Hello everybody,
I am a little confused how to interprete Stata 13.1's output from the unit root tests dfuller and pperron.
I'm using monthly data from Jan 1985 to Jan 2016.
The variable FEDD contains the value of $100 from Jan 2004, in/decreasing with the federal funds rate.
The Variable CPIC is the core CPI
When checking for unit root without trend for CPIC , there is no unit root at the 1% level but at the 5% level for perrons(-3.055) and no unit root at all for dfuller (-4.046).
If i allow trend, the Z(t) statistics are -1.821 and -1.696 ( bigger than the 10% CV -3.130) , making it impossible to reject H0 -> CPIC is non-stationary.
When checking for unit root without trend for FEDD , there is no unit root (dfullers -10.16 and perrons -4.290 are both smaller than the 1% CV of -3.450).
If I allow trend, the Z(t) statistics turn positive (8.788 and 3.157).
What does that mean/How do I have to interpret that?
the outputs are:
dfuller FEDD
Dickey-Fuller test for unit root Number of obs = 371
---------- Interpolated Dickey-Fuller ---------
Test 1% Critical 5% Critical 10% Critical
Statistic Value Value Value
------------------------------------------------------------------------------
Z(t) -10.160 -3.450 -2.875 -2.570
------------------------------------------------------------------------------
MacKinnon approximate p-value for Z(t) = 0.0000
////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
pperron FEDD
Phillips-Perron test for unit root Number of obs = 371
Newey-West lags = 5
---------- Interpolated Dickey-Fuller ---------
Test 1% Critical 5% Critical 10% Critical
Statistic Value Value Value
------------------------------------------------------------------------------
Z(rho) -0.965 -20.397 -14.000 -11.200
Z(t) -4.290 -3.450 -2.875 -2.570
------------------------------------------------------------------------------
MacKinnon approximate p-value for Z(t) = 0.0005
////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
. dfuller FEDD, trend regress
Dickey-Fuller test for unit root Number of obs = 371
---------- Interpolated Dickey-Fuller ---------
Test 1% Critical 5% Critical 10% Critical
Statistic Value Value Value
------------------------------------------------------------------------------
Z(t) 8.788 -3.985 -3.425 -3.130
------------------------------------------------------------------------------
MacKinnon approximate p-value for Z(t) = 1.0000
------------------------------------------------------------------------------
D.FEDD | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
FEDD |
L1. | .0115549 .0013148 8.79 0.000 .0089694 .0141403
_trend | -.0035999 .000331 -10.87 0.000 -.0042508 -.0029489
_cons | -.1061739 .0538242 -1.97 0.049 -.2120154 -.0003323
-------------------------------------------------------------------------------------
MacKinnon approximate p-value for Z(t) = 1.0000
////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
pperon FEDD, trend regress
Phillips-Perron test for unit root Number of obs = 371
Newey-West lags = 5
---------- Interpolated Dickey-Fuller ---------
Test 1% Critical 5% Critical 10% Critical
Statistic Value Value Value
------------------------------------------------------------------------------
Z(rho) 3.718 -28.642 -21.397 -18.048
Z(t) 3.157 -3.985 -3.425 -3.130
------------------------------------------------------------------------------
MacKinnon approximate p-value for Z(t) = 1.0000
------------------------------------------------------------------------------
FEDD | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
FEDD |
L1. | 1.011555 .0013148 769.37 0.000 1.008969 1.01414
_trend | -.0035999 .000331 -10.87 0.000 -.0042508 -.0029489
_cons | -.1061739 .0538242 -1.97 0.049 -.2120154 -.0003323
------------------------------------------------------------------------------
I am a little confused how to interprete Stata 13.1's output from the unit root tests dfuller and pperron.
I'm using monthly data from Jan 1985 to Jan 2016.
The variable FEDD contains the value of $100 from Jan 2004, in/decreasing with the federal funds rate.
The Variable CPIC is the core CPI
When checking for unit root without trend for CPIC , there is no unit root at the 1% level but at the 5% level for perrons(-3.055) and no unit root at all for dfuller (-4.046).
If i allow trend, the Z(t) statistics are -1.821 and -1.696 ( bigger than the 10% CV -3.130) , making it impossible to reject H0 -> CPIC is non-stationary.
When checking for unit root without trend for FEDD , there is no unit root (dfullers -10.16 and perrons -4.290 are both smaller than the 1% CV of -3.450).
