topic Re: Clarification on PROC ARIMA manual (p. 209) in SAS Forecasting and Econometrics

Clarification on PROC ARIMA manual (p. 209)

sasalex2024 — Sun, 01 Dec 2024 12:47:41 GMT

Dear SAS Community,

I am referring to the SAS ARIMA manual, page 209 ("Stationarity and Input Series"). I find the following statement confusing, and I apologize if I lack the knowledge to fully understand it:

"If the inputs are nonstationary, the response series will be nonstationary, even though the noise process might be stationary."

The reason I find this confusing is that if we have a raw data series for Yt and Yt is stationary to begin with, then simply by regressing Yt on some nonstationary Xt, it should not make original Yt nonstationary because Yt is a known and given series (assumed to be stationary). Does SAS refer to the fitted values of Yt? Or is there something else I am missing?

Thank you for your help.

Re: Clarification on PROC ARIMA manual (p. 209)

sbxkoenk — Thu, 05 Dec 2024 11:03:53 GMT

This was first posted in "Statistical Procedures"-board and hence is a duplicate of
https://communities.sas.com/t5/Statistical-Procedures/Clarification-on-SAS-ARIMA-Manual-p-209/m-p/952208

I do not want to stop the discussion with this, of course, because the question has still not received a conclusive answer (otherwise it would not have been asked again, of course ... and this is indeed a more appropriate board for the topic at hand).

Ciao, Koen

Re: Clarification on PROC ARIMA manual (p. 209)

SASCom1 — Tue, 10 Dec 2024 21:03:43 GMT

@sasalex2024

My understanding of this line is, if

y_t = a + b*x_t + v_t,

where x_t is nonstationary input, v_t is stationary noise term. Then the non-stationarity of x_t will also transmit to the response y_t. If you know for a fact that y_t is actually stationary, then the non-stationary x_t would not be appropriate explanatory variable for y_t. The simplest example is, if x_t has an upward trend, but y_t does not, then you probably will not think the upward trending x_t explains the non-trending y_t series. For example, if

x_t = c+ d*t + u_t,

with t being the time trend variable,

then since y_t = a + b*x_t + v_t, you now have

y_t = a + b*(c+d*t + u_t) + v_t

y_t = (a + b*c) + (b*d)*t + b*u_t + v_t

this implies that y_t also has a trend term, which is not true, since you know y_t is stationary and does not have trend.

I hope this helps.