It means that variables are not integrated of same order. So you can not run Johansen Test of cointegration. So in this case, you can only run VAR model, not VECM.
Sometime it is suggested that if most of the variables are integrated of same order, we can go for Johansen Cointegration but ideal is all variables should be integrated of same order to run Johansen cointegration. Search literature about it.
Rejecting null means there is no unit root for that variable and there is P value(Prob) value to reject null. If P is less than 5 percent (0.05), you can reject null.
Suppose X, Y and Z variables have unit root at level but if after first differenced they all become stationary, then we can go for johansen cointegration. But here we shall use the X Y and Z variable (having unit root) for Johansen test.
Both tests are equality important to me. If you choose Trace Statistics, then you should choose VECM but if you choose Max-Eigen, then only VAR. Now it is up to you which test you will choose as benchmark. But try to do something so that both tests provide the same conclusion so that you can be more confident.
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Thanks again. I did the Johansen test for cointegration, and Eviews gave me what Iconsider as two conflicting results: The Trace Statistics suggests 1 cointegrating equation while Max-Eigen Value suggests 0 i.e no cointegrating equations. I'm not sure what to make out of this.Should I take this result as meaning that there are no cointegrating equations, right? If that the case, then it means I can not go ahead with the VECM, right? Thanks
Normally data are non-stationary at level. So I would suggest you to either increase the sample size or convert the variables in log and then check again
Another thing I need to point out Sir is that for the Johansen test for cointegration I used 5 lags based on the lowest AIC and SIC for optimal lag selection (I used the restricted VAR ). When I however selected other random number of lags both the Trace statistics and Max eigenvalue in some cases suggest that there are cointegrating equations - must I stick with the AIC and SIC lag selection?
If we cant reject null hypothesis for a variable at none and intercept but we reject null hypothesis at trend and intercept then can we say that variable has a unit root? or we need to satisfiy all the three condition for ADF test to become a variable unit root.
Hi Sir, On your videoyou express that if Y(-1) 's coëfficiënt is not negative the model is not viable. Other than taking your word for it as an expert do you have some references for this ? Thanking you in advance
You can only run Johansen test when all your variables will be integrated of same order meaning that You have five variables and all will have to become stationary after first difference. Only then you can run the Johansen test and you should use non-stationary data to run Johansen that is data at level.
Hi Sayed, thanks for the previous response. For one of my variables, with just the intercept I reject a unit root at the 5% level, but with intercept and trend I accept the unit root. How best should I interpret that outcome?
If a variable is found to be stationary then can we go further process with that variable for co-integration test? is that feasible...please let me know
Curiosity question. If we do a decomposition on a data like x12 / hodrick-prescott filter in order to have only a trend-cycle data, do we need still to do a unit-root test? If we want to compare two or more trend-cycle series? Most literature just focus on raw data, seasonal adjusted or seasonal. Thanks Marc
You try again to get all stationary after 1st differenced, that is integrated of same order, so that you can run Johansen Test. If it is not possible, meaning that variables are integrated of different order. In that case u have to run ARDL model.
Mr. Hossain, In my country (Mozambique) we are facing shortage of data related to high frequency observation (e.g. quarterly or monthly) can you help me on how to temporal disaggregating time series. In eviews (version 5 that I am using) there are several ways of doing that. So which one would you advise me to use to convert from annual frequency to monthly or to quarterly period? In the literature about that are pointed many ways (models), namely: Chow and Lin (1971); Lisman/Sandee (1964); Fernandez (1981) and Litterman (1983). Is one of these models used on eviews? If you have a video about it, may upload it, please! This question is not related to what is discussed here...so i am sorry...but i need your help!
Thanks Sir for your prompt reply. I increased the data sample size such that the data range is from 1971 to 2009. After taking the natural logs and testing for unit root all natural log variables were found to have unit root at level, however after taking 1st difference, all variables including CPI were stationary i.e integrated of the order I(1) -i.e ADF test result. Please would you recommend caarying out any further tests before I move on to testing for cointegration? Thanks
Hi Dr. Sayed. Is it a must to do the three tests (intersect, trend and none) for any VAR model? and what should I do if one of the test shows different result. that is, two tests show unit root while the other test shows no unit root?
