Chapter 7 Time series regression model (an question)

[li0510]

1. In chapter 7.4, Seasonal dummy variables:
   a. Notice that only six dummy variables are needed to code seven categories. That is because the seventh category (in this case Sunday) is captured by the intercept, and is specified when the dummy variables are all set to zero.
   b. Many beginners will try to add a seventh dummy variable for the seventh category. This is known as the “dummy variable trap”, because it will cause the regression to fail

2. In chapter 7.4, Trading days:
   a. The number of trading days in a month can vary considerably and can have a substantial effect on sales data. To allow for this, the number of trading days in each month can be included as a predictor.
   b. An alternative that allows for the effects of different days of the week has the following predictors:
   x1=number of Mondays in month;
   x2=number of Tuesdays in month;
   ⋮
   x7=number of Sundays in month.

3. Here is my question: in Trading days part, the alternative method exhibits an example that has seven (x1,...,x7) variables, so is this just a new method that does not have to follow the rule, or we should still have to drop one to avoid the dummy variable trap?

Thanks,

[robjhyndman]

Counting the number of each type of day within a month does not give you dummy variables, and is designed for monthly data. Seasonal dummy variables for days of the week is designed for daily data.

In general, if you can compute one of the variables from the other ones, then you have too many. For example, with seasonal dummy variables for days of the week, if you know Mon -- Sat, then Sun = 1 - (Mon + Tue + Wed + Thu + Fri + Sat). You can't do that with the numbers of day types in a month.

[li0510]

Thanks for your explanation.

I just realize that either counting the numbers of trading days or each types of day within a month gives a numerical summary which has satisfied the basic rule of the predictor variable in a multiple regression model, therefore the dummy variable does not need to be applied here and so its trap.

This one can be closed, and appreciate again for taking your time.