ARIMA model, cannot get rid of low order ACF spike

I've gone through all the steps to fit a good ARIMA model - I plotted the data, I looked at the ADF tests, I looked at the ACF plot with no AR and MA terms just a constants. I came up with an ARMA(0,1,1) model as the ACF cut off after two lags (the second was negative) and the PACF decayed exponentially from the first order being negative.

The problem is I cannot get rid of a large positive spike at the first order lag in the ACF plot of the residuals once my model is fitted. I've tried increasing the number of MA terms, but the lag doesn't go away and the second term isn't significant. Given it is an MA model, I don't think further orders of differencing are need.

I've coded my model in R

Edit: I've included some of the graphs below. I tested my model with and without a constant, as the constant was not significant, however the AIC was lower with a constant. Theoretically thought, I think no constant makes more sense as I don't think there is a constant average trend. However, excluding the constant (with the argument include.mean=FALSE) doesn't change the ACF or PACF of ther residuals. The code I used to fit the models is:

ArmaOhdifc01 = armaFit( ~arma(0, 1), data=OhDiff)
ArmaOhdif01 = armaFit( ~arma(0, 1), data=OhDiff, include.mean=FALSE)


Below are the graphs - I didn't include the ACF and PACF of the first model becuase there is no difference to that of the second.

• The fact that the residuals are not entirely uncorrelated does not mean that the model must be entirely rejected. You may use other measures, e.g. how well it predicts the data. Dec 10, 2014 at 14:41
• What is the input data? Can you provide the values or a plot of the acf or pacf of the data? Here you find a chapter of the online textbook which I post in this forum nearly every second day. Dec 11, 2014 at 14:23
• You difference the data once ... mabye there is something with using a constant as described in the chapter above ... Dec 11, 2014 at 14:24
• @Richard I actually looked through that e-book, as well as some others, and it was helpful (note: it would be great if I could order a pdf copy to read on my ipad). I've added some more details above. I had tested the model without a constant as well as with, althought it didn't change the ACF/PACF (might be a coding error?) Dec 15, 2014 at 22:33
• I think you can order the book as pdf - it is definately worth the money. I bought it as paperback. As I see in the remark below your problem is solved ;) Dec 16, 2014 at 8:08