Actually, rethinking a little, I realize that the syntax by @Edoedoedo also results in the same model I specified, without having to explicitly difference x (but including diferencing in the trend statement).  So, in fact the parameter estimates and the forecasts according to both specs will be quite close.  However, the appearance of the output will be different in many ways because the state space formulations of these two specs differ.    Although more tedious, the alternate spec I provided allows more control over the terms included in the model.  ... View more

I am sorry, I forgot to include the regressor in the model statement! The revised model statement is: model v = airLags x_1_52 noise; ... View more

Specifying ARIMAX models in the SSM (or CSSM) syntax can be a bit tedious.  I am assuming that you want to specify the model (1-B)(1-B^52) v = (1-B)(1-B^52) x + ARMA(1,1)(0,1)52 Noise.   Since the SSM DATA-step statements currently don't allow differecing, you must difference the x variable prior to its use in PROC SSM.  Let's say the appropriately differenced x is called x_1_52 and is part of the input data set (casuser.series).  Then you can specify your model as follows:   proc ssm data=casuser.series;     id date interval=week;     trend noise(arma(p=1 q=1 sq=1 s=52));     deplag airLags(v) v(lags=(1 52 53) coeff=(1 1 -1));     model v = airLags noise;     output out=for; run;   Please see the SSM (or CSSM) doc for more info on the DEPLAG statement.     ... View more

Some comments: 1. The sign convention for SAS and R ARMA parameters seems opposite. 2. In SAS/ETS, in addition to PROC ARIMA, you can do similar modeling with PROC UCM and PROC SSM.  Each has some advantages and disadvantages. ... View more

Hello, ARIMAX model class specifications can be tedious and matching specs and results in two different languages is not easy.  Even if matching specs are created, the numbers may not match because the iterative model fitting phase may lead to different parameter estimates and then, in turn, different forecasts.  Therefore, for this illustration I am choosing a data set, Box & Jenkins's Series R, and a slightly simplified version of the Box & Tiao model (Example 4 in the ARIMA doc SAS Help Center: An Intervention Model for Ozone Data).  Please see the attached files, ozone.txt gives the R code, and ozone.sas gives the SAS code.  Essentially, the R spec: fit = dt %>% model(arima=ARIMA(ozone~ 0 + x1 + pdq(0,0,1) + PDQ(0,1,1), method="ML")) corresponds to  identify var=ozone(12) crosscorr=(x1(12)) noprint; estimate q=(1)(12) input=(x1) noint method=ml;   The parameter estimates and forecasts match well. R: Series: ozone Model: LM w/ ARIMA(0,0,1)(0,1,1)[12] errors Coefficients: ma1 sma1 x1 0.3043 -0.6932 -1.2404 s.e. 0.0612 0.0662 0.2219 sigma^2 estimated as 0.6328: log likelihood=-245.25 AIC=498.5 AICc=498.7 BIC=511.77 Warning messages: 1: package ‘fable’ was built under R version 4.3.1 2: package ‘fabletools’ was built under R version 4.3.1 > fit %>% forecast(new_data=extra) # A fable: 12 x 5 [1M] # Key: .model [1] .model date ozone .mean x1 <chr> <mth> <dist> <dbl> <dbl> 1 arima 1973 Jan N(1.6, 0.63) 1.55 1 2 arima 1973 Feb N(2.1, 0.69) 2.07 1 3 arima 1973 Mar N(2.7, 0.69) 2.72 1 4 arima 1973 Apr N(3, 0.69) 3.05 1 5 arima 1973 May N(3.4, 0.69) 3.40 1 6 arima 1973 Jun N(3.4, 0.69) 3.44 1 7 arima 1973 Jul N(4, 0.69) 4.01 1 8 arima 1973 Aug N(4.2, 0.69) 4.18 1 9 arima 1973 Sep N(3.6, 0.69) 3.58 1 10 arima 1973 Oct N(2.9, 0.69) 2.90 1 11 arima 1973 Nov N(2, 0.69) 1.97 1 12 arima 1973 Dec N(1.5, 0.69) 1.45 1   SAS: Maximum Likelihood Estimation Parameter Estimate Standard Error t Value Approx Pr > |t| Lag Variable Shift MA1,1 -0.30436 0.06618 -4.60 <.0001 1 ozone 0 MA2,1 0.69325 0.06273 11.05 <.0001 12 ozone 0 NUM1 -1.24034 0.21442 -5.78 <.0001 0 x1 0 Forecasts for variable ozone Obs Forecast Std Error 95% Confidence Limits 217 1.5514 0.7955 -0.0076 3.1105 218 2.0651 0.8315 0.4354 3.6948 219 2.7236 0.8315 1.0939 4.3533 220 3.0485 0.8315 1.4188 4.6781 221 3.3960 0.8315 1.7663 5.0257 222 3.4374 0.8315 1.8077 5.0671 223 4.0125 0.8315 2.3828 5.6422 224 4.1797 0.8315 2.5500 5.8094 225 3.5754 0.8315 1.9457 5.2051 226 2.8963 0.8315 1.2666 4.5260 227 1.9678 0.8315 0.3381 3.5975 228 1.4521 0.8315 -0.1776 3.0818 ... View more

