# SARIMA Model Identification

So I am currently having trouble trying to come up with an initial model for this data. I am trying to model 10 years of monthly CO2 levels at Mauna Loa.

The original data looks like this:

After detrending and deseasonalizing, I get ACF and PACF of:

My initial guesses were that the ACF is showing 3 seasonal AR components and PACF is showing an non seasonal MA(4).
SARIMA(0,1,4)(3,1,0)_12 or SARIMA(0,1,7)(3,1,0)_12 are the models I came up with, but I am not really sure how close it is.
The ACF of the detrended and deseasonalized data is throwing me off.

• post your data in a csv file – IrishStat Jun 1 at 6:01
• @IrishStat I uploaded the CSV file to dropbox. I'm using CO2PPM <- ts(co2_mm_gl_csv[349:456,3], freq = 1) for my data (months 349 to 456 and the average column) – AJ M Jun 1 at 6:14

Sometimes simple methods fitting a pre-set set of models using a simple statistic occasionally work ,particularly when the data is uncomplicated. Your data is complicated thus it is necessary to roll out aggressive/thorough (read: complicated) approaches to forming a useful model.

Let us review the assumptions that are made when it is safe to visually or computationally map the sample acf and pacf to a useful arima model. Firstly there must be no deterministic structure latent in your data i.e. no pulses , no step/level shifts , no seasonal pulses and no time trends (often called Deterministic Trends) . This is reasonably satisfied in your data .

A second assumption is that the parameters of the identified model are constant over time. This is not satisfied in your data as the following was found using the CHOW procedure to search for the most significant points in time where model parameters became statistically significant from a prior set of parameters.

AUTOBOX found that the parameters of a (0,1,0)(1,1,1)12 model indicated that the first 383 values had a pattern that was different from the most recent 80 values thus data segregation was suggested . Other models achieved the same conclusion that too much data was being modelled as homogenous. Note that you delivered 463 historical monthly values and in this case it appears that something ( read: unspecified exogenous factor) caused a seismic shift in the data approximately 6-7 years ago or so.

To confirm this consider the acf of the first 383 values and the acf of the most recent 80 values

Using the last 80 values we obtained the following Actual/Fit and Forecast Graph . The equation is here including an identified pulse and here with statistics here leading to the following residual plot .

The Actual & Cleansed graph is here

Hope this helps .

• The appropriate model is (1,1,0)(0,1,0)12 with 1 pulse indicator using the last 80 values – IrishStat Jun 3 at 7:44
• If you found my answer useful ... then either upvote it or accept it to close tge question. – IrishStat Jun 3 at 22:07