The study of the seasonality of a historical series can have the purpose of:

• Simply estimating the seasonal component
• Eliminating it from the general course once it has been estimated

If you have to compare several time series with different seasonality, the only way to compare them is by a seasonal adjustment of them.

There are several ways to estimate the seasonal component. One of these is the use of a regression model using dichotomous auxiliary variables (dummy variables).

Suppose the existence of an additive model without a trend component:

Y(t) = S(t) + r(t)

And suppose we have measured the series on a monthly basis. The dummy variables can be defined in the following way:

• d_j(t): 1 if the observation t is relative to the j^th month of the year
• d_j(t): 0 otherwise

Once the periodic dummy variables have been created, the seasonal component can be estimated using the following regression model:

Y(t) = β₁D₁ + β₂D₂ + ... + β_nD_n + ε(t)

The remaining ε(t) part of the model represents the part of the series not explained by seasonality. If a trend component is present in the series, it will coincide precisely with ε(t).