time series

[bara]

Hi! 

How can I interpret the seasonal ARIMA Model (0,1,1)(1,0,0)[12] ?

[dw_sas]

Hi @bara ,

The model, ARIMA(0,1,1)(1,0,0)12, represents a seasonal ARIMA model with a:

• first non-seasonal difference,
• first-order non-seasonal moving average term, and
• first-order seasonal autoregressive term. 

The seasonal index for your model is 12, which is typically used for monthly time series.

In general, ARIMA models are described as:  ARIMA(p,d,q)(P,D,Q)s.  The lowercase p, d, q represent the non-seasonal autoregressive (p), differencing (d), and moving average (q) orders, respectively.   The uppercase P, D, Q represent the seasonal autoregressive (P), differencing (D) and moving average (Q) orders, respectively.

For additional details about the mathematical model and notation for ARIMA models, please see the following link in the PROC ARIMA documentation:

https://go.documentation.sas.com/?docsetId=etsug&docsetTarget=etsug_arima_gettingstarted13.htm&docse... 

I hope this helps!

DW

[bara]

@dw_sas  thanks,

p=1 in the non seasonal ARIMA part indicates that the  current observations of the series are correlated with themselves at lag 1

  what is mean if P=1 in the seasonal ARIMA part ? 

[solarflare · Accepted solution]

The P=1 for the seasonal part of the model means that the current observation is correlated with themselves at lag = number of periods in the season.

For example, if you are using monthly data then the current observation is correlated to itself at lag = 12.

Likewise, if you are using quarterly data, then the auto-correlation would be at lag = 4.