Method for non-stationay time series data

[cuongnh]

It is so kind of you!
1. "the level VAR suggested that 3 lags is the best, then you should use lags 2 for your Johansen's cointegration test."
Just in one case is that the best lag lag suggested by VAR is lag "0" (top of the criterion table), then I should use (0, 0) in the Johansen Cointegration test. Am I right?
2. "(2) Computed the ADF test for the saved residuals, the compare the ADF statistics with the critical values tabulated in Engle and Granger (1987) or MacKinnon (1993)"
Do you mean the critical values are available somewhere (in tables) or in the ADF test?
3. Regarding the result in my Johansen Cointegration test, I have some questions in understanding the results:
- In case of i.e there is one cointegration equation, i have to look for the coefficients in the "1 Cointegrating Equation(s)", and so on. Is that right? And in case there are more than one cointegrating equations, how should I interpret the coeeficients, relationships? I am confusing.
- The coefficients of explanatory variables become opposite in SIGN, means that coeffients expected to be positive, becomes negative. The book you suggested mentions the cointegrating vector (1, -betahat), is that the reason? Could you please briefly explain me that? And can I interpret the as "increase" even it takes minus sign?
Unfortunately, the Professors in my Uni. are new to this method and only used to OLS regression with Eviews. I have to dig knowledge for myself.
Once again, I do appreciate your strong supports to me recently!
Cuong

[tcfoon]

Dear Coungnh,

1. Yes, you are right.

2. Do you mean the critical values are available somewhere (in tables) or in the ADF test?
You should refer to Engle and Granger (1987) article for the cointegration test critical values. This is because the critical values reported by Eviews is not for the error term in particular cointegration test. Therefore, you only use Eviews to compute the stationary test statistics - ADF.

3. Your can normalised "unrestricted cointegration coefficients" section to get the long run relationship. You can use the CE proposed by Eviews or normalised by yourself in accordance to the theory.

4. It is hard for me to describe through this, please read the following book:
Asterious, D. and Hall, S. (2006) Applied Econometrics: A Modern Aproach Using Eviews and Microfit. New York: Palgrave Macmillan

Thank you,

Regards,
CF Tang

[cuongnh]

Thank you for your answers. I found out the solution for the question regarding Engle-Granger test with critical values.
Unfortunately, I cannot find the book your recommended for reading.

[tcfoon]

Dear Coungnh,

Check with your library whether there is inter-library loan or not. If yes, then you may borrow the book from others university within your country. Alternatively, you may purchase a copy for yourself. For me I do suggest you to buy a copy rather than borrow from the library as this is one of the basic econometrics book for Eviews and Microfit users.

Good luck.

Thank you,

Regards,
CF Tang

[cuongnh]

Dear CF Tang, I did order a book from the internet already. That book must be very useful for me. Thank you very much for everything you did for me recently.

[cuongnh]

Dear CF Tang, could you please do me a favor?
As you mentioned before that "Strictly speaking, the existing critical values for Johansen's cointegration test are not suitable when dummy variable(s) is included.", I did include the dummies both as endogenous and exogenous variables in the tests in order to see differences, the resulting coefficients of the explanatory variable (endogenous) from the two tests were not much different. However, if I include dummies as exogenous variables in the Johansen test, their coefficients are not reported. I guess I can get them from the VEC test later on. In the VEC test, those dummy coefficients are quiet different with ones I got from johansen test where I include them as endogenous variables also. This makes me confusable. Could you please advise me what should I do in this case, and where can i get the coefficients for dummies?
And, regarding VAR, you said "Of course, sometime there are many lags then cause some problem on interpretation, but usually we will look at the contemporaneous effect (t or t-1) only, alternatively we may also use the summation of the coefficients of the first different variables". Contemporanous effect (t or t-1), do you mean the coefficients in for example, d(variable(-1)) and d(variable(-2), what do you mean by summation of coefficients? Please help me. Thank you very much!

[tcfoon]

Dear Coungnh,

1. I did include the dummies both as endogenous and exogenous variables in the tests in order to see differences, the resulting coefficients of the explanatory variable (endogenous) from the two tests were not much different.

To the best of my knowledge, dummy variables either seasonal dummy or intervention dummy both are stationary and exogenous variables, thus I don't see any rationality to treat it as endogenous variables as you did. Of course, Eviews will run when you specified your intervention dummy as Endogenous variables but this doesn't comply to econometric theory and also doesn't make sense to specified dummy variables as endogenous.

