ADF Lag Length Selection Process

Toni2 — Sat, 24 Jul 2021 16:12:45 GMT

hi, i am quite new with SAS and i am struggling to understand the ADF process for selecting the correct number of lags

As a first step for the ADF test i tried to identify the correct number of lags that i have to include. I use monthly data, therefore i added ADF=12 lags and run the below code :

***ADF test***;
PROC ARIMA DATA= rethouse_reg1 ;
IDENTIFY VAR = DEPPC_forc STATIONARITY=(ADF=12) ;
RUN;
QUIT;

then i looked at the ADF and Trend Correlation analysis :

i looked at the trend and correlation analysis graph (see below). My series doesn't have trend (based on the graph) and has mean different than zero (based on table below mean = 6.381432) therefore, i concluded that i have to use the single mean in ADF.

After this i looked at the ADF table (see at the bottom) in the single mean model and starting from the bottom (12 lags) I found that the 9 lags are statistical significant (0.0146<0.05). Based on this i concluded that i have to use 9 lags in the ADF test.

Then i looked at the ACF graph and counted the number of columns which are outside the shed blue area and found 11lags and i understood that i had to include 11lags for the ADF (compare to 9lags that found earlier)

my questions are :

1) Is the steps that i followed correct for selecting the appropriate number of lags for the ADF?

2) If yes, which one of the above results for the correct number of lags i can trust and include in my ADF test and why?

Name of Variable = DEPPC_forc
Mean of Working Series	6.381432
Standard Deviation	2.35614
Number of Observations	277

Augmented Dickey-Fuller Unit Root Tests
Type	Lags	Rho	Pr < Rho	Tau	Pr < Tau	F	Pr > F
Zero Mean	0	0.4318	0.7889	0.37	0.792
	1	0.3733	0.7738	0.3	0.7728
	2	-0.0458	0.6719	-0.03	0.6726
	3	-0.5249	0.5642	-0.3	0.5756
	4	-0.6041	0.5474	-0.34	0.5629
	5	-0.595	0.5493	-0.33	0.564
	6	-0.6329	0.5414	-0.34	0.561
	7	-0.8189	0.5049	-0.42	0.5322
	8	-1.4697	0.3989	-0.65	0.4358
	9	-1.5907	0.3821	-0.68	0.422
	10	-0.8402	0.5009	-0.43	0.5252
	11	-0.5906	0.5502	-0.33	0.5657
	12	-0.145	0.6494	-0.12	0.641
Single Mean	0	-2.7088	0.6911	-0.81	0.8142	0.57	0.9306
	1	-3.6673	0.5752	-1.01	0.7512	0.74	0.8816
	2	-8.616	0.1846	-1.81	0.3773	1.82	0.6057
	3	-12.848	0.0651	-2.2	0.2058	2.52	0.4246
	4	-15.2504	0.0354	-2.34	0.1595	2.84	0.3433
	5	-15.8331	0.0305	-2.33	0.1647	2.79	0.3552
	6	-19.2865	0.0127	-2.49	0.1191	3.21	0.2497
	7	-25.4427	0.0028	-2.72	0.0731	3.78	0.1015
	8	-45.8484	0.0015	-3.18	0.0228	5.1	0.0347
	9	-64.8018	0.0015	-3.34	0.0146	5.61	0.0205
	10	-35.3822	0.0015	-2.8	0.0601	4	0.0875
	11	-29.8813	0.0015	-2.61	0.0917	3.51	0.1724
	12	-9.0271	0.1669	-1.7	0.4324	1.5	0.6861
Trend	0	-1.8741	0.9729	-0.55	0.9808	0.95	0.9735
	1	-2.8408	0.9428	-0.76	0.9668	0.89	0.9788
	2	-8.555	0.5357	-1.72	0.7411	1.62	0.8528
	3	-13.339	0.2423	-2.14	0.5208	2.43	0.6899
	4	-16.6115	0.1298	-2.32	0.423	2.8	0.6158
	5	-17.441	0.1099	-2.29	0.4385	2.76	0.6237
	6	-23.2314	0.0324	-2.53	0.3138	3.29	0.5173
	7	-34.3311	0.0025	-2.82	0.1909	4.05	0.3633
	8	-82.3673	0.0006	-3.35	0.0604	5.71	0.0814
	9	-210.116	0.0001	-3.58	0.0332	6.51	0.0441
	10	-70.2109	0.0006	-2.99	0.136	4.58	0.2574
	11	-59.658	0.0006	-2.82	0.1932	4.05	0.3632
	12	-10.7044	0.3831	-1.6	0.7915	1.48	0.8809

Re: ADF Lag Length Selection Process

Ksharp — Sun, 25 Jul 2021 11:20:59 GMT

Why not post it at Forecasting Forum
https://communities.sas.com/t5/SAS-Forecasting-and-Econometrics/bd-p/forecasting_econometrics

Since it is a time series analysis question.

Re: ADF Lag Length Selection Process

Toni2 — Sun, 25 Jul 2021 12:04:45 GMT

you are right, i have now posted here :

https://communities.sas.com/t5/SAS-Forecasting-and-Econometrics/ADF-Lag-Length-Selection-Process/m-p/756490#M4208

topic ADF Lag Length Selection Process in Statistical Procedures

ADF Lag Length Selection Process

Re: ADF Lag Length Selection Process

Re: ADF Lag Length Selection Process