If I allow trend, the Z(t) statistics turn positive (8.788 and 3.157).
What does that mean/How do I have to interpret that?
the outputs are:
dfuller FEDD
Dickey-Fuller test for unit root Number of obs = 371
---------- Interpolated Dickey-Fuller ---------
Test 1% Critical 5% Critical 10% Critical
Statistic Value Value Value
------------------------------------------------------------------------------
Z(t) -10.160 -3.450 -2.875 -2.570
------------------------------------------------------------------------------
MacKinnon approximate p-value for Z(t) = 0.0000
////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
pperron FEDD
Phillips-Perron test for unit root Number of obs = 371
Newey-West lags = 5
---------- Interpolated Dickey-Fuller ---------
Test 1% Critical 5% Critical 10% Critical
Statistic Value Value Value
------------------------------------------------------------------------------
Z(rho) -0.965 -20.397 -14.000 -11.200
Z(t) -4.290 -3.450 -2.875 -2.570
------------------------------------------------------------------------------
MacKinnon approximate p-value for Z(t) = 0.0005
////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
. dfuller FEDD, trend regress
Dickey-Fuller test for unit root Number of obs = 371
---------- Interpolated Dickey-Fuller ---------
Test 1% Critical 5% Critical 10% Critical
Statistic Value Value Value
------------------------------------------------------------------------------
Z(t) 8.788 -3.985 -3.425 -3.130
------------------------------------------------------------------------------
MacKinnon approximate p-value for Z(t) = 1.0000
------------------------------------------------------------------------------
D.FEDD | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
FEDD |
L1. | .0115549 .0013148 8.79 0.000 .0089694 .0141403
_trend | -.0035999 .000331 -10.87 0.000 -.0042508 -.0029489
_cons | -.1061739 .0538242 -1.97 0.049 -.2120154 -.0003323
-------------------------------------------------------------------------------------
MacKinnon approximate p-value for Z(t) = 1.0000
////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
pperon FEDD, trend regress
Phillips-Perron test for unit root Number of obs = 371
Newey-West lags = 5
---------- Interpolated Dickey-Fuller ---------
Test 1% Critical 5% Critical 10% Critical
Statistic Value Value Value
------------------------------------------------------------------------------
Z(rho) 3.718 -28.642 -21.397 -18.048
Z(t) 3.157 -3.985 -3.425 -3.130
------------------------------------------------------------------------------
MacKinnon approximate p-value for Z(t) = 1.0000
------------------------------------------------------------------------------
FEDD | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
FEDD |
L1. | 1.011555 .0013148 769.37 0.000 1.008969 1.01414
_trend | -.0035999 .000331 -10.87 0.000 -.0042508 -.0029489
_cons | -.1061739 .0538242 -1.97 0.049 -.2120154 -.0003323
------------------------------------------------------------------------------
FEDD values
| FEDD |
| 20.9676142 |
| 21.1975046 |
| 21.4714597 |
| 21.7679727 |
| 21.9581071 |
| 22.1268223 |
| 22.2873196 |
| 22.4558308 |