2. If I include dummies as exogenous variables in the Johansen test, their coefficients are not reported.

Yes, I do try it. For your information, if our objective is to determine the presence of long run relationship, we only look at the two likelihood ratio (trace and maximum eigenvalue statistics) to examine whether the variables under investigate are cointegrated or not. However, the estimated coefficients for dummy variables will appear only in the VECM. For my point of view, this is rational as the intervention / shock effect usually for short run only.

3. Contemporary effect mean the initial effect.

4. What do you mean by summation of coefficients?

If your specified lags length is 2, then just sum up the coefficients D(rice(-1))+D(rice(-2)) as the short run effect for rice to your dependent variable.

Thank you,

Regards,
CF Tang

[cuongnh]

Dear CF Tang,
Could you please have a look at the result table of VEC below:
Vector Error Correction Estimates
Cointegrating Eq: CointEq1
PRICE(-1) 1.000000
POIL(-1) -0.084138
(0.00912)
[-9.22957]
C -8.038052
Error Correction: D(PRICE) D(POIL)
CointEq1 -0.052225 0.152461
(0.01264) (0.09620)
[-4.13277] [ 1.58488]
C -0.011190 -0.407770
(0.02591) (0.19727)
[-0.43181] [-2.06710]
DRICQ -0.133341 1.027798
(0.06303) (0.47979)
[-2.11562] [ 2.14218]
SDMEP 0.002652 -0.003364
(0.00072) (0.00547)
[ 3.69278] [-0.61536]
SDVXB 0.005206 -0.006814
(0.00100) (0.00763)
[ 5.19643] [-0.89344]
DTHS 0.180595 -0.492143
(0.06851) (0.52149)
[ 2.63623] [-0.94372]
Since the suggested lag length by VAR model is (0 0), so I use this lag length in the VEC model too. It gave the same coefficients in the cointegrating equation part with that in Johansen test (before, whenever I ran VEC, I always used the default lag length generated by Eviews, that is (1 2), then it gave a little bit different results with Jonhansen test). I dont know what is the correct way. According to the above result table, i think the equation for PRICE is "PRICE = 8.038052 + 0.084138POIL - 0.133341DRICQ + 0.002652SDMEP + 0.005206SDVXB + 0.180595DTHS". This is the long-run relationship, isnt it? And -0.052225; 0.152461 are coefficients for speed of adjustment of PRICE and POIL, respectively. I dont really understand how to interpret the coefficients in cointegrating equation part and in the error correction part, could you please help me, too?
And regarding coefficients in VAR as you explained in the previous post, could you please help me to define in the table below. I think I couldnt understand fully your suggestion "If your specified lags length is 2, then just sum up the coefficients D(rice(-1))+D(rice(-2)) as the short run effect for rice to your dependent variable", since there are two columns in the table d(PRICE) and d(POIL):
Vector Autoregression Estimates
D(PRICE) D(POIL)
D(PRICE(-1)) 0.097777 0.265666
(0.05179) (0.38684)
[ 1.88791] [ 0.68676]
D(PRICE(-2)) 0.048024 0.682192
(0.05165) (0.38576)
[ 0.92987] [ 1.76842]
D(POIL(-1)) -0.003271 -0.089851
(0.00693) (0.05173)
[-0.47221] [-1.73685]
D(POIL(-2)) -0.006567 -0.098396
(0.00693) (0.05178)
[-0.94716] [-1.90011]
C -0.054370 -0.253650
(0.02375) (0.17737)
[-2.28956] [-1.43003]
DRICQ 0.069790 0.405260
(0.03832) (0.28625)
[ 1.82108] [ 1.41575]
SDMEP 0.000762 0.001450
(0.00059) (0.00439)
[ 1.29717] [ 0.33017]
SDVXB 0.001821 0.001477
(0.00066) (0.00494)
[ 2.75312] [ 0.29909]
DTHS 0.062659 -0.300075
(0.06509) (0.48614)
[ 0.96271] [-0.61726]
I am terribly sorry for disturbing you too much. But your explanations are really invaluable to me. I highly appreciate your kindness!

