# Adding up events in time series forecasting

Let us say that we have an event - variable (1/ 0) that denotes the occurence of an event on a daily basis e.g. a strike. Let us now say that we have a continuous variable (sales) that that we want to forecast. The interval on which the variable is measured is monthly. We want to incorporate the event variable in a model that will be used for forecasting sales but the event variable is measured in a more detailed interval. If there were 5 days in a month that a strike took place can we say that the event variable value for that month is 5? More generally can we create a derived event variable by aggregating the values of the original dalily event variabe? In this way we will have an independent variable with value ranging from 0 (no strikes occured the specific month) to 30 (if a strike occured every day in the specific month)?

Does this process stand from a statistical point of view and is this variable going to have any predictive power?

Andreas

Thnaks for your answer. Let us make things less complicated assuming that the dependent variable is electricity consumption and the event is a day with extremely low average temperature (day with extreme cold). With this case we don;t care about weekends and the rest of the problems that are coused in the case of strikes. Let us say that we have electricity consumption per month period so 12 observations per year. Let us also say that we have recorder the days woth extereme cold daily by using a binary variable (so approximately 365 observations per year. What would you do if you wnated to incorporate the daily event in the model of forecasting the monthly series. Would you add up the 1, would you take the percentage of days over the month that exhibit the extreme cold or what else? What do you htink is the better solution?

There may be a more authoritative answer for your specific case, but derived/transformed variables are used routinely in regressions.

Given that, I can see three issues in your case:

1. How do you express your count? For example, it may be better to express strikes as a percentage of the days in the month that had strikes, rather than a count.

2. How do you count strikes and how can they occur? Can people be on strike for an hour rather than a whole day? Do you count days from the beginning of a strike to the end, or only days they'd otherwise work? (E.g. if people don't normally work on weekends, do they count as strike days?)

(If you wish to do something that would require forecasting strike probabilities, this could also determine whether you need to account for a zero-inflation effect.)

3. If strikes can occur for multiple days, is a seven-day strike the same as seven one-day strikes or might it have greater or less effect?

EDIT: Gelman mentions on page 69 of Gelman & Hill (2007) that, "... sometimes several inputs can be averaged or summed to create a 'total score' that can be used as a single predictor in the model." I don't immediately have other references or any particularly for aggregate variables.

We have seen the use of percentage of days in the month. If you have 3 days with a strike out of 30 days then the dummy variable would be .1.

I would note that there is a significant literature on predicting low frequency time series using a higher frequency time series. MIDAS regression and state space representations are more often seen in the literature. These techniques can be more complicated than the approach you intend to use (which is perfectly fine, taking into account Wayne's points), but may be helpful if you have other daily or weekly indicators you wish to consider.