| 22.6443064 |
| 22.870538 |
| 23.143823 |
| 23.4792939 |
| 23.8269636 |
| 24.1255721 |
| 24.4032433 |
| 24.6980528 |
| 25.0530637 |
| 25.4190587 |
| 25.790581 |
| 26.1495102 |
| 26.4741836 |
| 26.7872361 |
| 27.0733979 |
| 27.3373988 |
| 27.6190799 |
| 27.9397988 |
| 28.2580826 |
| 28.5868439 |
| 28.9158616 |
| 29.2343929 |
| 29.5271188 |
| 29.769328 |
| 30.0112555 |
| 30.2469003 |
| 30.4730394 |
| 30.6872662 |
| 30.9058387 |
| 31.1173796 |
| 31.3332537 |
| 31.5559443 |
| 31.7748609 |
| 32.0014248 |
| 32.2411729 |
| 32.4871687 |
| 32.731304 |
| 32.9810395 |
| 33.227367 |
| 33.4770647 |
| 33.7355679 |
| 33.9929658 |
| 34.2611739 |
| 34.5401277 |
| 34.8247735 |
| 35.1310629 |
| 35.441641 |
| 35.7672738 |
| 36.0891531 |
| 36.3802384 |
| 36.6555832 |
| 36.9019421 |
| 37.1502424 |
| 37.4036626 |
| 37.6608355 |
| 37.9124925 |
| 38.1576001 |
| 38.3879621 |
| 38.6313723 |
| 38.8772267 |
| 39.123437 |
| 39.3751583 |
| 39.6291108 |
| 39.888699 |
| 40.1540071 |
| 40.4083033 |
| 40.6535135 |
| 40.8846478 |
| 41.1110092 |
| 41.3399132 |
| 41.5616561 |
| 41.7715038 |
| 41.9695452 |
| 42.1701852 |
| 42.37645 |
| 42.6097414 |
| 42.8319293 |
| 43.0448122 |
| 43.257734 |
| 43.4785319 |
| 43.7212999 |
| 43.9589068 |
| 44.1933159 |
| 44.4331411 |
| 44.6902843 |
| 44.9555512 |
| 45.1981006 |
| 45.4455072 |
| 45.6971202 |
| 45.9415165 |
| 46.1857756 |
| 46.4414871 |
| 46.7044378 |
| 46.9860338 |
| 47.2795773 |
| 47.5834084 |
| 47.8958387 |
| 48.2151461 |
| 48.5380759 |
| 48.8770532 |
| 49.2338401 |
| 49.5973956 |
| 49.9868285 |
| 50.379319 |
| 50.7737356 |
| 51.1599648 |
| 51.5412807 |
| 51.9123584 |
| 52.2865076 |
| 52.6593254 |
| 53.0217972 |
| 53.3822549 |
| 53.735657 |
| 54.0913987 |
| 54.450753 |
| 54.8124946 |
| 55.1728158 |
| 55.5397819 |
| 55.9057453 |
| 56.2706517 |
| 56.6414309 |
| 57.0106998 |
| 57.3695332 |
| 57.7087158 |
| 58.0322967 |
| 58.3285075 |
| 58.6220922 |
| 58.9018781 |
| 59.1792715 |
| 59.4584396 |
| 59.7431573 |
| 60.0188364 |
| 60.2857937 |
| 60.5424438 |
| 60.7813766 |
| 61.005223 |
| 61.2073898 |
| 61.4112102 |
| 61.6122545 |
| 61.8025534 |
| 61.9964264 |
| 62.186913 |
| 62.3584111 |
| 62.5268519 |
| 62.6932181 |
| 62.852919 |
| 63.008441 |
| 63.1643478 |
| 63.3206404 |
| 63.4773198 |
| 63.6379892 |
| 63.7928727 |
| 63.9496857 |
| 64.1094772 |
| 64.2707074 |
| 64.4307799 |
| 64.5922959 |
| 64.7526456 |
| 64.9123431 |
| 65.0719079 |
| 65.2334483 |
| 65.4059599 |
| 65.5831619 |
| 65.774621 |
| 65.9862475 |
| 66.2128693 |
| 66.4466423 |
| 66.6881613 |
| 66.9444262 |
| 67.2054184 |
| 67.4909924 |
| 67.7922563 |
| 68.0927129 |
| 68.4166221 |
| 68.7474811 |
| 69.0853707 |
| 69.4227387 |
| 69.7606574 |
| 70.0930526 |
| 70.4198209 |
| 70.7497851 |
| 71.0829752 |
| 71.417172 |
| 71.7489822 |
| 72.0692528 |
| 72.374348 |
| 72.6893651 |
| 72.9982419 |
| 73.3095922 |
| 73.6263501 |
| 73.9474016 |
| 74.2616241 |
| 74.5807248 |
| 74.8994177 |
| 75.223045 |
| 75.5492661 |
| 75.871497 |
| 76.1914813 |
| 76.5200857 |
| 76.8659023 |
| 77.2096235 |
| 77.5561068 |
| 77.9059904 |
| 78.2580703 |
| 78.6105 |
| 78.9626462 |
| 79.3176227 |
| 79.6729365 |
| 80.0330017 |
| 80.3908852 |
| 80.7497312 |
| 81.1082565 |
