Is the OUTEST = option in PROC CALIS statement what you are looking for? see below:   https://go.documentation.sas.com/doc/en/pgmsascdc/9.4_3.5/statug/statug_calis_syntax13.htm#statug.calis.calisoutest   OUTEST=SAS-data-set creates an output data set that contains the parameter estimates, their gradient, Hessian matrix, and boundary and linear constraints. For METHOD=ML, METHOD=GLS, and METHOD=WLS, the OUTEST= data set also contains the information matrix, the approximate covariance matrix of the parameter estimates ((generalized) inverse of information matrix), and approximate standard errors.    For more details on this data set, see: https://go.documentation.sas.com/doc/en/pgmsascdc/9.4_3.5/statug/statug_calis_details07.htm#statug.calis.calisoutestds   The _TYPE_ = COV corresponds to covariance matrix of the parameter estimates.       ... View more

My understanding is that, the ARCH tests supported in PROC AUTOREG, the Breusch-Pagan test and White test supported in PROC MODEL, they all test for heteroskedasticity in the residuals, but they are just testing against different forms of heteroskedasticity, or no form specified in the White test case. I have only seen the ARCH model being referenced as 'conditional heterskedastic', due to Engle(1982), which describes the conditional variance depending on the past.   For the ARCH test, it is testing against alternative of ARCH process, which means,  h_t = alpha0 + alpha1*(epsilon_t-1)^2 + alpha2*(epsilon_t-2)^2 + ..... + alpha_p*(epsilon_t-p)^2, not all alpha_i equal to 0.      For the Breusch-Pagan test, it is testing against alternative that error variance depends on a set of variables which you specify on the BREUSCH = (  ) option: h_t = sigma^2*(alpha0 + alpha1*z1 + alpha2*z2 + ...  + ), not all alpha_i equal 0.    You can do ARCH test in PROC AUTOREG, and Breusch-Pagan test in PROC MODEL. However, both of these procedures perform the test on the residuals directly from the specified regression in the procedure. If you get residuals outside of these procedures, and you want to perform these tests on the residual series, then you may fit a 'regression' of the residual series on zero mean and no regressor,  so that the residual from this 'regression' is still the residual series itself. For example,   /* ARCH test on the residuals */ proc autoreg data= residualdata; model residual = /noint archtest=(all); run;   /* Breusch-Pagan test on the residuals */ proc model data=residualdata; parms const ; residual = const ; fit residual / breusch=(1 z1 z2); restrict const = 0 ; run;quit;   I hope this helps. ... View more

The %BOXCOXAR macro does not output AR parameter estimates.   I do not know if there is a specific process that one must follow which is considered 'the correct' approach. When I posted my previous response, I honestly did not think of such process you outlined:-) My previous response was only meant for some things you may consider to help you decide what large number to specify for AR = option for a process with MA terms in using the %BOXCOXAR macro. My thought was simply this, if you fit an AR model, with the differencing applied, though not transformed, the significance of the AR parameters will give you some indication, may not be accurate indication, if certain lags are better included when you specify the AR = option. You can also try some different AR orders and see if and how %BOXCOXAR results change.        ... View more

Hi @sasalex2024 , Large AR = option is recommended for a process with moving average terms because MA(q) process can be expressed as AR process of infinite order.  I don't know if there is a rule of thumb saying how large is large enough, but you may make the decision by considering the length of the data, the significance of the AR parameters, etc.  I hope this helps. ... View more

You may take a look at the %BOXCOXAR macro which is designed to find the optimal Box-Cox transformation for a time series:   SAS Help Center: BOXCOXAR Macro     I hope this helps.  ... View more

In order to further look into this and determine the cause, it may be necessary to have your data set to test the code. If you cannot upload the .sas7bdat file sufficient to produce the error here, perhaps you can open a case with Technical Support to get further help:   https://support.sas.com/en/technical-support.html     ... View more

Thanks for providing the reference. From your reference, chapter 5, p.184, it discusses how you can obtain estimate for the IPACF, in the second paragraph right after equation 5.3.4. You may follow the discussed methods there to obtain the estimated IPACF, for example, for the first method discussed, 'replace the rho_i,k by sample IACF r_i,k, and solve the inverse Yule-Walker equations for the estimated theta_k,k', you only need to have the sample IACF r_i,k , which you can obtain in PROC ARIMA, you can then solve the inverse Yule-Walker equations (5.3.4) to get the estimated theta_k,k.    I hope this helps. ... View more

PROC ARIMA produces ACF, IACF, PACF plots, but no IPACF. I have not seen discussions on IPACF, can you provide references for the text book(s) you mentioned with information on IPACF?  ... View more

Hi  @sasalex2024    When I said the two codes are 'essentially the same',  I was only saying in the sense that in both cases, first differencing is applied on both response series and input series before applying the prewhitening filter, even though the first code did not specify differencing on either the response series or the input series in the second IDENTIFY statement.  However, the two codes are *not exactly the same code*,  the different specifications could imply different handlings in some steps during the prewhitening stage, resulting in somewhat different prewhitened series, hence different ccfs. So it is a bit loose to say they are the same, and I should take the statement back to avoid confusion.   I hope that helps.         ... View more

In both your first PROC ARIMA code and second PROC ARIMA code, first differencing is applied to both response and input series before the MA prewhitening filter is applied. The filtered response series is then cross-correlated with the filtered input series. So your two steps of PROC ARIMA are essentially the same-- as mentioned earlier, the first code also applies differencing to both series before applying the prewhitening filter due to the differencing specified in previous IDENTIFY statement; the second code also applies differencing to both series before applying the prewhitening filter since differencing order is specified consistently in all VAR = and CROSSCORR = options. Personally, I prefer the second syntax specification since it is clearer.  In general, you apply prewhitening on the input series to obtain white noise residuals. The same prewhitening filter is then applied to the response series, and the filtered response is cross correlated with the filtered input.   I hope this helps. ... View more

hello @samp945    I cannot say doing the following will help you find a 'better ' model, but here are a couple of things you may consider when trying to explore model diagnostics:   1. you may find it helpful to plot the time series and see if you can visually identify some patterns. I used the following to produce a time series plot and the first thing that I noticed from the plot, is that there may be some level shift around 2016~2017, so having a CHECKBREAK option in the LEVEL statement may help.   proc timeseries data = a(where = (CauseOfDeath='Traffic')) plot = series; id DeathMonth interval = month; var count ; run;   2. you may consider starting from a baseline model similar to the following example in the doc(or some other baseline model you find appropriate for your data), and check for breaks in the baseline model using the CHECKBREAK option in the LEVEL statement,   SAS Help Center: A Seasonal Series with Linear Trend   I tried the above baseline model and the results seem to indicate level shift in Aug. 2016 in the baseline model.    3.  If level shift is confirmed in the baseline model (as is the case using the above baseline model),  you may want to include the level shift dummy variable as a regressor in the model, following shows an example of level shift detection and how to account for it:   https://go.documentation.sas.com/doc/en/pgmsascdc/9.4_3.5/etsug/etsug_ucm_examples07.htm     You may want to do some further data explorations that may help you find alternative candidate models that suite your data, but I hope the above several notes are helpful to you.         ... View more