Seasonality

1
Seasonality

• Diebold, Chapter 5

2
Seasonality

• A seasonality pattern is one that repeats itself
  every year.
• Caused by holidays, weather, etc.
• Seasonality is pervasive in business and economics

3
Dealing with seasonality

• Remove it and model and forecast the seasonally
  adjusted series
• Model seasonality directly

4
Modeling Seasonality

• Seasonal dummy variables (quarterly)
• D1 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0,.
• D2 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, .
• D3 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, .
• D4 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, .
• Seasonal dummy variables (monthly)
• D1 through D12

5
Using Seasonal Dummies

• What happens if you include all seasonal dummies
  and a constant in a regression?
• Usually include s-1 dummies and constant

6
Creating Seasonal Dummies in Eviews

• _at_SEAS(season_number) returns a dummy variable
  based on the period within the current year in
  which the current observation occurs, where the
  year is divided up according to the workfile
  frequency.
• "_at_SEAS(1)", "_at_SEAS(2)", "_at_SEAS(3)", and
  "_at_SEAS(4)" correspond to the set of dummy
  variables for the four quarters of the year.
• GENR D1_at_SEAS(1)

7
Calendat Effects

• Holiday variation Easter
• Full set of seasonal dummies
• Easter dummy 1 in month the contains Easter 0
  otherwise
• Trading day variation
• Different month contain different trading days or
  business days
• Values of each month is the number of
  trading/business days that month

8
Date Function in Eviews

• _at_DATE returns the start date of the period of
  time of the current observation of the workfile.
• _at_ENDDATE returns the end date of the period of
  time associated with the current observation of
  the workfile.
• Each date is returned in a number using standard
  EViews date representation (fractional days since
  1st Jan 1AD, see Dates).

9
Business Days in Eviews

• The _at_DATE and _at_ENDDATE functions can be combined
  with the EViews date manipulation functions to
  provide a wide variety of calendar information
  about a dated workfile.
• For example, if we had a monthly workfile
  containing sales data for a product, we might
  expect the total sales that occurred in a given
  month to be related to the number of business
  days (Mondays to Fridays) that occurred within
  the month. We could create a new series in the
  workfile containing the number of business days
  in each month by using
• series busdays _at_datediff(_at_date(1), _at_date, "B")