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.

4. ,

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.

2. .

3. .

4. .

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.