Time Series Forecasting with (week)day data in R

Question

I was hoping to ask this community for a little advice. I’m doing a bit of daily forecasting, and, because it has always served me so well, I’m using Prof. Hyndman's now famous 'forecast' package. At a high level, I’m simply feeding auto.arima a timeseries object of frequency 5 (I’m only using business days), along with 2 columns of simple exogenous regressors—a dummy variable for “Holiday” and a dummy variable for “last business day of the month”. For most of my product forecasts, this works quite well, but for the odd product or two, I’m not quite satisfied with the model output. My questions, then are: 1. Do you think that I should add additional dummy variables for things like “Monday” or “Tuesday after a holiday” or perhaps every day of the week (save one)? I’m worried about overfitting, but I’m also worried about the seasonal AR/MA terms getting confused by situations where Mondays are either higher than the average weekday or zero (in the case of a holiday) 2. I only have 9 months or so of data…do you think I should try to add additional seasonality to the model, or wait until I have a full year?

Answer 1

1. A dummy variable for the day after a holiday can be effective (and sometimes also the day before a holiday). I wouldn't add a dummy for every different day of the week following a holiday as that will probably overfit. Any regular seasonality should be captured by the seasonal ARMA part of the model, although you could instead handle that with four day-dummies but then make the ARMA part of the model non-seasonal.

2. You can't add additional annual seasonality until you have at least a year of data as you can't separate trend from annual seasonality.

Answer 2

I would add 4 day-of-the-week and also allow for changes in the day-of-the-week and a holiday variable for each holiday as you are assuming all holidays have the same effect. I would look for level shifts and local time trends over time. I would look for monthly effects and weekly effects . I would look for and deal with non-constanterror variance using weighted least squares or power tranforms . I would look for one-time anomalies and create dummy pulse indicators as needed. I would look for day-of-the-month effects.