Trading Day Effects in Time Series

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?

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.

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

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

Example: single family permits

Trading day

Trading day effect

Mon 12.1Tue 4.9

Wed 26.3Thu -2.0

Fri 0.3Sat -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

Example: single family permits

Trading day

Trading day effect

Mon 12.1Tue 4.9

Wed 26.3Thu -2.0

Fri 0.3Sat -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

Trading day adjustment

Trading day

Trading day effect

Mon 12.1Tue 4.9

Wed 26.3Thu -2.0

Fri 0.3Sat -19.5

Sun -22.0

Day Effect Day EffectSun -22.0 Tue 4.9

Mon 12.1 Wed 26.3Tue 4.9 Thur -2.0

Sum -5.1 Sum 29.2

2011 2012

• The trading day effect makes 2011 too low and 2012 too high

Trading day adjustment

• Solution: subtract the sum of the trading day effects from the original values

Trading day adjustment

2011 2012Growth

rateSingle family permits (May) 347 475 36.9%

Less: trading day effects -5.1 29.2Equals: Adjusted single family permits 352 446 26.6%

• 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.

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