Dear Sir, I am investigating the relationship between Energy Consumption (E) and economic growth, where E is the dependent vairable such that E= f( GDP, P) is energy demand equation- Y is income and P is energy energy prices. GDP is my proxy for economic growth and CPI as a proxy for enegy prices another independent variable in my model. I carried out ADF unit root test and found E and GDP to be stationary after taking 1st differencee i.e I(1), but CPI is I(2). Please advice on what to do
Hi Dr, thank you for your video lecture. In running a unit root test, for five variables, two stationery at level, one in first difference and other two in second difference. what model should i run?
sir i am working on 11 yr data with monthly frequency..and have 6 variables....out of it 2 are stationary at levels and other 4 are not....and also those other 4 variables become stationary at first difference...now i want to perform johansen cointegration test. how should i do it as it says all variables must be integrated of same order..and also i want to apply VAR...should i apply it on first difference of all 6 variables or first difference of 4 variables and take 2 at levels??
but sir, if one variable is I(0) and other 2 variable is I(1) then how should we go about it in unristrcited VAR model. can we use one at level and other 2 at difference. i dont think it will be a right approach...
Hi Hossain, my question is that if the time series with intercept only is non stationary at level and needs to be differenced twice in order to achieve stationarity but with both the intercept and trend and none it needs to be differenced once to achieve stationarity. then what can be the general conclusion and can we apply the johansen cointegration test in such case.
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Hi Sayed, My coefficient is coming positive in the level test but getting it negative in all the three equations of First differencing? Is the model still applicable for my data?
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Mr. Dr. Hossain! do we have to test all variable( dependent and independent variables) for stationerity ? if yes how (joint or seperately)? also I use panel data, can I apply this test?
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Eventually I got the logic I think. There are 2 hypothesis_ H0 Gamma 0 (rho 1) nonstationary (unit root) H1 GammaLess0 (rhoLess1) stationary (no unit root). The possibility GammaBigger0 (rhoBigger1) is ruled out in advance since it makes the underlying time series explosive (Gujarati, 2004, 4E, p. 815). Hence, we are left with either Gamma 0 or GammaLess0. i.e. There is no way to expect GammaBigger0 in ADF test for the coefficient of Yt-1 (i.e. Y(-1)).
Mr. Hossain, Congratulations about your videos with eviews tests, they helped me a lot. I have a question and i need your help: I study on eviews about 3 countries if there are optimum currency areas and in unit root test, for the first country unit root eliminated in 1st difference but for the other two, unit root eliminated in 2nd difference. What can i do? Because i think that all unit root test must end up in the same level (1st differ) and I want to continue with cointegration tests later.
Sir,a When I am applying ADF for my variable for all situations (intercept, trend and none) , the p value is > the 5% value, but the Test Statistics is positive and Critical values are negative, hence TS > CV, and the coefficient is not negative in any case. Kindly tell where is the problem, what I am doing wrong or what to do in this situation.
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Thank you. I would like to invite you to join Hossain Academy Facebook at below link and post your question there for feedback. Thank you, Sayed Hossain from Hossain Academy facebook.com/groups/hossainacademy/
Good Day Sir, Really appreciate your effort and your useful tutorials. My question is rather a simple one,how does one treat observations with negative value? I am using EViews 6,After converting those figures to log,the data doesnt appear anymore and when I run some tests e.g ADF test on trend and intercept the software tells me I have "insufficient observations". Need your help,What should I do? Thank you in anticipation.
Rodwell Tundu That part I am not sure from here....that is I guess technical matter....or you did not set data properly in eviews...Follow instruction...
Dear sir, if each variable is significance in level one. is that means they are stationary or not. Because I watched your another video said. the variable should be not significance in level's option, then they should be significance in first difference selection. After that, they can do the VECM test. Could you explain to me, do I still can use my data to test Granger causality test under VAR model if they are significance in levels
qj x You can run Johansen cointegration test when variables are non-stationary at level but when you convert them into first differenced, they will be stationary.
nice video! i have a question.. if the data is stationary at 1st difference with "none" and "intercept", but when include "trend and intercept" it becomes not stationary. so, can we call it stationary or should we continue checking it at 2nd difference? thanks before.
Adiatma Kasim Already answered. However, I would like to invite you to join Hossain Academy Facebook for greater interaction about economics, finance and econometrics. Thank you Sayed Hossain from Hossain Academyfacebook.com/groups/hossainacademy/
I am working on my thesis and ran into this video. i want to ask, is the Unit root testing only done on the Dependent variable or should it be done for both the dependent and independent variable.
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ASALAM ul KUM Sir; I had taken log of all five variables and now all five variables are stationary at second difference (NONE). Is it possible to proceed to next test with variables stationary at second difference or need to transform the variables to make them stationary at first difference then can proceed to next test? I'll be using ARDL model to test the long run relationship then to VECM followed by Granger Causality test. I am really struck jazakallah if you can help me to proceed.
