ARIMAX times series with nonlinear input variable

[mmrekabdar]

Hi All,

I'm looking for SAS procedures that can help me to fit an ARIMAX model to my data when the exogenous variables(input variables) have a nonlinear relationship with the dependent variable (target time series).

To capture this non linearity I simply enter the interaction of exogenous variable with itself in the model, for example I enter X and X*X in the model.

I know in this way we could not capture all non linearity in ARIMAX models.

please correct me if you have any suggestion.

Thanks,

Marjan  

[mmrekabdar]

Hi All,

I'm looking for SAS procedures that can help me to fit an ARIMAX model to my data when the exogenous variables(input variables) have a nonlinear relationship with the dependent variable (target time series).

To capture this non linearity I simply enter the interaction of exogenous variable with itself in the model, for example I enter X and X*X in the model.

I know in this way we could not capture all non linearity in ARIMAX models.

please correct me if you have any suggestion.

Thanks,

Marjan  

[rselukar]

You can do this in a few different ways:  

1.  You can create and add the nonlinear effects (x*x, sin(x), etc)  in the input data set by using the DATA step and then use them as any other regressors in PROC ARIMA.

2.  More complex nonlinear effects could also be created by using the BSPLINE function in PROC IML (for an example of how to add BSPLINE basis to a data set see https://go.documentation.sas.com/?docsetId=etsug&docsetVersion=15.1&docsetTarget=etsug_ssm_examples0... ) and then these basis columns can be used as usual regressors in PROC ARIMA (you might have to drop one of the columns to avoid multicollinearity since they always add up to 1). 

3.  You can use PROC UCM for your time series analysis and use the SPLINEREG statement to add nonlinear regression effects (see https://go.documentation.sas.com/?docsetId=etsug&docsetTarget=etsug_ucm_examples06.htm&docsetVersion... ).  Note that you can specify ARIMA models with regressors in PROC UCM too (differencing is specified via DEPLAG statement and the stationary ARMA term is specified using the IRREGULAR statement).

Hope one of these ways works for you.