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).