predicting a rv based on past time series results

Hi all,

I have 3 previous years data (ie 3 time series) going from 05/05

may 05 - august 25 , the curve for the current year has data plotted from
may 05 to may 26th (plotted every Thursday) so how would I use the previous data to predict the curve into the future? Time Series does not see like a good choice as there is no real seasonality as its always a growing number. see graph below