Dummy variables for seasonality

In the context of financial markets, and especially in the case of equities, a number of ‘seasonal effects’ have been noted. Such effects are usually known as ‘calendar anomalies’ or ‘calendar effects’ and result in systematically different behaviour in one or more seasons compared with the others. Examples include open- and close-of-market effects, the ‘January effect’, weekend effects and bank holiday effects.

One very simple method for coping with this and examining the degree to which seasonality is present is the inclusion of dummy variables in regression equations. The number of dummy variables that could sensibly be constructed to model the seasonality would depend on the frequency of the data. For example, four dummy variables would be created for quarterly data, twelve for monthly data, five for daily data and so on. In the case of quarterly data, the four dummy variables would be defined as follows:

1. D1t = 1 in quarter 1 and zero otherwise

2. D2t = 1 in quarter 2 and zero otherwise

3. D3t = 1 in quarter 3 and zero otherwise

4. D4t = 1 in quarter 4 and zero otherwise

It is important to remember that if an intercept term is used in the regression, the number of dummies that could also be included would be one less than the ‘seasonality’ of the data. So for quarterly data, we could either use four dummy variables and no intercept or three dummies and an intercept to avoid falling into the ‘dummy variable trap’.