| 81.4690174 |
| 81.8346149 |
| 82.2057472 |
| 82.5766071 |
| 82.9471751 |
| 83.2884164 |
| 83.618446 |
| 83.9417733 |
| 84.2562876 |
| 84.5834271 |
| 84.9152132 |
| 85.2421981 |
| 85.5738462 |
| 85.9054179 |
| 86.2547226 |
| 86.6075096 |
| 86.9762171 |
| 87.3444189 |
| 87.7252888 |
| 88.1106066 |
| 88.4934175 |
| 88.9038646 |
| 89.3239568 |
| 89.7608624 |
| 90.2147787 |
| 90.6901709 |
| 91.1723469 |
| 91.6513507 |
| 92.1350338 |
| 92.6205449 |
| 93.1086144 |
| 93.5992558 |
| 94.0504172 |
| 94.4709824 |
| 94.8799256 |
| 95.2581573 |
| 95.5898954 |
| 95.9020633 |
| 96.1990441 |
| 96.4891926 |
| 96.7388919 |
| 96.9405222 |
| 97.1077642 |
| 97.2586043 |
| 97.3961233 |
| 97.5362338 |
| 97.6757458 |
| 97.8162585 |
| 97.9585779 |
| 98.1011044 |
| 98.2414243 |
| 98.3827508 |
| 98.5250876 |
| 98.6684383 |
| 98.7803836 |
| 98.8818811 |
| 98.9826681 |
| 99.0860045 |
| 99.1886324 |
| 99.2921838 |
| 99.3958433 |
| 99.4979732 |
| 99.5829751 |
| 99.6680496 |
| 99.7507281 |
| 99.8351223 |
| 99.9179394 |
| 100 |
| 100.08378 |
| 100.167629 |
| 100.251549 |
| 100.33554 |
| 100.420429 |
| 100.525266 |
| 100.640972 |
| 100.772533 |
| 100.919154 |
| 101.076741 |
| 101.25525 |
| 101.442347 |
| 101.650475 |
| 101.868963 |
| 102.101177 |
| 102.352158 |
| 102.606246 |
| 102.880913 |
| 103.174612 |
| 103.479976 |
| 103.798756 |
| 104.137731 |
| 104.492037 |
| 104.854255 |
| 105.237896 |
| 105.629678 |
| 106.042333 |
| 106.468446 |
| 106.901363 |
| 107.355616 |
| 107.81436 |
| 108.275065 |
| 108.737738 |
| 109.202388 |
| 109.669024 |
| 110.136782 |
| 110.608286 |
| 111.081809 |
| 111.556475 |
| 112.03317 |
| 112.511902 |
| 112.993575 |
| 113.460226 |
| 113.920668 |
| 114.361165 |
| 114.77959 |
| 115.186674 |
| 115.559134 |
| 115.843197 |
| 116.101615 |
| 116.318988 |
| 116.509195 |
| 116.699712 |
| 116.894361 |
| 117.088378 |
| 117.276008 |
| 117.381038 |
| 117.416194 |
| 117.435745 |
| 117.450415 |
| 117.471926 |
| 117.490509 |
| 117.505186 |
| 117.522797 |
| 117.543344 |
| 117.559004 |
| 117.575646 |
| 117.590333 |
| 117.602085 |
| 117.613839 |
| 117.625594 |
| 117.636371 |
| 117.649107 |
| 117.664782 |
| 117.684375 |
| 117.703971 |
| 117.721612 |
| 117.739256 |
| 117.757882 |
| 117.77749 |
| 117.796122 |
| 117.814757 |
| 117.833394 |
| 117.850075 |
| 117.865776 |
| 117.879519 |
| 117.889337 |
| 117.898175 |
| 117.907014 |
| 117.91389 |
| 117.923712 |
| 117.932552 |
| 117.939429 |
| 117.947289 |
| 117.955149 |
| 117.96301 |
| 117.972836 |
| 117.985609 |
| 117.999365 |
| 118.014105 |
| 118.03081 |
| 118.046536 |
| 118.059317 |
| 118.074064 |
| 118.088813 |
| 118.104547 |
| 118.121265 |
| 118.13602 |
| 118.150777 |
| 118.165536 |
| 118.179313 |
| 118.191125 |
| 118.200969 |
| 118.209831 |
| 118.218693 |
| 118.226571 |
| 118.235435 |
| 118.244299 |
| 118.253163 |
| 118.260059 |
| 118.266955 |
| 118.274837 |
| 118.283704 |
| 118.292572 |
| 118.302425 |
| 118.311294 |
| 118.320163 |
| 118.329034 |
| 118.337905 |
| 118.346777 |
| 118.358605 |
| 118.370434 |
| 118.381279 |
| 118.392125 |
| 118.403958 |
| 118.416778 |
| 118.428613 |
| 118.441435 |
| 118.455244 |
| 118.468069 |
| 118.480896 |
| 118.492737 |
| 118.514439 |
| 118.547966 |