[tcfoon]

Dear Coungnh,

1. Since the suggested lag length by VAR model is (0 0), so I use this lag length in the VEC model too.

Theoretically yes, but in practice when the suggested lag length for the first differenced VAR is zero (0), then the practitioner may not use the Johansen cointegration test as there may have some problems in their interpretation for the coefficient in the vector error-correction model (VECM) as there is no endogenous will show. Nevertheless, as I said in the beginning of my post, there are two parts in the Johansen cointegration test. (1) testing the presence of cointegration with the likelihood ratio tests statistics – trace and maximum eigenvalues; (2) if the variables are cointegrated then the VECM can be form, otherwise the first differenced VAR should be used. Therefore, even though the suggested lag length is zero, you still can determine the presence of cointegrating relations via the trace and maximum eigenvalue statistics developed by Johansen (1988) and Johansen and Juselius (1990). In view of error-correction model (ECM), there are two approaches that we may used to obtain the ECM to measure short run relationship that is either ECM results from Eviews (uniform lag structure) as you did or non-uniform lag structure ECM. The non-uniform lag structure ECM means that the lag order for each variable within the ECM can be differ. In other word, we follow the Autoregressive Distributed Lag (ARDL) framework to perform the ECM. In this case, you need to determine the optimal lag length for each variable in the ECM. What you can do is that, you estimate the long run relationship by OLS, then save the residuals for your ECM. In term of determining the optimal lag length for each variable under ECM, you could either write a programme or used the procedure suggested by Hsiao (1981) – Journal of Monetary Economics or any other recognised procedure that you know. You may also see the following link http://forums.eviews.com/viewtopic.php?f=5&t=875

2. It gave the same coefficients in the cointegrating equation part with that in Johansen test (before, whenever I ran VEC, I always used the default lag length generated by Eviews, that is (1 2), then it gave a little bit different results with Johansen test). I don’t know what is the correct way?

You have to re-specify the lag length according to the lag order used to perform the Johansen cointegration test. Therefore, as your selected lag length is zero, the lagged endogenous variables should not appear. In your case, you may only see the constant term, one period lagged error-correction term and exogenous variables (your dummy variables)

3. According to the above result table, I think the equation for PRICE is "PRICE = 8.038052 + 0.084138POIL - 0.133341DRICQ + 0.002652SDMEP + 0.005206SDVXB + 0.180595DTHS". This is the long-run relationship, isn’t it? And -0.052225; 0.152461 are coefficients for speed of adjustment of PRICE and POIL, respectively. I dont really understand how to interpret the coefficients in cointegrating equation part and in the error correction part, could you please help me, too?

NO, the VECM in Eviews were separated into two part (1) cointegrating equation (long run relationship); (2) the VECM. Based on your estimation result, the cointegrating equation for rice price should be: PRICE = 8.038 + 0.084138POIL only. Yes, –0.052225 and 0.152461 are coefficients for speed of adjustment of PRICE and POIL, respectively.

4. Regarding coefficients in VAR as you explained in the previous post, could you please help me to define in the table below. I think I couldn’t understand fully your suggestion "If your specified lags length is 2, then just sum up the coefficients D(rice(-1))+D(rice(-2)) as the short run effect for rice to your dependent variable", since there are two columns in the table D(PRICE) and D(POIL).

Caution: If the variables are cointegrated, you can’t estimate the first differenced VAR as you did because this will cause the loss of long run information (i.e. one period lagged error-correction term has been omitted) (see Granger, 1988, Journal of Econometrics, 39, pp. 199-211). Thus, you can’t use this output to measure your short run effect if the variables are cointegrated. Anyway, for your understanding now, I assumed that your variables are not cointegrated, then you are allowed to estimate the first differenced VAR to measure the short run relationship, and the short run effect of oil price (POIL) on rice price (PRICE) should be either –0.003271 or –0.00984 that is [–0.003271 + (–0.006567)]. This can also applied to the ECM.

I hope the explanation helped you.

Thank you,

Regards,
CF Tang

[cuongnh]

Dear CF. Tang, I do appreciate your help.
As you suggested to use ARDL, I just read a little about it before, however, I should complete my research soon, thus i think currently I should follow the Johansen and VECM as I used before.
1. "According to the above result table, I think the equation for PRICE is "PRICE = 8.038052 + 0.084138POIL - 0.133341DRICQ + 0.002652SDMEP + 0.005206SDVXB + 0.180595DTHS". This is the long-run relationship, isn’t it? And -0.052225; 0.152461 are coefficients for speed of adjustment of PRICE and POIL, respectively. I dont really understand how to interpret the coefficients in cointegrating equation part and in the error correction part, could you please help me, too?

