help with unit root testing!

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NipNip
Posts: 32
Joined: Thu Oct 20, 2016 4:46 pm

help with unit root testing!

Postby NipNip » Thu Oct 20, 2016 4:57 pm

Hello!

After reading several websites, i still can't be 100% sure when chosing between none, Intercept only, Trend only and both (trend and inercept) for unit root testing. So, i will really appreciate any suggestion when choosing between the models mentioned above, especialy when working with the next tests:

- ADF
- Phillips - Perron
- Kpss
- Zivot - Andrews

looking forward to your help.

Regards,

Joel

EViews Gareth
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Re: help with unit root testing!

Postby EViews Gareth » Thu Oct 20, 2016 5:44 pm

Depends on your data.
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NipNip
Posts: 32
Joined: Thu Oct 20, 2016 4:46 pm

Re: help with unit root testing!

Postby NipNip » Thu Oct 20, 2016 5:50 pm

I'm working with some time series. in order to run an ARDL model i need to examine their integration order. i always wondering "am i doing it correctly?"

Thank, for your replies.

jmagomez
Posts: 68
Joined: Wed Aug 08, 2012 10:24 am

Re: help with unit root testing!

Postby jmagomez » Fri Oct 21, 2016 9:01 am

Dear NipNip,

How many observations do you have?

Best Regards.

NipNip
Posts: 32
Joined: Thu Oct 20, 2016 4:46 pm

Re: help with unit root testing!

Postby NipNip » Fri Oct 21, 2016 1:04 pm

Hello!

I am working with 49 observations (1965 - 2014). I'm trying to determine the integration order of my variables. but i want to do it correctly. Since i'm not an expert in time series analysis, i would like to follow your suggestions.

Attached is my workfile.

Regards,

Joel
Attachments
data.WF1
data
(12.91 KiB) Downloaded 227 times

NipNip
Posts: 32
Joined: Thu Oct 20, 2016 4:46 pm

Re: help with unit root testing!

Postby NipNip » Fri Oct 21, 2016 3:37 pm

This might be helpful for noobs like me. https://tamino.wordpress.com/2010/03/11/not-a-random-walk/

NipNip
Posts: 32
Joined: Thu Oct 20, 2016 4:46 pm

Re: help with unit root testing!

Postby NipNip » Fri Oct 21, 2016 4:37 pm

When testing for unit root in a differenced serie, would you use the option "intercept" or "none" in the "unit root test" window?

jmagomez
Posts: 68
Joined: Wed Aug 08, 2012 10:24 am

Re: help with unit root testing!

Postby jmagomez » Mon Oct 24, 2016 3:42 am

Dear Nipnip,

I think you should use the same specification that you are working with. So if you use intercept at your equation, you should use intercept. But this is not an obligation.

And could you explain your data, what is the difference between lpibpc from lpibpcsq. Is it just the square? What is lop and lco2pc?

c is almost zero all the period.

Regards!

NipNip
Posts: 32
Joined: Thu Oct 20, 2016 4:46 pm

Re: help with unit root testing!

Postby NipNip » Mon Oct 24, 2016 6:11 am

all variables are in log form.

lop = log(oil prices)
lco2pc = log(per capaita co2 emissions)
lpibpc = log(per capita pib)
lpibpcsq = (log(per capita pib))^2

jmagomez
Posts: 68
Joined: Wed Aug 08, 2012 10:24 am

Re: help with unit root testing!

Postby jmagomez » Mon Oct 24, 2016 8:14 am

Dear Nipnip,
I ran your data and I find two solutions:
1) The Trace Test -> indicates three cointegration vectors; and
2) The Max-Eigenvalue indicates no cointegration vector.
Normally, the latter test is recognized as being better than the first. Could you think about others variables that could fit this analysis?
And I prefer running ADF Test with Intercept without Trend.
Regards.

NipNip
Posts: 32
Joined: Thu Oct 20, 2016 4:46 pm

Re: help with unit root testing!

Postby NipNip » Mon Oct 24, 2016 10:08 am

Dear jmagomez,

First, I want to say thank you for sharing your experience. I`m trying to follow the EKC (enviromental Kuznets curve) hypotesis.
In order to do that i need to be sure if my variables are I(0) or I(1), but not I(2).