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Hi Hossain, my question is not related to working with Unit root test, but it will be really helpful if you could share a tutorial video on using various types of filters on time series data ( eviews).
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Asalaamualykum sir, I have data on five economic variables and i have checked the stationary which is within acceptable limits. Sir my question is, do i now use regression on it or i should further go for cointegration test.
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I am new with ADF and i want to test unit root test for domestic interest rate and foreign interest rate through ADF.Kindly guide me how to "input" data. Thanks! PS:I have to make project replying early would be highly appreciated
what if one variable at level is less than 0.1 can i still proceed on to johansen test or does at level the p-value have to be less than 0.1 also to be stationary.
In reply to JML335, you say "Out of three options, at least two should be negative". So, Dr. Sayed, you make a statement based on the coefficients of y(-1) i.e. first lag of dependent variable in ADF regression. The coefficients of y(-1) say something about the "INCONCLUSIVITY" of the variable. That is OK. So, here, I think, you are making a statement about the STATIONARITY fron the "INCONCLUSIVITY" criteria of the test. Q1. What is your source about "at least 2 of 3 of y(-1) coefficients must be negative" to make an inference from ADF? Q2: Assume: "Test for unit root in: LEVEL". Then, assume we tried ALL 3 cases (intercept, trend and intercept, None). If we find AT LEAST 2 of 3 of these 3 cases says the analyzed variable is STATIONARY, then can we conclude the variable is I(0)? If ONLY 1 of these 3 cases says the analyzed variable is STATIONARY, then can we conclude the variable is I(0)?. Thx in advanced.
I forget what I said but what I prefer, all three should say same thing. Only then you can take decision about a variable whether stationary or not. However, please join Hossain Academy Facebook where we are discussing about various models. The link is below. facebook.com/groups/hossainacademy/
It means that variables are not integrated of same order. So you can not run Johansen Test of cointegration. So in this case, you can only run VAR model, not VECM.
I did not check yet whether Eview can operate Monte Carlo or not ...
Sometime it is suggested that if most of the variables are integrated of same order, we can go for Johansen Cointegration but ideal is all variables should be integrated of same order to run Johansen cointegration. Search literature about it.
Hi...Your variables become stationary at differeent diffenced, right? So you can not run the Johansen Cointegration test. You can run other model.
You can increase sample size or you can change the variable into natural log or you can change data
Are u referring to restricted VAR (VECM) or unrestricted VAR?
If the variable is stationary at level, then you can use the variable to run regression or VAR model directly.
Rejecting null means there is no unit root for that variable and there is P value(Prob) value to reject null. If P is less than 5 percent (0.05), you can reject null.
Suppose X, Y and Z variables have unit root at level but if after first differenced they all become stationary, then we can go for johansen cointegration. But here we shall use the X Y and Z variable (having unit root) for Johansen test.
Both tests are equality important to me. If you choose Trace Statistics, then you should choose VECM but if you choose Max-Eigen, then only VAR. Now it is up to you which test you will choose as benchmark. But try to do something so that both tests provide the same conclusion so that you can be more confident.
It's really helped me to obtain my MS thesis results👍
hello mr ,i'am greateful for you. how we check the type of unit root with the attached hypoteses??
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Thanks again. I did the Johansen test for cointegration, and Eviews gave me what Iconsider as two conflicting results: The Trace Statistics suggests 1 cointegrating equation while Max-Eigen Value suggests 0 i.e no cointegrating equations. I'm not sure what to make out of this.Should I take this result as meaning that there are no cointegrating equations, right? If that the case, then it means I can not go ahead with the VECM, right? Thanks
thank you very much Mr. Sayeed. This video like others helped me pretty much to cover t-stat and p analysis.
Normally data are non-stationary at level. So I would suggest you to either increase the sample size or convert the variables in log and then check again
dear sir, how did you choose 5 in the lag length with SIC(schwarz info criterion). please answer, big thanks.
SIr, why we take log of variables?
Another thing I need to point out Sir is that for the Johansen test for cointegration I used 5 lags based on the lowest AIC and SIC for optimal lag selection (I used the restricted VAR ). When I however selected other random number of lags both the Trace statistics and Max eigenvalue in some cases suggest that there are cointegrating equations - must I stick with the AIC and SIC lag selection?
Hi...You can see but you can not download as per copyright.
