# forecasting sharp seasonal peak in time series

I have time series data on a daily level over the past 4 years. What is clear from examining past data is that there are two very clear peaks in the time series around the same time of year (they shift a bit based on holidays, weekends, etc and the peaks are growing each year). Moreover, these peaks in the time series, particularly the second one, are very sharp and large; in that, the peaks tower above the rest of the data and there is only a build up to the peaks over a few days.

I want to forecast using these data. When I examined how well I could forecast activity during last year's second peak, an ARIMA model severely underestimated the peak in activity. A GBM model (machine learning model) did a much better job at predicting how high activity would go during the peak.

Question - are there known methods that are good for forecasting sharp, high peaks that are very seasonal (happen a particular times of year).

Thanks

• why don't you post your data and perhaps we can be of help . – IrishStat Dec 8 '14 at 22:42
• ARIMA models are not useful on their own for predicting isolated peaks - you need a model that incorporates the possibility. The fact that you know where they happen suggests using dummies as regressors. – Glen_b Dec 9 '14 at 0:02
• @Glen_b A model that includes both the ARIMA structure and and user-specified predictors or identified deterministic structure like Level Shifts/Local Time Trends etc. can often be useful. – IrishStat Dec 9 '14 at 0:46
• @IrishStat I was trying to suggest an ARIMA model with user-specified predictors above. – Glen_b Dec 9 '14 at 0:52

You can use an ARIMAX model and include eXternal or eXplanatory variables. These could be 0-1 dummies, or ramp-ups. You just need to know beforehand when these peaks will occur, of course. In R, look at auto.arima(), where you feed these explanatory variables into the xreg parameter.

We use dummies in similar cases. e.g. tax season elevation in some product types. We use both ARIMA (for times series) and regression model with dummies for a quarter or a month. In daily data, you can still have seasonal dummies such as seasons of year, or even months. You can also place them around specific dates such as Apr 15. You can have a dummy as num of days after the specific seasonal event such as Xmas, Valentines, 4th July.