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st: Lag lengh for dfuller test; arima identification based on correlogram
Hi there,
I would be grateful for advice on how to choose the "right" lag length when
carrying a augmented Dfuller test. What I have been doing so far is to carry
a DFgls and then, use the recommended lag length from that to carry the Df
test
As below:
dfgls ukequity
DF-GLS for ukequity Number of obs =
306
Maxlag = 16 chosen by Schwert criterion
DF-GLS tau 1% Critical 5% Critical 10%
Critical
[lags] Test Statistic Value Value Value
-----------------------------------------------------------------------------
-
16 -1.756 -3.480 -2.812 -2.531
15 -1.825 -3.480 -2.819 -2.538
14 -1.970 -3.480 -2.825 -2.544
13 -1.952 -3.480 -2.832 -2.550
12 -2.069 -3.480 -2.839 -2.556
11 -2.265 -3.480 -2.845 -2.562
10 -2.424 -3.480 -2.851 -2.567
9 -2.589 -3.480 -2.857 -2.573
8 -2.888 -3.480 -2.863 -2.578
7 -3.410 -3.480 -2.869 -2.583
6 -3.675 -3.480 -2.874 -2.588
5 -4.062 -3.480 -2.880 -2.593
4 -4.646 -3.480 -2.885 -2.598
3 -5.555 -3.480 -2.890 -2.602
2 -6.964 -3.480 -2.894 -2.606
1 -9.277 -3.480 -2.899 -2.610
Opt Lag (Ng-Perron seq t) = 15 with RMSE .0463504
Min SC = -5.943121 at lag 4 with RMSE .0488832
Min MAIC = -5.969767 at lag 16 with RMSE .0462955
. dfuller ukequity, trend regress lags(15)
Augmented Dickey-Fuller test for unit root Number of obs =
307
---------- Interpolated Dickey-Fuller
---------
Test 1% Critical 5% Critical 10%
Critical
Statistic Value Value Value
-----------------------------------------------------------------------------
-
Z(t) -4.528 -3.988 -3.428
-3.130
-----------------------------------------------------------------------------
-
MacKinnon approximate p-value for Z(t) = 0.0014
-----------------------------------------------------------------------------
-
D.ukequity | Coef. Std. Err. t P>|t| [95% Conf.
Interval]
-------------+---------------------------------------------------------------
-
ukequity |
L1. | -1.260002 .278274 -4.53 0.000 -1.807702
-.712301
LD. | .2516197 .2681984 0.94 0.349 -.2762502
.7794895
L2D. | .1797329 .2590063 0.69 0.488 -.330045
.6895107
L3D. | .1392168 .2489641 0.56 0.576 -.3507959
.6292296
L4D. | .1102949 .2379413 0.46 0.643 -.3580227
.5786125
L5D. | .0961308 .2262593 0.42 0.671 -.3491941
.5414557
L6D. | .0707118 .2145085 0.33 0.742 -.3514853
.4929089
L7D. | .0218922 .2017615 0.11 0.914 -.375216
.4190005
L8D. | -.044679 .1867235 -0.24 0.811 -.4121894
.3228313
L9D. | .0107564 .1716596 0.06 0.950 -.3271051
.3486179
L10D. | .0347913 .1566438 0.22 0.824 -.273516
.3430986
L11D. | .0149585 .1410219 0.11 0.916 -.2626016
.2925187
L12D. | .0054756 .1234088 0.04 0.965 -.2374185
.2483697
L13D. | .0324817 .1039914 0.31 0.755 -.1721949
.2371583
L14D. | .0484601 .0822194 0.59 0.556 -.1133647
.2102848
L15D. | -.0409168 .0577236 -0.71 0.479 -.1545288
.0726953
_trend | -.000059 .0000333 -1.77 0.078 -.0001246
6.62e-06
_cons | .0253424 .0082827 3.06 0.002 .0090403
.0416445
-----------------------------------------------------------------------------
-
. dfuller ukequity, trend regress lags(4)
Augmented Dickey-Fuller test for unit root Number of obs =
318
---------- Interpolated Dickey-Fuller
---------
Test 1% Critical 5% Critical 10%
Critical
Statistic Value Value Value
-----------------------------------------------------------------------------
-
Z(t) -8.538 -3.987 -3.427
-3.130
-----------------------------------------------------------------------------
-
MacKinnon approximate p-value for Z(t) = 0.0000
-----------------------------------------------------------------------------
-
D.ukequity | Coef. Std. Err. t P>|t| [95% Conf.