If we cant reject null hypothesis for a variable at none and intercept but we reject null hypothesis at trend and intercept then can we say that variable has a unit root? or we need to satisfiy all the three condition for ADF test to become a variable unit root.
This video really helped me to do my coursework. Thank You Sir.
Hi Sir,
On your videoyou express that if Y(-1) 's coëfficiënt is not negative the model is not viable.
Other than taking your word for it as an expert do you have some references for this ?
Thanking you in advance
You can only run Johansen test when all your variables will be integrated of same order meaning that You have five variables and all will have to become stationary after first difference. Only then you can run the Johansen test and you should use non-stationary data to run Johansen that is data at level.
does that mean under 0.1 is non stationary but greater than 0.05
if i want to use ARDL method ,than do i have to check stationarity of data/
Sir.
This is regarding threshold regression model.
Is there a requirement that the variables need to be stationery to run the TAR model.
and if X, Y and Z became stationary after second differenced then still we can go to Johansen Cointegration test. Please let me know.
Hi Sayed, thanks for the previous response. For one of my variables, with just the intercept I reject a unit root at the 5% level, but with intercept and trend I accept the unit root. How best should I interpret that outcome?
How can i write the variable which it stationary with (Philps and Burni test) in the second level?
Sir,if i am using secondary time series data than do i have to check stationarity of data? kindly guide
If a variable is found to be stationary then can we go further process with that variable for co-integration test? is that feasible...please let me know
It is automatically selecting by Eviews software, not by me.
Curiosity question.
If we do a decomposition on a data like x12 / hodrick-prescott filter in order to have only a trend-cycle data, do we need still to do a unit-root test? If we want to compare two or more trend-cycle series? Most literature just focus on raw data, seasonal adjusted or seasonal.
Thanks Marc
this has helped me for my masters thesis, thanks
What to do when coefficient of variable is not negative in the model in ADF test
You try again to get all stationary after 1st differenced, that is integrated of same order, so that you can run Johansen Test. If it is not possible, meaning that variables are integrated of different order. In that case u have to run ARDL model.
Mr. Hossain,
In my country (Mozambique) we are facing shortage of data related to high frequency observation (e.g. quarterly or monthly) can you help me on how to temporal disaggregating time series. In eviews (version 5 that I am using) there are several ways of doing that. So which one would you advise me to use to convert from annual frequency to monthly or to quarterly period?
In the literature about that are pointed many ways (models), namely: Chow and Lin (1971); Lisman/Sandee (1964); Fernandez (1981) and Litterman (1983). Is one of these models used on eviews? If you have a video about it, may upload it, please!
This question is not related to what is discussed here...so i am sorry...but i need your help!
Sorry I have not done anything with disaggregatig data
Y(-1) is one period lag of Y variable. It is not negative.
sir, how to take log if the series contain negative observations??
Thanks Sir for your prompt reply. I increased the data sample size such that the data range is from 1971 to 2009. After taking the natural logs and testing for unit root all natural log variables were found to have unit root at level, however after taking 1st difference, all variables including CPI were stationary i.e integrated of the order I(1) -i.e ADF test result. Please would you recommend caarying out any further tests before I move on to testing for cointegration? Thanks
Hi Dr. Sayed. Is it a must to do the three tests (intersect, trend and none) for any VAR model? and what should I do if one of the test shows different result. that is, two tests show unit root while the other test shows no unit root?
Dear Sir, I am investigating the relationship between Energy Consumption (E) and economic growth, where E is the dependent vairable such that E= f( GDP, P) is energy demand equation- Y is income and P is energy energy prices. GDP is my proxy for economic growth and CPI as a proxy for enegy prices another independent variable in my model. I carried out ADF unit root test and found E and GDP to be stationary after taking 1st differencee i.e I(1), but CPI is I(2). Please advice on what to do
Hi Dr, thank you for your video lecture. In running a unit root test, for five variables, two stationery at level, one in first difference and other two in second difference. what model should i run?
Yes frustration may come sometime. So you better convert all variables into log, then try.
sir i am working on 11 yr data with monthly frequency..and have 6 variables....out of it 2 are stationary at levels and other 4 are not....and also those other 4 variables become stationary at first difference...now i want to perform johansen cointegration test. how should i do it as it says all variables must be integrated of same order..and also i want to apply VAR...should i apply it on first difference of all 6 variables or first difference of 4 variables and take 2 at levels??
but sir, if one variable is I(0) and other 2 variable is I(1) then how should we go about it in unristrcited VAR model. can we use one at level and other 2 at difference. i dont think it will be a right approach...
