I'm testing unit roots for monthly time series data in Stata 12.
I have some questions about dfgls and kpss tests:
1. dfgls have information criteria methods to choose the optimal lag order, for kpss test, there’s no such options. Which lag order to use from kpss test, could I use the optimal lag order reported by dfgls test for kpss test?
2. When test results from dfgls and kpss contradict, which one should be preferred?
3. If the series is still non-stationaty, after seasonal and non-seasonal differencing, what kind of transformation can I use to make it stationary?
Does any encounter the same situation? Any thoughts on how to deal with it.
Thanks.
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The following is some test statistics from Stata for one series, please correct me if I interpret those results wrong.
lcqS12D1 is the first-and-twelfth differences of lcq.
Unit root tests for the log-transformed level (lcq) and the twelfth-differenced series (lcqS12) both indicate non-stationarities.
dfgls lcqS12D1
DF-GLS for lcqS12D1 Number of obs = 141
Maxlag = 13 chosen by Schwert criterion
DF-GLS tau 1% Critical 5% Critical 10% Critical
[lags] Test Statistic Value Value Value
------------------------------------------------------------------------------
13 -2.171 -3.514 -2.789 -2.513
12 -2.546 -3.514 -2.807 -2.530
11 -3.117 -3.514 -2.825 -2.547
10 -2.362 -3.514 -2.842 -2.563
9 -2.719 -3.514 -2.859 -2.578
8 -2.649 -3.514 -2.875 -2.593
7 -3.234 -3.514 -2.890 -2.607
6 -4.063 -3.514 -2.905 -2.621
5 -5.376 -3.514 -2.919 -2.634
4 -6.445 -3.514 -2.932 -2.646
3 -6.549 -3.514 -2.944 -2.657
2 -7.184 -3.514 -2.956 -2.667
1 -8.646 -3.514 -2.966 -2.677
Opt Lag (Ng-Perron seq t) = 13 with RMSE .3580469
Min SC = -1.562817 at lag 13 with RMSE .3580469
Min MAIC = -1.018508 at lag 13 with RMSE .3580469
For lags 1-7, null hypothesis of unit root is rejected at the 5% significance level.
For lags 8-13, null hypothesis cannot be rejected at the 5% significance level.
The optimal lags suggested by Ng-Perron tests is 13.
dfgls statistic for lag order of 13 is -2.171, can’t reject the null hypothesis of unit root at even the 10% significance level.
So accepting the null, lcqS12D1 is a random walk, possibly with drift.
kpss lcqS12D1
KPSS test for lcqS12D1
Maxlag = 13 chosen by Schwert criterion
Critical values for H0: lcqS12D1 is trend stationary
10%: 0.119 5% : 0.146 2.5%: 0.176 1% : 0.216
Lag order Test statistic
0 .00927
1 .00984
2 .011
3 .0123
4 .0144
5 .0184
6 .0232
7 .0263
8 .0265
9 .0247
10 .0252
11 .0254
12 .0315
13 .0386
Can’t reject the null hypothesis of trend stationaries at all lag orders.
corrgram lcqS12D1, lags(13)
-1 0 1 -1 0 1
LAG AC PAC Q Prob>Q [Autocorrelation] [Partial Autocor]
-------------------------------------------------------------------------------
1 -0.0730 -0.0734 .84254 0.3587 | |
2 -0.1188 -0.1259 3.0866 0.2137 | -|
3 -0.1098 -0.1322 5.017 0.1706 | -|
4 -0.1116 -0.1557 7.025 0.1346 | -|
5 -0.2001 -0.2808 13.523 0.0189 -| --|
6 -0.0058 -0.1428 13.529 0.0354 | -|
7 0.1310 -0.0076 16.348 0.0221 |- |
8 0.1217 0.0309 18.799 0.0160 | |
9 0.1424 0.1357 22.177 0.0083 |- |-
10 -0.1565 -0.1567 26.288 0.0034 -| -|
11 0.0300 0.0710 26.44 0.0056 | |
12 -0.4528 -0.5181 61.331 0.0000 ---| ----|
13 0.0464 0.0044 61.7 0.0000 | |
I have some questions about dfgls and kpss tests:
1. dfgls have information criteria methods to choose the optimal lag order, for kpss test, there’s no such options. Which lag order to use from kpss test, could I use the optimal lag order reported by dfgls test for kpss test?
