ADF Lag Length Selection Process

Toni2 — Sun, 25 Jul 2021 12:04:05 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

ugmented 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

sbxkoenk — Sun, 25 Jul 2021 16:33:43 GMT

Hello,

I do not master the peculiarities and intricacies of the ADF test anymore. I did, but I haven't used it since a long time.

It takes a while before you can fluently use it (in my case at least).

However, I think this paper may help you out :

Paper 3294-2015
An Introduction to Testing for Unit Roots Using SAS®:

The Case of U.S. National Health Expenditures
Donald McCarthy, Department of Research and Evaluation, Kaiser Permanente

https://support.sas.com/resources/papers/proceedings15/3294-2015.pdf

There are 10 occurrences of 'lag length' in the paper and a macro that implements the Ng and Perron (2001) approach.

Ng, S and P. Perron. 2001. “Lag Length Selection and the Construction of Unit Root Tests with Good Size and Power.” Econometrica, Vol. 69, No. 6: 1519–1554.

There's also a a rule of thumb based on the number of observations in the sample.

Good luck,

Koen

Re: ADF Lag Length Selection Process

Toni2 — Sun, 25 Jul 2021 18:22:24 GMT

hi there, thank you. i am going to have a look at this. I have searched on google and to be honest there is no one clear guidance on the steps that have to be followed (or it is not clear to me). The same happens with the ADF approach. Many people try to explain but they miss to provide crucial details. Anyway, i am going to have a look. thanks again

topic Re: ADF Lag Length Selection Process in SAS Forecasting and Econometrics

ADF Lag Length Selection Process

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