a one-dimensional array of cells (e.g., rows or columns)).

Remarks

1. The time series is homogeneous or equally spaced.
2. The two time series must be identical in size.
3. A missing value (e.g., $x_k$ or $\hat x_k$) in either time series will exclude the data point $(x_k,\hat x_k)$ from the SSE.
4. The sum of the squared errors, $\mathrm{SSE}$, is defined as follows: $$\mathrm{SSE}=\sum_{i=1}^N \left(x_i-\hat x_i \right )^2$$ Where:
   • $\{x_i\}$ is the actual observations time series.
   • $\{\hat x_i\}$ is the estimated or forecasted time series.

Files Examples

Related Links

• Wikipedia - Residuals sum of squares.

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.