2. When test results from dfgls and kpss contradict, which one should be preferred?
3. If the series is still non-stationaty, after seasonal and non-seasonal differencing, what kind of transformation can I use to make it stationary?
Does any encounter the same situation? Any thoughts on how to deal with it.
Thanks.
************************************************** ************************************************** ************************************************** *********************
The following is some test statistics from Stata for one series, please correct me if I interpret those results wrong.
lcqS12D1 is the first-and-twelfth differences of lcq.
Unit root tests for the log-transformed level (lcq) and the twelfth-differenced series (lcqS12) both indicate non-stationarities.
dfgls lcqS12D1
DF-GLS for lcqS12D1 Number of obs = 141
Maxlag = 13 chosen by Schwert criterion
DF-GLS tau 1% Critical 5% Critical 10% Critical
[lags] Test Statistic Value Value Value
------------------------------------------------------------------------------
13 -2.171 -3.514 -2.789 -2.513
12 -2.546 -3.514 -2.807 -2.530
11 -3.117 -3.514 -2.825 -2.547
10 -2.362 -3.514 -2.842 -2.563
9 -2.719 -3.514 -2.859 -2.578
8 -2.649 -3.514 -2.875 -2.593
7 -3.234 -3.514 -2.890 -2.607
6 -4.063 -3.514 -2.905 -2.621
5 -5.376 -3.514 -2.919 -2.634
4 -6.445 -3.514 -2.932 -2.646
3 -6.549 -3.514 -2.944 -2.657
2 -7.184 -3.514 -2.956 -2.667
1 -8.646 -3.514 -2.966 -2.677
Opt Lag (Ng-Perron seq t) = 13 with RMSE .3580469
Min SC = -1.562817 at lag 13 with RMSE .3580469
Min MAIC = -1.018508 at lag 13 with RMSE .3580469
For lags 1-7, null hypothesis of unit root is rejected at the 5% significance level.
For lags 8-13, null hypothesis cannot be rejected at the 5% significance level.
The optimal lags suggested by Ng-Perron tests is 13.
dfgls statistic for lag order of 13 is -2.171, can’t reject the null hypothesis of unit root at even the 10% significance level.
So accepting the null, lcqS12D1 is a random walk, possibly with drift.
kpss lcqS12D1
KPSS test for lcqS12D1
Maxlag = 13 chosen by Schwert criterion
Critical values for H0: lcqS12D1 is trend stationary
10%: 0.119 5% : 0.146 2.5%: 0.176 1% : 0.216
Lag order Test statistic
0 .00927
1 .00984
2 .011
3 .0123
4 .0144
5 .0184
6 .0232
7 .0263
8 .0265
9 .0247
10 .0252
11 .0254
12 .0315
13 .0386
Can’t reject the null hypothesis of trend stationaries at all lag orders.
corrgram lcqS12D1, lags(13)
-1 0 1 -1 0 1
LAG AC PAC Q Prob>Q [Autocorrelation] [Partial Autocor]
-------------------------------------------------------------------------------
1 -0.0730 -0.0734 .84254 0.3587 | |
2 -0.1188 -0.1259 3.0866 0.2137 | -|
3 -0.1098 -0.1322 5.017 0.1706 | -|
4 -0.1116 -0.1557 7.025 0.1346 | -|
5 -0.2001 -0.2808 13.523 0.0189 -| --|
6 -0.0058 -0.1428 13.529 0.0354 | -|
7 0.1310 -0.0076 16.348 0.0221 |- |
8 0.1217 0.0309 18.799 0.0160 | |
9 0.1424 0.1357 22.177 0.0083 |- |-
10 -0.1565 -0.1567 26.288 0.0034 -| -|
11 0.0300 0.0710 26.44 0.0056 | |
12 -0.4528 -0.5181 61.331 0.0000 ---| ----|
13 0.0464 0.0044 61.7 0.0000 | |
