Just wondering how to setup xreg variables for ARIMAX models? I am particularly interested in whether I should be grouping together events for dummy variables. For example should I create 1 dummy variable and store all public holidays or should I create a dummy variable for each public holiday (this could lead to many dummy variables). BTW - I am using R and the Forecast package.
This was already answered for you here Approaches to Forecasting with Daily Timeseries
You would want a dummy for each holiday. But what about lead and lag impacts?
Build a regression model at the daily level using promotional variables(lead and lag impacts) and the future expected promotions, 16 U.S. holidays(lead and lag impacts), days of the week with 6 dummy variables, search for special days of the month, months of the year, impact on Mondays after holiday, impact on Fridays before a holiday, along with checking for changes in trend, level shifts, outliers and seasonal pulses to get a forecast. We recommend 3 years of historical data so that you can get a good measure on the holidays. For example, in 2010 and 2011 Christmas landed on a weekend so you have no measure of the impact of Christmas on a weekday. You could include a causal that explains the macro direction of the business (ie # of outlets your product is sold in) always be used as a good causal to help explain the overall trend in the call volume. You could provide future sales estimates using a forecast to help guide the direction of the forecast as well as allow the managements input on expected future business success for upcoming months.
should I create 1 dummy variable and store all public holidays or should I create a dummy variable for each public holiday (this could lead to many dummy variables).
The basic consideration is whether you anticipate the effect will be the same (or almost the same) for every such holiday, or whether it might differ from one to the next.
If you expect the holiday effect to be essentially exactly that - a single effect no matter which holiday it was - then you would code a single dummy. If you expect there would be substantive differences in holidays, then you'd code them differently.
Usually, one would expect there to be differences, but it may depend on the application (and how much of an effect there is in the first place; if the effects aren't all that huge to begin with, the improvement in bias may not be worth the tradeoff in accuracy).
Beware of anticipatory effects - with at least some holidays, there can often be effects for some days beforehand (especially if you're looking at things like food or fuel sales), and sometimes effects in the immediate aftermath as well.