NO, the VECM in Eviews were separated into two part (1) cointegrating equation (long run relationship); (2) the VECM. Based on your estimation result, the cointegrating equation for rice price should be: PRICE = 8.038 + 0.084138POIL only. Yes, –0.052225 and 0.152461 are coefficients for speed of adjustment of PRICE and POIL, respectively."
How and from where can i get the coefficients for dummy variables?. And could you please explain me how should I interpret the meaning of speed of adjustment? What do you think if I interpret like this: The prices of rice and oil have to adjust themselves at the rate of –0.052225 and 0.152461, respectively in order to restore to the long-run equilibrium. for example of rice, the coefficient is -0.0522, it means price of rice has to reduce at that amount to restore to the long-run equilibrium. Is that fine?

2. "Regarding coefficients in VAR as you explained in the previous post, could you please help me to define in the table below. I think I couldn’t understand fully your suggestion "If your specified lags length is 2, then just sum up the coefficients D(rice(-1))+D(rice(-2)) as the short run effect for rice to your dependent variable", since there are two columns in the table D(PRICE) and D(POIL).

Caution: If the variables are cointegrated, you can’t estimate the first differenced VAR as you did because this will cause the loss of long run information (i.e. one period lagged error-correction term has been omitted) (see Granger, 1988, Journal of Econometrics, 39, pp. 199-211). Thus, you can’t use this output to measure your short run effect if the variables are cointegrated. Anyway, for your understanding now, I assumed that your variables are not cointegrated, then you are allowed to estimate the first differenced VAR to measure the short run relationship, and the short run effect of oil price (POIL) on rice price (PRICE) should be either –0.003271 or –0.00984 that is [–0.003271 + (–0.006567)]. This can also applied to the ECM."
The example of VAR i sent you is for rice (in fact, if I dont include dummy variables, the price data series of rice and oil are not cointegrated). But in my case, I did use dummies. However, in the case of other commodity, such as wheat, including dummies does not make the price of wheat and oil be cointegrated, it means i need to understand how to get coefficients in VAR results table. However, in your explanation, "and the short run effect of oil price (POIL) on rice price (PRICE) should be either –0.003271 or –0.00984 that is [–0.003271 + (–0.006567)]. This can also applied to the ECM.", the sign of the coefficient is minus (what I expect is positive), why is it like that?
Thankful to your answer again!

[cuongnh]

Dear CF Tang, I have other questions relating to short-run dynamics that when I summed up the coefficients as you recommended, the t-value was too low (not significant), however, if I increase lag interval (e.g. to (1 5)), there is coefficient of diferrent lag length which are significant. Could I take this coefficient instead of summing up the first and second as before?
And, could you please tell me how to interpret the short-run coefficients? Do they mean the relationships in the duration of my sample only?

[cuongnh]

Dear CF Tang,
I attach herewith the result tables of my research. I can interpret the long-run relationships, however the different significance levels of the coefficients in the short-run relationships and error corrections are challenging me. Could you give me a hand? I expect to have your answer latest tomorrow morning (Japan time, now is 18:15 in Japan). I am sorry for this request!

[tcfoon]

Dear Cuongnh,

Regret to inform that, I can't open your xls file, may be owing to the version I am using only 2003. Is it plausible for you to email your data in Eviews workfile to me? I would like to have a look and email together with your concern relationship.

Thank you,

Regards,
CF Tang

[Kinga]

Dear CF Tang

I am using EViews6 and I am testing for cointegration between two variables using Engle-Granger two step procedure. I concluded that my variables are integrated of order one I(1) but they are not cointegrated. This means I should test for short run relationship using standard Granger causality test. Do I need to use first differenced data for standard Granger causality test in Eviews? How many lags should I include?


Kinga

[sly86]

Hi, my problem ist i have 4 stationary variables (I(0)) and 5 integrated of order 1. While doing the estimation on Eviews, here is how i proceed (and i want to know if its correct): In the endogenous box i inserted all the variables that are integrated of order 1 and in the exogenous box i inserted all the stationary variables.
I want to know if this procedure is alright. Thank you