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
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