Can you log the values when you perform the uni root? when I log the values, the null is rejected at level for logGDPpercapita, can this be possible?
sir, just want to confirm for share prices shud i use natural logarithm or just take raw data for ADF unit root testing, thanking u in advance
Hi Hossain, my question is that if the time series with intercept only is non stationary at level and needs to be differenced twice in order to achieve stationarity but with both the intercept and trend and none it needs to be differenced once to achieve stationarity. then what can be the general conclusion and can we apply the johansen cointegration test in such case.
Jan Khan You can not run Johansen as in Johansen all variables should be I(1).
iam testing unit roots using ADF. with 0 lags, I find that the series is trend stationary at level. What can i do to remove trend
i have two variable, i find one of them I(0), can i use it in the VAR model??
Hi, if we use the DF - GLS test can we also assume the model to be correct if the b1 coefficient Y(-1) is negative?
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Hi, i posted on your FB group and no one answered. It is not a complicated question so if you could you just answer here? thanks
Hi Sayed,
My coefficient is coming positive in the level test but getting it negative in all the three equations of First differencing? Is the model still applicable for my data?
What is meant by lag ..like in this vdo 5lag?
Sir, my coefficient in the unit root test is positive in the constant but become negative at first difference,is my model valid ?
whats about kpss? if LM test is greater and lower than deterministic value, how can you definite it?
+Niraj Paija I have not done KPSS yet. However, I would like to invite you to join Hossain Academy Facebook for greater interaction about economics, finance and econometrics with me. Thank you Sayed Hossain from Hossain Academy. Please join below and post your question.facebook.com/groups/hossainacademy/
Mr. Dr. Hossain! do we have to test all variable( dependent and independent variables) for stationerity ? if yes how (joint or seperately)?
also I use panel data, can I apply this test?
Yes all variables should include into testing unit root...
Sayed Hossain do we test each variable separately or jointly?
Unit root we do for each variable separately...
Yes you can convert to logarithm first then can do all tests.
You need to convert all variables into stationary. But if it is already stationary, then you can use the variable directly.
Sir I was trying to download your videos, but I cnt. Can you please help to those video?
Dear sir, great video. What happens if say 5 out of 6 variables are I(1) but one is I(2). Can we still carry out cointegration?
what if you want to test the significance of the constant?
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Eventually I got the logic I think. There are 2 hypothesis_ H0 Gamma 0 (rho 1) nonstationary (unit root) H1 GammaLess0 (rhoLess1) stationary (no unit root). The possibility GammaBigger0 (rhoBigger1) is ruled out in advance since it makes the underlying time series explosive (Gujarati, 2004, 4E, p. 815). Hence, we are left with either Gamma 0 or GammaLess0. i.e. There is no way to expect GammaBigger0 in ADF test for the coefficient of Yt-1 (i.e. Y(-1)).
yes sometime it happens. But you go for trial and error so that all three equation suggest that there is no unit root.
Mr. Hossain,
Congratulations about your videos with eviews tests, they helped me a lot. I have a question and i need your help: I study on eviews about 3 countries if there are optimum currency areas and in unit root test, for the first country unit root eliminated in 1st difference but for the other two, unit root eliminated in 2nd difference. What can i do? Because i think that all unit root test must end up in the same level (1st differ) and I want to continue with cointegration tests later.
Hi Mr thanks for your beautiful and clear teaching i use it for my research.
Milad Roohi Dear Milad, Thanks. Please join Hossain Academy facebook group for discussion. thanks Sayed.facebook.com/groups/hossainacademy/
I have failed to understand your question. Please ask me again
Sir,a
When I am applying ADF for my variable for all situations (intercept, trend and none) , the p value is > the 5% value, but the Test Statistics is positive and Critical values are negative, hence TS > CV, and the coefficient is not negative in any case.
Kindly tell where is the problem, what I am doing wrong or what to do in this situation.
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so there is no need to remove trend
thank mr sayed for your lectures
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Thank you so much indeed for your explanations. very useful and effective way to understand clearly.
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Good Day Sir,
Really appreciate your effort and your useful tutorials. My question is rather a simple one,how does one treat observations with negative value? I am using EViews 6,After converting those figures to log,the data doesnt appear anymore and when I run some tests e.g ADF test on trend and intercept the software tells me I have "insufficient observations". Need your help,What should I do?
Thank you in anticipation.
