Econometric Theory/Summation and Product Operators
To sum a series of variables , the Greek capital letter sigma Σ is used:
There are some properties concerning the summation operator Σ:
1. , where k is a constant.
2. , where k is a constant.
3. , where a and b are constants. This is a result of rules 1 and 2 above.
The double summation operator is used to sum up twice for the same variable:
The double summation operator has the following properties:
1. . The order of the summation signs is interchangeable.
Finally, the product operator Π is defined as: .
- Gujarati, D.N. (2003). Basic Econometrics, International Edition - 4th ed.. McGraw-Hill Higher Education. pp. 869-870. ISBN 0-07-112342-3.