Hello Professor Wood, I downloaded the paper and will go over it and the macros.  I am familiar with the CALIS procedure and have always been interested in the possibility of providing better dynamic factor modeling support for longitudinal data in the state space modeling procedure, PROC SSM (and PROC CSSM it's cloud-enabled SAS Viya version), that I support.  If you want to use PROC SSM for dynamic factor modeling for any of your projects, I will gladly work with you.  Please feel free to contact me at rajesh.selukar@sas.com. Thanks,  Rajesh   Doc link for PROC CSSM: https://go.documentation.sas.com/doc/en/pgmsascdc/v_040/casecon/casecon_cssm_gettingstarted.htm Dynamic factor models are illustrated in two econometric examples: https://go.documentation.sas.com/doc/en/pgmsascdc/v_040/casecon/casecon_cssm_examples07.htm, and https://go.documentation.sas.com/doc/en/pgmsascdc/v_040/casecon/casecon_cssm_examples14.htm.       ... View more

Tell me more precisely the mathematical equations that involve your variable REFI. ... View more

Hello Nico98, The VARMA type in the STATE statement of PROC SSM has relatively limited functionality. If you describe your model in more detail (all the variables in your data set, precise formulation of your SSM with these variables in mind, etc), I can try to provide the PROC SSM syntax for your model.   If you also provide some test data to along with this model, that will be even better.  Any reference article that explains/illustrates this model? ... View more

The bounds in the PARM statement must be known numbers.  As @sbxkoenk said, you will need to use a macro variable that will substitute appropriate value of Upper_limit_Var1 for each BY group to do what you are trying to do (basically a separate PROC SSM call per BY group).   ... View more

I am adding some code to this discussion that should clarify things a little.  I am going to use PROC ARIMA rather than CARIMA because you can fix parameter values in ARIMA but CARIMA doc does not show any way to do that (otherwise, the results should match because they both use the same underlying code). 1. PROC ARIMA code for the model ARIMA (1,1,1)(0,1,1)52 NOINT model: proc arima data=test;     identify var=v(1, 52) noprint;     estimate p=1 q=(1)(52) noint method=ml;     forecast lead=1; quit; For these data the parameter estimation leads to an unstable model (the seasonal MA parameter is close to the boundary).  Forecast at the end is 56.2380.  The parameter estimates are different from the SARIMA model estimates (shown in Tammy's code).     2.  PROC ARIMA code for the model ARIMA (1,1,1)(0,1,1)52 NOINT model with parameters fixed at SARIMA estimates (note that the sign convention of SARIMA and PROC ARIMA appears to be opposite for MA parameters): proc arima data=test; i var=v(1, 52) noprint; e p=1 q=(1)(52) noint method=ml ar=0.8550 ma=0.9781 0.9990 noest; f lead=1; quit; Now the forecast at the end is 55.6832, which essentially is the same as the SARIMA forecast.  By the way, SARIMA estimates also suggest an unstable model.   So, in fact, both SARIMA and PROC ARIMA are doing the same likelihood and forecast calculations but for many problematic optimization situations the nonlinear optimization processes can lead to different final results.  This is the case in this particular data/model situation. Hopefully this helps.     ... View more

By the way, as I mentioned earlier, the turning points are for the underlying smooth signal (s_level).   You can slightly alter @jacksharp's code to get the plot of turning points of s_level as follows:   data all;     set change turns(keep=n s_level rename=(n=_n s_level=_v)); run; proc sgplot data=all;    title Plot of smoothed_value with identified turning points;    series x=n y=s_level;    scatter x=_n y=_v/markerattrs=(symbol=starfilled color=red); run; Which results in the following plot: Of course, @jacksharp's way of showing the turning points is much better than my earlier plots.  Thanks! ... View more

A correction: Case 1: Your series does not have an obvious trend. PROC UCM data=test; model y=x1 x2; level checkbreak; irregular; run; ... View more

Hello pjy1006, Outlier detection in time series modeling (and in other types of modeling) is an art rather than science.  If you are using outlier detection facility of PROC ARIMA (the OUTLIER statement) and PROC ESM then you are already on the right track.  Since you want to know if there are additional facilities in SAS/ETS I am going to suggest PROC UCM (for a quick illustration, see SAS Help Center: Detection of Level Shift).   The outlier detection technology behind ARIMA and UCM is very similar.  Outlier detection often requires iterative steps.  One starts with a reasonable baseline model and adjusts the model based on the most obvious breaks that are detected.  This adjusted model becomes the new baseline.  For UCM setting I will suggest the following types of initial baseline models. Suppose your input data set is test, your response series is y, and you already know external variables X1 and X2 affect y.   Case 1:  Your series does not have an obvious trend. PROC UCM data=test;     model y=x1 x2;     level variance=0 noest checkbreak;     irregular; run;   Case 2: Your series does have some type of movement: PROC UCM data=test;    model y=x1 x2;    level variance=0 noest checkbreak;    slope;    irregular; run;   Case 3: Your series is seasonal with season length slength: PROC UCM data=test;    model y=x1 x2;    level variance=0 noest checkbreak;    slope;    season length=slength type=trig;    irregular; run;   Depending on the length of the series and the inherent noise, you may have to adjust the alpha levels for additive outlier and level shift detections (see SAS Help Center: OUTLIER Statement ).   For more general outlier detection and general logic behind this type of outlier detection you can see Detecting and Adjusting Structural Breaks in Time Series and Panel Data Using the SSM Procedure (sas.com)   Hope this helps.     ... View more