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 |