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 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?