Dear SAS Community, In one of the previous discussion threads, I received help from you conducting a heteroskedasticity test for a time series variable. Essentially, the problem is that I have an ARIMA model, and I want to thoroughly check if the fitted residuals exhibit heteroskedasticity. I was recommended (as the code below illustrates) to use the 'archtest' option in 'proc autoreg' for a sample ARIMA model. However, it is my understanding that this tests for conditional heteroskedasticity. Yet is seems like, technically, the absence of conditional heteroskedasticity does not imply the absence of unconditional heteroskedasticity (I hope I am using the correct terminology), where variance changes proportionally with the trend. In the latter case, data transformations often help stabilize the variance of the residuals of the fitted model. Nonetheless, my question is: if I have run an ARIMA model and want to conduct heteroskedasticity tests for model residuals, should I also use the 'White and Breusch' options in 'proc model'? Is that correct? Kindly see the code below. Thank you! /*-- Seasonal Model for the Airline Series --*/ data seriesg; set sashelp.air; xlog = log( air ); run; proc arima data=seriesg; identify var=xlog(1,12); estimate q=(1)(12) noint method=ml; forecast id=date lead=0 interval=month printall out=b; run; quit; data c; set b; where residual is not missing; Time + 1; run; /* Test for Conditional Heteroscedasticity in Residuals */ proc autoreg data=c; model residual = Time / archtest=(all); output out=r r=yresid; run; /* Test for Unconditional Heteroscedasticity in Residuals */ proc model data=c; parms const beta; residual = const + beta * time; fit residual / white breusch=(1 time); run; ... View more

Dear SAS Community,   I am working with an annual univariate time series consisting of 75 observations. I suspect that at observation 33, an intervention caused a downward shift in the mean of the series. My dataset contains a time variable labeled "Date" and a response variable "Yt". In the code below, I define the target mean as the average of the first 32 observations, along with the corresponding estimate of the standard deviation. I then apply the CUSUM test to detect a potential mean shift. Could you please review my approach and let me know if this is the correct way to detect a mean shift in the series using PROC CUSUM?  Thank you for your insights! proc means data=a(obs=32); var Yt; output out=stats mean=mu0 std=sigma0; run; /* Store computed values as macro variables */ data _null_; set stats; call symputx("mu0", mu0); call symputx("sigma0", sigma0); run; ods graphics on; title 'Two-sided CUSUM Chart'; proc cusum data=a; xchart Yt*Date / mu0 = &mu0 sigma0 = &sigma0 delta = 2.6 alpha = 0.10; label Yt = 'Cumulative Sum'; run; ... View more

Dear SAS Community,   I apologize for the lengthy message.   As you know, the VARMAX procedure in SAS allows for the computation of the accumulated impulse response in the transfer function and provides standard errors for the long-run response elements.   I am wondering if similar functionality exists in PROC ARIMA (or in HPF procedures). While I understand that VARMAX can be used to model a univariate series, my understanding is that the mathematical formulation of the transfer function in a VARMAX model differs from that in an ARIMA model. Specifically, in an ARIMA model, the transfer function has a specific rational form, where the numerator and denominator polynomials define the distributed lag structure of the input series.   Consider the following scenario: I have a transfer function model in PROC ARIMA where the input variable St​ is a standard step function, taking the value 0 before a certain time point and 1 thereafter.   The code is:   proc arima data=A; identify var=Y crosscorr=St; estimate p=(1)(12) q=1 input=( / (1) st ) method=ml outmodel=Results; run; The estimated transfer function weights are given by ω0 (SAS estimates it as ‘NUM1’)​ and δ1 (SAS estimates it as ‘DEN1,1’), where the accumulated response evolves as follows:   ω0 (initial period response), ω0*(1+δ1) (next period response), ω0*(1+δ1+δ1^2) (following period response), etc.   While I can manually compute the accumulated response since PROC ARIMA estimates ω0 and δ1, I am looking for a more efficient ("automatic?") way to obtain these values directly in SAS.    Additionally, PROC ARIMA provides standard errors (and thus, confidence intervals) only for the estimated parameters ω0 and δ1, but in reality, each accumulated response term has its own confidence interval. I am unsure how to obtain these confidence bands in SAS for all these separate added responses. Is there a formula for it?   Any insights on this would be greatly appreciated. Thank you again. ... View more