How can I identify ARIMA model for this data? My data, its ACF, PACF looks like this
The data is daily data and has period of 365 days though with varying mean. 
I tried fitting ARIMA (0,1,1) model (following suggestion from ESACF), it cannot pass the Ljung-Box test and the residual distribution does not have normal distribution.
When to take into account seasonality I add seasonal differencing 
identify var=x(1,365)
the data looks like this-
 
When I fit (0,1,1) (0,1,1)_365 seasonal ARIMA model to it, the residual diagnostic again cannot pass the Ljung-Box test. I also tried taking logarithm of x, but no luck there either.
No matter which model I fit, It cannot pass the Ljung-Box test 
Any suggestion on how to model this data so the residuas would be white noise?
 A: I took your 1461 observations (4 years) into AUTOBOX ( a software package that I have helped to develop) and obtained the ACF of the original series  . Standard (i.e. almost always naive ) model identification strategy assumes no outliers/level shifts/seasonal pulses/special causes are present. AUTOBOX developed a first-pass model that identified a plethora of pulse outliers for the months of September and October for the first 2 years.
We have seen retails sales buildup starting about Nov 15th of each year and lasts about 60 days requiring model structure to deal with this recurring phenomenon. In a similar way I suggested that a similar variable be considered/ used for a 75 day window stating at 9/1 for each of the first 2 years.
The fully resolved model combining this "special variable" , month of the year and ARIMA structure and allowances for identified pulses is here in two images  and   . The statistical summary is here  . The residuals from the model are plotted here  with an ACF here . The Actual/Fit and Forecast graph is here  with the Actual and Cleansed presented here 
Finally the ARIMA model (in concert with other structure) is essentially a (0,1,0)(0,0,0) as the AR(1) coefficient is nearly 1.0 .
EDITED AFTER OP REEQUSTED SOME ADDITIONAL DETAILS OF THE ANALYSIS"
I added one series call M_DYN175 and placed 0's everywhere except for 9/1/09 and 9/1/2010 . For example this is a snapshot around 9/1/09 . AUTOBOX has a feature that enables a "long polynomial" .. in this case up to lag75 providing a shortcut to estimate 75 individual coefficients .In this example some 46 were found to be statistically significant and the others deleted. You can effect the same solution by creating 46 individual pulse indicators (0/1) in your regression model. Now as to how PULSE VARIABLES (OUTLIERS) were found this is accomplished by enabling Intervention Detection procedures following Tsay  http://onlinelibrary.wiley.com/doi/10.1002/for.3980070102/abstract ( a feature of AUTOBOX and elsewhere ).

