# What is the ARIMA model for this data?

I have made my series stationary by using one difference and have plotted the following acf & pacf:  So I have decided to test the following models:

• ARIMA(0,1,1) since the acf cuts off after lag one.

• ARIMA(1,1,0) since the pacf cuts off at lag one.

• Since the spikes cut off and level off again for a while it could be combination of both models so it may be an ARIMA(1,1,1) model.

Now, for both the ARIMA(0,1,1) and ARIMA(1,1,0) the p-value for the residuals being independent are all < 0.05 so we reject the null hypothesis and clearly this model is no good!!

But... the ARIMA(1,1,1) won't work on minitab it says "Relative change in each estimate less than 0.0010"

So my question is, have i chosen the correct models? And why won't an ARIMA(1,1,1) work? If so, is it okay to accept them if the p-values are < 0.05 for the residuals?

• Putting aside the complicated question of how to choose models, you may have numerical issues with an ARIMA(1,1,1) model because of numerical near-cancellation: the line in parameter space where the AR and MA coefficients are equal (or when they sum to zero, depending on the parametrization) reduces the problem to an objective function that doesn't depend on either (the model reduces to ARIMA(0,1,0)). Nov 24, 2016 at 17:18
• why don't you post your data and I will try and follow up on Chris. Is the data set monthly ? Nov 24, 2016 at 17:36
• @IrishStat I am unsure on that as I have not been given what the data has been recorded in. I have put the data in the question for you though. Many thanks! Nov 24, 2016 at 18:11
• can u post it as a single column Nov 24, 2016 at 18:44
• @IrishStat Of course. I've updated it now. Nov 24, 2016 at 21:00

I took your data (252 monthly values into AUTOBOX and automatically obtained the following plot and the following model (2,0,0)(1,0,0) 12 using GLS because the error variance changed at two distinct points in time . In addition there was an inteercept change and 1 pulse . The ACF of the original series is here and the ACF of the residual series here . The plot ofthe final residuals is here . THe ACTOUT ( OBSERVED AND ADJUSTED ) is here . The plot of actual/fit anf forecast is here with forecasts here • @IrishStat Are you referring to the R function forecast::auto.arima? Because it does pick up seasonality here: it comes up with (0,1,2)(0,0,2). It doesn't attempt to look for level shifts or additive outliers or volatility level shifts though, which are all very present and problematic here, that is true. Nov 25, 2016 at 15:40