Decomposition of daily time series (several years) with multiple seasonal patterns i have a daily time series of several years.
Graph &
CSV-file
So far i could figure out with an based on an acf graph and this method:

timeSeriesObj = ts(x,start=c(1999,1,1),frequency=7)
  fit <- tbats(timeSeriesObj)
  seasonal <- !is.null(fit$seasonal)
  seasonal

returns: TRUE

timeSeriesObj = ts(x,start=c(1999,1,1),frequency=365.25)
  fit <- tbats(timeSeriesObj)
  seasonal <- !is.null(fit$seasonal)
  seasonal

returns: TRUE
that i have a weekly as well as an annual seasonality.
How do i look for monthly seasonality? Is it a legit way to sum up all days of a month so i get 12 months a year and then check the acf graph again?
My final goal would be to estimate the different seasonal factors and remove them from the data in order to analyse the effects of different dates as for example easter or 4th of july.
 A: As @Aksakal wisely pointed out daily data analysis can reveal a ton of information. Look at http://www.autobox.com/cms/index.php/afs-university/intro-to-forecasting/doc_download/53-capabilities-presentation particularly slides 42-55 for a demonstration of this. One can break out daily-effects, weekly effects , monthly effects , level shifts . local trends in order to reveal pre,contemporary and lag effects of known events. If you wish you can post your data and I can demonstrate this for you. Please use an excel format and indicate the country as holiday effects can be quite different and the start date. If you have any user-suggested causal series like price/promotion etc please add additional columns to your data matrix.
EDIT AFTER RECEIPT OF DATA:
I took the last 5 years of daily data (1/1/2004-12/31/2008)  and used AUTOBOX in a totally automatic manner. The Actual/Fit and Forecast graph is here . The close-up / forecast for the next 31 days is  and here  . The plot of the model's residuals suggests sufficiency  further supported by the acf of the model's residuals.  . The equation is presented in the next 3 pix  and  and . In summary Christmas , Halloween , New Year's and Thanksgiving are suggested important holidays along with a long-weekend effect around a holiday. The data is seasonal with respect to monthly effects and there are 4 day's of the week that appear to be statistically significant [saturday (+) ,sunday (-),monday(-) and tuesday (-) ].In addition there is an identifiable level shift upwards at 11/03/06 and a reversal at 10/31/07. There are significant seasonal pulses (read changes in day-of-the-week-effects at specific points in time ) and a large amount of pulses ( one-time irregularities). Since I started with the US calendar of holidays these outliers may reflect omitted variables ( e.g. Ramadan etc. ) and should be possibly matched to other events. I have presented here a an example listing of these exceptional days which might help you match up with possible new variables that you can add to the model.