Also i found this: you should start from ''with trend and intercept'' then 'with intercept but no trend''
then 'no interecpt and no trend'' and stop where you find the series is stationary. you can learn more details in
ENDERS APPLIED TIME SERIES.

Regards,

Joel

jmagomez
Posts: 68
Joined: Wed Aug 08, 2012 10:24 am

Re: help with unit root testing!

Postby jmagomez » Mon Oct 24, 2016 10:17 am

Dear Joel,

Actually, I do appreciate the opportunity for developing myself discussing these points that you bring to us.

The sequence that you mentioned means that the first test you accept easier than other ones that the series is not stationary. The latter would be the restrictive case.

Regards.

NipNip
Posts: 32
Joined: Thu Oct 20, 2016 4:46 pm

Re: help with unit root testing!

Postby NipNip » Mon Oct 24, 2016 10:43 am

Dear jmagomez,

Do you think it is correct if i follow the sequence mentioned above?
Also, if you tested the integration order of the variables in the attached file, I think I would like to see your result.

This is the first time i`m modeling, so your opinion is highly appreciated.

Regards,

Joel

jmagomez
Posts: 68
Joined: Wed Aug 08, 2012 10:24 am

Re: help with unit root testing!

Postby jmagomez » Tue Oct 25, 2016 7:59 am

Dear Nipnip,

There is no rule. Or a paper that discusses the way that you have to follow to adopt one or another unit root test.

And this is an unrestricted VAR:

Vector Autoregression Estimates
Date: 10/25/16 Time: 12:57
Sample (adjusted): 1966 2014
Included observations: 49 after adjustments
Standard errors in ( ) & t-statistics in [ ]

LCO2PC LOP LPIBPC LPIBPCSQ

LCO2PC(-1) 0.418562 -0.003564 -0.024958 -0.411827
(0.12059) (0.25367) (0.02690) (0.42646)
[ 3.47107] [-0.01405] [-0.92787] [-0.96570]

LOP(-1) 0.117987 0.529144 0.012805 0.215716
(0.06654) (0.13998) (0.01484) (0.23533)
[ 1.77310] [ 3.78005] [ 0.86270] [ 0.91665]

LPIBPC(-1) 14.17479 19.44161 0.636550 -6.299076
(6.92405) (14.5658) (1.54448) (24.4872)
[ 2.04718] [ 1.33474] [ 0.41214] [-0.25724]

LPIBPCSQ(-1) -0.860836 -1.054589 0.020799 1.363474
(0.42726) (0.89882) (0.09531) (1.51104)
[-2.01476] [-1.17331] [ 0.21823] [ 0.90234]

C -58.31674 -86.58974 1.566160 26.93902
(28.0649) (59.0387) (6.26017) (99.2524)
[-2.07793] [-1.46666] [ 0.25018] [ 0.27142]

R-squared 0.930120 0.953207 0.980220 0.980348
Adj. R-squared 0.923767 0.948953 0.978422 0.978561
Sum sq. resids 0.808725 3.578892 0.040239 10.11479
S.E. equation 0.135573 0.285199 0.030241 0.479460
F-statistic 146.4119 224.0793 545.1133 548.7335
Log likelihood 31.02286 -5.417197 104.5381 -30.87137
Akaike AIC -1.062158 0.425192 -4.062781 1.464137
Schwarz SC -0.869115 0.618235 -3.869738 1.657180
Mean dependent 0.449035 2.850849 8.009598 64.19518
S.D. dependent 0.491023 1.262306 0.205868 3.274554

Determinant resid covariance (dof adj.) 1.22E-10
Determinant resid covariance 7.91E-11
Log likelihood 291.7585
Akaike information criterion -11.09218
Schwarz criterion -10.32001



And this is the Cointegration Test:

Date: 10/25/16 Time: 12:58
Sample (adjusted): 1967 2014
Included observations: 48 after adjustments
Trend assumption: Linear deterministic trend
Series: LCO2PC LOP LPIBPC LPIBPCSQ
Lags interval (in first differences): 1 to 1

Unrestricted Cointegration Rank Test (Trace)

