How to specify a Seasonal ARIMA model?

How to specify a seasonal ARIMA model with 1 AR term, 1 SAR term with seasonality = 12, and seasonal differencing = 1 (differencing=0, MA=0, SMA=0) using arima?

* Using ARIMA model notations, model specification is arima(1, 0, 0)(1, 1, 0)x12

(R2023a)

Answer 1

[Shivam Lahoti]

Hi Dinuka,

To specify a seasonal ARIMA model with the given parameters in MATLAB (R2023a), you can use the 'arima' function as follows:

model = arima('ARLags',1, 'D',0, 'MALags',[], 'SARLags',12, 'Seasonality',12, 'SMALags',[], 'D',1);

In this model specification:

• 'ARLags',1 specifies the non-seasonal AR term at lag 1.
• 'D',0 sets the non-seasonal differencing order to 0.
• 'MALags',[] indicates no non-seasonal MA terms.
• 'SARLags',12 sets the seasonal AR term at lag 12 (which corresponds to the seasonal period).
• 'Seasonality',12 defines the number of periods in a season (indicating monthly data if 12).
• 'SMALags',[] indicates no seasonal MA terms.
• 'D',1 (the second 'D' in the argument list) sets the seasonal differencing order to 1, which is part of the seasonal component of the model.

This will create an ARIMA(1,0,0)(1,1,0)_12 model as you described. To understand more about the 'arima' function, kindly refer to the following documentation:

https://www.mathworks.com/help/econ/arima.html

I hope it was helpful.

Regards,

Shivam.

[Dinuka]

@Shivam Lahoti Thanks for the answer. This helps.

[Dinuka]

@Shivam Lahoti Please note that this doesn't appear to me as an 'Answer' and 'Accept' option is not enabled for me. If this appears as an Answer, I'll accept it.