Interval]
-------------+---------------------------------------------------------------
-
ukequity |
L1. | -1.162101 .1361069 -8.54 0.000 -1.429907
-.8942938
LD. | .1509211 .119604 1.26 0.208 -.0844143
.3862564
L2D. | .0697618 .1011059 0.69 0.491 -.1291763
.2687
L3D. | .0220896 .0798874 0.28 0.782 -.1350985
.1792778
L4D. | .0045536 .056008 0.08 0.935 -.1056489
.1147561
_trend | -.0000637 .0000289 -2.20 0.028 -.0001206
-6.81e-06
_cons | .0253618 .0060062 4.22 0.000 .0135438
.0371798
-----------------------------------------------------------------------------
-
My second question involves how to identify an ARIMA process by looking the
associated correlogram (see below)
Thank you very much in advance
Jose Seisdedos
corrgram ukbond
-1 0 1 -1 0
1
LAG AC PAC Q Prob>Q [Autocorrelation] [Partial
Autocor]
-----------------------------------------------------------------------------
--
1 0.0023 0.0023 .00177 0.9664 | |
2 0.0365 0.0365 .43703 0.8037 | |
3 -0.0464 -0.0466 1.1418 0.7670 | |
4 -0.0138 -0.0150 1.2047 0.8773 | |
5 0.0153 0.0189 1.2819 0.9368 | |
6 0.0215 0.0203 1.4353 0.9637 | |
7 -0.0031 -0.0062 1.4385 0.9844 | |
8 -0.0491 -0.0490 2.2426 0.9727 | |
9 0.0319 0.0353 2.5821 0.9786 | |
10 0.0061 0.0093 2.5944 0.9894 | |
11 0.0908 0.0842 5.367 0.9121 | |
12 -0.0275 -0.0287 5.6229 0.9339 | |
13 -0.0036 -0.0044 5.6273 0.9587 | |
14 -0.0638 -0.0550 7.0115 0.9343 | |
15 -0.0644 -0.0633 8.4262 0.9056 | |
16 -0.0547 -0.0585 9.4488 0.8938 | |
17 -0.0500 -0.0491 10.305 0.8903 | |
18 0.0662 0.0648 11.813 0.8567 | |
19 0.0318 0.0404 12.162 0.8786 | |
20 0.0173 0.0010 12.265 0.9066 | |
21 -0.0605 -0.0592 13.539 0.8886 | |
22 -0.0124 -0.0195 13.593 0.9153 | |
23 0.1074 0.1186 17.631 0.7772 | |
24 -0.0061 -0.0136 17.644 0.8199 | |
25 0.0467 0.0529 18.414 0.8243 | |
26 0.0163 0.0482 18.508 0.8565 | |
27 -0.0282 -0.0220 18.791 0.8775 | |
28 -0.0186 -0.0285 18.913 0.9008 | |
29 -0.0216 -0.0409 19.079 0.9192 | |
30 0.1284 0.1250 24.986 0.7257 |- |-
31 0.0719 0.0767 26.842 0.6801 | |
32 -0.0653 -0.0731 28.38 0.6505 | |
33 -0.0792 -0.0734 30.647 0.5848 | |
34 0.0225 0.0254 30.832 0.6237 | |
35 0.0050 0.0140 30.841 0.6692 | |
36 0.0336 0.0055 31.255 0.6937 | |
37 0.0384 0.0428 31.796 0.7114 | |
38 -0.0358 -0.0144 32.268 0.7311 | |
39 -0.0117 -0.0000 32.319 0.7667 | |
40 -0.0376 -0.0313 32.844 0.7816 | |
. corrgram ukequity
-1 0 1 -1 0
1
LAG AC PAC Q Prob>Q [Autocorrelation] [Partial
Autocor]
-----------------------------------------------------------------------------
--
1 0.0019 0.0019 .00114 0.9730 | |
2 -0.0696 -0.0697 1.5874 0.4522 | |
3 -0.0356 -0.0354 2.0029 0.5718 | |
4 -0.0017 -0.0059 2.0038 0.7351 | |
5 0.0156 0.0110 2.0845 0.8373 | |
6 -0.0200 -0.0220 2.2163 0.8988 | |
7 -0.0326 -0.0321 2.5686 0.9218 | |
8 -0.0399 -0.0434 3.1001 0.9279 | |
9 0.0881 0.0836 5.6975 0.7698 | |
10 0.0492 0.0415 6.5098 0.7708 | |
11 -0.0267 -0.0190 6.7504 0.8189 | |
12 -0.0016 0.0094 6.7513 0.8736 | |
13 0.0378 0.0402 7.2356 0.8896 | |
14 0.0346 0.0323 7.6422 0.9071 | |
15 -0.0714 -0.0701 9.3815 0.8567 | |
16 0.0421 0.0554 9.9861 0.8674 | |
17 0.0058 0.0080 9.9975 0.9037 | |
18 0.0590 0.0611 11.196 0.8858 | |
19 -0.0060 -0.0117 11.209 0.9166 | |
20 -0.0634 -0.0517 12.604 0.8937 | |
21 -0.0206 -0.0178 12.752 0.9171 | |
22 0.0729 0.0671 14.605 0.8786 | |
23 0.0616 0.0453 15.934 0.8581 | |
24 0.0435 0.0634 16.597 0.8653 | |
25 0.0155 0.0309 16.682 0.8930 | |
26 0.0072 0.0138 16.7 0.9179 | |
27 0.0262 0.0213 16.943 0.9325 | |
28 0.0769 0.0783 19.046 0.8967 | |
29 0.0273 0.0436 19.311 0.9131 | |
30 0.0433 0.0713 19.982 0.9170 | |
31 -0.0756 -0.0659 22.038 0.8818 | |
32 -0.0421 -0.0451 22.676 0.8883 | |
33 0.0141 0.0066 22.747 0.9097 | |
34 0.0871 0.0845 25.505 0.8528 | |
35 0.0175 0.0118 25.617 0.8768 | |
36 -0.0274 -0.0218 25.891 0.8934 | |
37 -0.0503 -0.0543 26.82 0.8914 | |
38 -0.0183 -0.0401 26.944 0.9097 | |
39 -0.0533 -0.0827 27.993 0.9049 | |
40 -0.0608 -0.0858 29.366 0.8921 | |
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