Hypothesized Trace 0.05
No. of CE(s) Eigenvalue Statistic Critical Value Prob.**

None * 0.409611 63.18702 47.85613 0.0010
At most 1 * 0.361237 37.89227 29.79707 0.0047
At most 2 * 0.230471 16.37764 15.49471 0.0367
At most 3 0.076167 3.802758 3.841466 0.0512

Trace test indicates 3 cointegrating eqn(s) at the 0.05 level
* denotes rejection of the hypothesis at the 0.05 level
**MacKinnon-Haug-Michelis (1999) p-values

Unrestricted Cointegration Rank Test (Maximum Eigenvalue)

Hypothesized Max-Eigen 0.05
No. of CE(s) Eigenvalue Statistic Critical Value Prob.**

None 0.409611 25.29475 27.58434 0.0955
At most 1 * 0.361237 21.51463 21.13162 0.0442
At most 2 0.230471 12.57488 14.26460 0.0909
At most 3 0.076167 3.802758 3.841466 0.0512

Max-eigenvalue test indicates no cointegration at the 0.05 level
* denotes rejection of the hypothesis at the 0.05 level
**MacKinnon-Haug-Michelis (1999) p-values

Unrestricted Cointegrating Coefficients (normalized by b'*S11*b=I):

LCO2PC LOP LPIBPC LPIBPCSQ
1.356357 -0.469511 -9.615164 0.192078
-8.074703 2.548502 146.4237 -9.028732
0.765670 3.472310 -74.61098 3.306127
-0.117285 0.846222 -358.0579 22.33341


Unrestricted Adjustment Coefficients (alpha):

D(LCO2PC) 0.015617 0.090637 -0.008246 0.002587
D(LOP) -0.056273 0.012236 -0.116733 0.009724
D(LPIBPC) 0.002674 -0.001623 -0.000960 0.006219
D(LPIBPCSQ) 0.035977 -0.025733 -0.013983 0.099500


1 Cointegrating Equation(s): Log likelihood 294.4528

Normalized cointegrating coefficients (standard error in parentheses)
LCO2PC LOP LPIBPC LPIBPCSQ
1.000000 -0.346156 -7.088963 0.141613
(0.51725) (49.9292) (3.09139)

Adjustment coefficients (standard error in parentheses)
D(LCO2PC) 0.021182
(0.03207)
D(LOP) -0.076326
(0.05350)
D(LPIBPC) 0.003627
(0.00482)
D(LPIBPCSQ) 0.048798
(0.07676)


2 Cointegrating Equation(s): Log likelihood 305.2101

Normalized cointegrating coefficients (standard error in parentheses)
LCO2PC LOP LPIBPC LPIBPCSQ
1.000000 0.000000 -132.2726 11.20998
(488.329) (30.8908)
0.000000 1.000000 -361.6393 31.97508
(1542.00) (97.5442)

Adjustment coefficients (standard error in parentheses)
D(LCO2PC) -0.710681 0.223655
(0.15607) (0.04940)
D(LOP) -0.175130 0.057605
(0.32259) (0.10210)
D(LPIBPC) 0.016732 -0.005392
(0.02899) (0.00918)
D(LPIBPCSQ) 0.256582 -0.082471
(0.46225) (0.14630)


3 Cointegrating Equation(s): Log likelihood 311.4976

Normalized cointegrating coefficients (standard error in parentheses)
LCO2PC LOP LPIBPC LPIBPCSQ
1.000000 0.000000 0.000000 -0.786281
(0.11810)
0.000000 1.000000 0.000000 -0.823247
(0.08934)
0.000000 0.000000 1.000000 -0.090693
(0.00511)

Adjustment coefficients (standard error in parentheses)
D(LCO2PC) -0.716994 0.195024 13.73639
(0.15641) (0.08240) (3.13090)
D(LOP) -0.264509 -0.347727 11.04229
(0.28816) (0.15182) (5.76827)
D(LPIBPC) 0.015997 -0.008723 -0.191755
(0.02910) (0.01533) (0.58243)
D(LPIBPCSQ) 0.245875 -0.131024 -3.070532
(0.46393) (0.24443) (9.28686)

Regards.

NipNip
Posts: 32
Joined: Thu Oct 20, 2016 4:46 pm

Re: help with unit root testing!

Postby NipNip » Tue Oct 25, 2016 11:00 am

ok! ill follow my heart! :D

Thank you for your time!

Regards.


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