Correlated residuals in estimated model I am working with the weekly data set from the Keeling Curve which can be accessed here: http://scrippsco2.ucsd.edu/data/atmospheric_co2/mlo (weekly in-situ CO2 data).
I selected an SARIMA model, but it fails the Ljung Box test with p < 0.05. 

Does anyone have any suggestions on how to find a better model?
I have tried to decrease the number of parameters, but the test still fails...
 A: Use 51 weekly indicators and/or 11 monthly indicators to deal with deterministic structure that might be in your data. Eliminate 1 of the weeks in a leap year to deal with the 53 week effect . Add arima structure as necessary and also deal with pulses by adding pulse indicators where necessary. This should enable your creation of uncorrelated residuals. If not you might need to segment your data as your model parameters may have changed over time and/or deal with an error variance that may not be constant over time.
EDITED AFTER RECEIPT OF DATA IN ORDER TO PROVIDE GUIDANCE ABOUT DATA THAT REQUIRES.
1) trend change point detection
2) error variance change point detection
3) arima structure
4) time trend variable
5) deterministic seasonal dummies representing fixed weekly effects
here is the equation  and here  with a residual plot here  and acf residual plot here 
The error variance detection was suggested here 
The model presented here provides a much better looking acf of the residuals than your pure ARIMA model BUT it is not perfect .
this is an example of a series whose 52 period seasonality dependence is deterministic rather than stochastic(ARIMA) and multiple break points (I_L) are found. The large sample size (3112) yield a (VERY APPROXIMATE) standard error of the acf to be 1/sqrt(3112) which is less than .02 which often yields false acf tests on the residuals.
