As I mentioned in my note above, I would treat this as a regression problem. Here is a link to constructing, in R, the lag (and lead) variables from your data (R Head).
Included in the post is a brief introduction to using the resulting data in a regression model. You might also want to do a bit of background digging on the R package dynlm (dynamic linear regression).
You should be evaluating models and forecasts from different origins across different horizons and not one one number in order to gauge an approach.
I assume that your data is from the US. I prefer 3+ years of daily data as you can have two holidays landing on a weekend and get no weekday read. It looks like your Thanksgiving impact is a day off in the 2012 or there was a recording error of some kind and caused the model to miss the Thanksgiving day effect.
Januarys are typically low in the dataset if you look as a % of the year. Weekends are high. The dummies reflect this behavior....MONTH_EFF01, FIXED_EFF_N10507,FIXED_EFF_N10607
I have found that using an AR component with daily data assumes that the last two weeks day of the week pattern is how the pattern is in general which is a big assumption. We started with 11 monthly dummies and 6 daily dummies. Some dropped out of the model. B**1 means that there is a lag impact the day after a holiday. There were 6 special days of the month (days 2,3,5,21,29,30----21 might be spurious?) and 3 time trends, 2 seasonal pulses (where a day of the week started deviating from the typical, a 0 before this data and a 1 every 7th day after) and 2 outliers (note the thanksgiving!) This took just under 7 minutes to run. Download all results here www.autobox.com/se/dd/daily.zip
It includes a quick and dirty XLS sheet to check to see if the model makes sense. Of course, the XLS % are in fact bad as they are crude benchmarks.
Try estimating this model:
Y(T) = .53169E+06
+[X1(T)][(+ .13482E+06B** 1)] M_HALLOWEEN
+[X2(T)][(+ .17378E+06B**-3)] M_JULY4TH
+[X3(T)][(- .11556E+06)] M_MEMORIALDAY
+[X4(T)][(- .16706E+06B**-4+ .13960E+06B**-3- .15636E+06B**-2
- .19886E+06B**-1)] M_NEWYEARS
+[X5(T)][(+ .17023E+06B**-2- .26854E+06B**-1- .14257E+06B** 1)] M_THANKSGIVI
+[X6(T)][(- 71726. )] MONTH_EFF01
+[X7(T)][(+ 55617. )] MONTH_EFF02
+[X8(T)][(+ 27827. )] MONTH_EFF03
+[X9(T)][(- 37945. )] MONTH_EFF09
+[X10(T)[(- 23652. )] MONTH_EFF10
+[X11(T)[(- 33488. )] MONTH_EFF11
+[X12(T)[(+ 39389. )] FIXED_EFF_N10107
+[X13(T)[(+ 63399. )] FIXED_EFF_N10207
+[X14(T)[(+ .13727E+06)] FIXED_EFF_N10307
+[X15(T)[(+ .25144E+06)] FIXED_EFF_N10407
+[X16(T)[(+ .32004E+06)] FIXED_EFF_N10507
+[X17(T)[(+ .29156E+06)] FIXED_EFF_N10607
+[X18(T)[(+ 74960. )] FIXED_DAY02
+[X19(T)[(+ 39299. )] FIXED_DAY03
+[X20(T)[(+ 27660. )] FIXED_DAY05
+[X21(T)[(- 33451. )] FIXED_DAY21
+[X22(T)[(+ 43602. )] FIXED_DAY29
+[X23(T)[(+ 68016. )] FIXED_DAY30
+[X24(T)[(+ 226.98 )] :TIME TREND 1 1/ 1 1/ 3/2011 I~T00001__010311stack
+[X25(T)[(- 133.25 )] :TIME TREND 423 61/ 3 2/29/2012 I~T00423__010311stack
+[X26(T)[(+ 164.56 )] :TIME TREND 631 91/ 1 9/24/2012 I~T00631__010311stack
+[X27(T)[(- .42528E+06)] :SEASONAL PULSE 733 105/ 5 1/ 4/2013 I~S00733__010311stack
+[X28(T)[(- .33108E+06)] :SEASONAL PULSE 370 53/ 6 1/ 7/2012 I~S00370__010311stack
+[X29(T)[(- .82083E+06)] :PULSE 326 47/ 4 11/24/2011 I~P00326__010311stack
+[X30(T)[(+ .17502E+06)] :PULSE 394 57/ 2 1/31/2012 I~P00394__010311stack
+ + [A(T)]
Best Answer
Not sure if this will help, but your problem reminds me a little bit of macroeconomic time series modelling where a similarly high number of regressors is available, although the time series are much shorter. J. Stock and M. Watson have a nice overview paper on dynamic factor models employed in this kind of setting.
There you should find some tips on how to reduce the number of variables in your system to a comfortable level. This would allow you to model them as a vector autoregression (VAR) or similar.
References