1. Trading Day Effects in Time Series

2. Example: single family construction Home construction activity at the state and local level is measured by permits issued Over the year, construction rose 37% in Nashville Or did it?

3. Trading Day Effects A trading day is a day in which an activity (sales, construction, air travel) takes place. Recurring day-of-the-week effects are called trading day effects. When these effects are significant and not taken into account, forecasting and analysis are hindered.

4. Days of the week Every month has at least 28 days Thus, every day of the week occurs at least 4 times a month Frequently, a day of the week occurs 5 times in a month Some days of the week generate more activity than other days Example: more permits are issued Wednesday than other days

5. Days of the week Thus, a month with 5 Wednesdays will show more permits than other months This suggests that construction activity has increased, but in reality the effect is simply due to the trading day effect

6. Example: single family permits Trading day Trading day effect Mon12.1 Tue4.9 Wed26.3 Thu-2.0 Fri0.3 Sat-19.5 Sun-22.0 Gretl estimated these trading day effects for Nashville MSA single family permits A month with 5 Wednesdays will have 26.3 more permits than other months A month with 5 Saturdays with have 19.5 fewer permits than other months

7. Example: single family permits Trading day Trading day effect Mon12.1 Tue4.9 Wed26.3 Thu-2.0 Fri0.3 Sat-19.5 Sun-22.0 In our Nashville example, – Sun, Mon, and Tue occur 5 times in May 2011 – Tue, Wed, and Thu occur 5 times in May 2012 – 2011 is low because it has an extra Sunday – 2012 is high because it has an extra Wednesday

8. Trading day adjustment Trading day Trading day effect Mon12.1 Tue4.9 Wed26.3 Thu-2.0 Fri0.3 Sat-19.5 Sun-22.0 The trading day effect makes 2011 too low and 2012 too high

9. Trading day adjustment Solution: subtract the sum of the trading day effects from the original values

10. Trading day adjustment 20112012 Growth rate Single family permits (May)34747536.9% Less: trading day effects-5.129.2 Equals: Adjusted single family permits35244626.6% Conclusion: adjusting for trading day effects has a large impact on calculated permit growth Adjusted growth rate is 26.6% (instead of 36.9%) Adjusted growth is 94 units instead of 128 units.

11. Trading day effects The trading day effect may be significant for any time series that is measured as a flow (per unit of time): – Retail sales – Housing construction – Stock trades – Airline passengers The trading day effect is not an issue for stock variables (measured at a point in time): – Employment – Personal income