Wrong predictions for weekend, but good predictions for weekdays I have a set of 3 years of daily data. I saw weekly and annual seasonality in the data so I used msts time series and tbats (from the forecast package in R) to fit the best fitted model. 
The predicted values for weekdays are with 5% of the actual data but it has very off predictions for weekend. I did not expect that as I included daily seasonality in a week (different weekday and weekend patterns) in my time series which I though will consider the seasonality correctly. I wonder if anybody have any idea whats going wrong with my data. 
I also used ts with single seasonality of frequency 7 and again used tbats to fit a model. Th new model has better predictions for weekend but worse predictions for weekday. I also tried auto.arima (also from the forecast package) but as I have a huge number of data points, arima was not able to find a good model. 
 A: Some exploratory data analysis:
In summarizing your data at the monthly level, I noticed you have couple of issues going on in your data. 


*

*In the test period data which begins at January 2010 there is a
significant "bending upwards" of trend.  

*In addition I also see there is a high degree of variability in
seasonality, so you might want to apply an appropriate
transformation using box-cox transformation.


Coming back to the first part of the issue, before using an extrapolation method such as ARIMA or exponential smoothing or fixated on data mining/dredging, I would recommend to find out "why" the trend changed direction and went upwards. Unless you know the "why" part of this trend change, no matter what method you use, it is going to be impossible to improve accuracy or build better forecast. As noted in answer to your earlier question, the only way to build good forecasts for your problem is to systematically adjust the forecast from an extrapolative method using a well structured judgement or use an analogous time series top forecast time series. You could also use an ensemble of judgemental forecasting and extrapolative methods. Using univariate extrapolative method alone on a non-experimental data such as yours bound to produce poor predictions. It is important to do some initial  data analysis before fixating on methods and techniques, it might go a long way in improving predictions. Also, using a low frequency data such as rolling the daily data to monthly data and doing data visualization also is very helpful to better understand the data and ultimately better predictions. 
Hopefully this analysis provided you some directions for future research.
I have to agree with Whuber, that only way to assess predictive performance of an extrapolation method is using hold out set. Simplest is the single origin forecast,If you have enough resources then I would do rolling forecast testing or cross-validation or jackknifing such as the one suggested by @Irishstat. See the link below for some nice blog post by Rob Hyndman on how to do this for time series data.
http://robjhyndman.com/hyndsight/tscvexample/
http://robjhyndman.com/hyndsight/rolling-forecasts/
I'm also curious to know why you would need a daily forecast for 1 year. In practice based on my own experience, you would use low frequency data (such as monthly/weekly) to do a full year forecast for planning purpose and use high frequency data such a hourly/daily to do a  very very short term forecast. When I mean very very short term, update and revise forecast every month. As an example, If I had your data (assuming you want to forecast for 2010), I would predict full year 2010 data using monthly data, and just produce daily forecast for January 2010. By this use you could get the bests of both worlds by have low frequency (less noise) and high frequency (daily data) forecasts. Once you have Jan 2010 data, you could produce daily forecast for February and keep producing and updating the daily forecast. You could repeat this for every month as the new data arrives. In addition you could also reconcile the monthly and daily forecast.

A: You data https://www.autobox.com/FATEME/TestData.xlsx is here . I suggest other readers take the data and try to analyze it. On first view the 1096 historical daily values appear to have a large number of "outliers". These unusual values are in effect mostly usual as certain holidays have a significant effect. The problem you are having has to with your design matrix. You assume that the effect is day-of-the-week vs weekend. This is wrong because each day has it's own effect and certainly the 5 work days are not equal and the two weekend days are not equal in their importance. There have been major shifts in the days-of-the=week effects. Furthermore specific days-of-the-month and specific months of the year are very important in addition to Friday before Holidays impacts. Next there is a visually obvious level shift ( on or about  1/27/09 ) in your data that needs to be accounted for such that the final model coefficients are robust and meaningful.
Using AUTOBOX (a piece of software available from http://www.autobox.com/cms/ which I have helped develop) in a totally automatic fashion a model containing both deterministic effects and memory (ARIMA) was forged.
Attached is the equation (in two parts)
 and . A test for the sufficiency of a model is the ACF of the errors suggests randomness. Following is the Forecast plot.. I have added a representative screen shot of the forecasts presented in tabular fashion (forecasts then lower limit then upper limit).
With apologies in advance the 1096 values were able to be characterized with 58 statistically significant coefficients.
The summary statistics from the model are as follows 
EDIT: I have added the 366 forecasts from 1 origin 12/31/2009 https://www.autobox.com/FATEME/AB50PRO.123