Rodwell Tundu That part I am not sure from here....that is I guess technical matter....or you did not set data properly in eviews...Follow instruction...
Sayed Hossain Thank you for the prompt response. But how does one treat negative original data values when converting them to log?
Rodwell Tundu Negative data can not convert to log. So take positive data if you want to convert to log.
Dear sir, if each variable is significance in level one. is that means they are stationary or not. Because I watched your another video said. the variable should be not significance in level's option, then they should be significance in first difference selection. After that, they can do the VECM test. Could you explain to me, do I still can use my data to test Granger causality test under VAR model if they are significance in levels
qj x You can run Johansen cointegration test when variables are non-stationary at level but when you convert them into first differenced, they will be stationary.
nice video! i have a question.. if the data is stationary at 1st difference with "none" and "intercept", but when include "trend and intercept" it becomes not stationary. so, can we call it stationary or should we continue checking it at 2nd difference?
thanks before.
Adiatma Kasim Already answered. However, I would like to invite you to join Hossain Academy Facebook for greater interaction about economics, finance and econometrics. Thank you Sayed Hossain from Hossain Academyfacebook.com/groups/hossainacademy/
prof. Hossain, did you made KPSS tutorial? if yes plz link
+Niraj Paija Not yet done
I am working on my thesis and ran into this video. i want to ask, is the Unit root testing only done on the Dependent variable or should it be done for both the dependent and independent variable.
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ASALAM ul KUM Sir; I had taken log of all five variables and now all five variables are stationary at second difference (NONE). Is it possible to proceed to next test with variables stationary at second difference or need to transform the variables to make them stationary at first difference then can proceed to next test? I'll be using ARDL model to test the long run relationship then to VECM followed by Granger Causality test. I am really struck jazakallah if you can help me to proceed.
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Hi Hossain, my question is not related to working with Unit root test, but it will be really helpful if you could share a tutorial video on using various types of filters on time series data ( eviews).
All data are uploaded already. You visit in my personal website Hossain Channel. Search in google and find it there
It is always better to satisfy all three conditions or equations to be in safe side
Yes you can log
How to solve problem of near singular matrix error
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Asalaamualykum sir,
I have data on five economic variables and i have checked the stationary which is within acceptable limits. Sir my question is, do i now use regression on it or i should further go for cointegration test.
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Need to try again and again to make it negative....
Hi Professor! Thank you again for your video! Can you explain what's meaning of B1 and ai at equations? Thank you.
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I am new with ADF and i want to test unit root test for domestic interest rate and foreign interest rate through ADF.Kindly guide me how to "input" data.
Thanks!
PS:I have to make project replying early would be highly appreciated
If the data becomes stationary, there should be ok so far. but you can see some other literature also about it.
Yes coefficient should be negative here..
Your question is not clear
Unit Root testing is already there i my videos
I didn't get you Sir. Can you explain me more.
The best would be to understand unit root testing is the Basic Econometrics by Gujarati.
Suppose you want to convert Y variables into log then you use the following variables:
log(Y)
No you just proceed to Johansen Test as all variables are integrated of same order.
what if one variable at level is less than 0.1 can i still proceed on to johansen test or does at level the p-value have to be less than 0.1 also to be stationary.
You are welcome
very helpful thanks a lot
Yes we can
Thank you so much :)
Thanks!
Already done :)
Out of three cases, at least 2 should be negative
In reply to JML335, you say "Out of three options, at least two should be negative". So, Dr. Sayed, you make a statement based on the coefficients of y(-1) i.e. first lag of dependent variable in ADF regression. The coefficients of y(-1) say something about the "INCONCLUSIVITY" of the variable. That is OK. So, here, I think, you are making a statement about the STATIONARITY fron the "INCONCLUSIVITY" criteria of the test. Q1. What is your source about "at least 2 of 3 of y(-1) coefficients must be negative" to make an inference from ADF? Q2: Assume: "Test for unit root in: LEVEL". Then, assume we tried ALL 3 cases (intercept, trend and intercept, None). If we find AT LEAST 2 of 3 of these 3 cases says the analyzed variable is STATIONARY, then can we conclude the variable is I(0)? If ONLY 1 of these 3 cases says the analyzed variable is STATIONARY, then can we conclude the variable is I(0)?. Thx in advanced.
I forget what I said but what I prefer, all three should say same thing. Only then you can take decision about a variable whether stationary or not. However, please join Hossain Academy Facebook where we are discussing about various models. The link is below. facebook.com/groups/hossainacademy/