Method for non-stationay time series data

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cuongnh
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Method for non-stationay time series data

Postby cuongnh » Mon May 18, 2009 8:33 pm

Dear,
I am trying to estimate using non-stationary time series data, which by using OLS gave a bad stats of presence of positive serial correlation. I studied the method of Cochrane-Orcutt (CO), but someone said that CO is not applicable with non-stationary time series data. Could anyone advise me which method is appropriate to estimate these data? Many thanks!

trubador
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Re: Method for non-stationay time series data

Postby trubador » Tue May 19, 2009 12:47 am

It depends on the nature of the nonstationarity and where you observe it (i.e. in mean and/or variance). If your time series is not stationary in the mean, then you can make it stationary via differencing or detrending. Time series decomposition models can also be helpful in this respect. Another option may be to find cointegrating relationships among your varibles and build a Vector Error Correction (VEC) model. If you observe the nonstationarity in variances, then you can set up GARCH-type models. As you see, there is more than one way to handle this issue and I strongly advise you to refer to a time series econometrics textbook.

cuongnh
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Re: Method for non-stationay time series data

Postby cuongnh » Tue May 19, 2009 12:55 am

Thanks, Trubador. I have been studying about the cointegration and VEC. As I tried the cointegration test, it indicated no cointegrating relation. How can I conclude this? And could you please explain me in a bit detail what the VEC is for? It is hard to understand in some text books.

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Re: Method for non-stationay time series data

Postby trubador » Tue May 19, 2009 2:32 am


tcfoon
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Re: Method for non-stationay time series data

Postby tcfoon » Tue May 19, 2009 6:00 am

Dear Coungnh,

First, it is well known that the cointegration tests (for example, Engle and Granger, 1987; Johansen, 1988; Johansen and Juselius, 1990; Pesaran et al., 2001) are used to ascertain the presence of potential long run equilibrium relationship. Why cointegration matter? This is because Granger and Newbold (1974) noted that the regression results with non-stationary variables will be spurious (nonsense). To avoid this, we may run the regression with the stationary variables (e.g. first differenced variables). Nevertheless, if the variables are non-stationary but is cointegrated, running a regression with first differenced variables may loss the long run information as the first differenced regression results is for short run relationship. Therefore, someone is advice to check the presence of cointegration.

Second, if the variables are found to be cointegrated, the regression result with variables at level are non-spurious and it also measure the long run relationship between the variables. Moreover, the vector error-correction model (VECM) will be performed to investigate the short run relationship including the Granger causal relationship (see Granger, 1986).

Third, if the variables are not cointegrated, we can only run the regression with the stationary variables (e.g. first differenced variables), and there is nothing deal with VECM.

For your cases, your cointegration test results showed that the variables are not cointegrated, meaning that the variables are not moving together in the long run although they may have some significant relationship in the short run. As your variables are not cointegrated, thus VECM is not required in this case.

I hope the above explanation help your understanding.

Thank you,

Regards,
tcfoon
Last edited by tcfoon on Mon Sep 27, 2010 4:46 pm, edited 1 time in total.

cuongnh
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Re: Method for non-stationay time series data

Postby cuongnh » Tue May 19, 2009 8:08 am

Dear CF Tang, thanks for your very clear explanation of cointegration and VECM. In fact, my study is trying to indicate the response of commodity prices (including rice, corn, wheat, and soybeans) to changes in crude oil prices. It means that I have to estimate equations for commodities individually with oil. My first try for rice/oil indicated no cointegration between them. However, second try for corn/oil indicates presence of cointegration. The problem is that I cannot define myself clearly the options in "deterministic trend assumption of test". And further more, the trace test indicates no cointegration, but maximum eigenvalue test denotes 1 cointegration. What should I do in this case? And could you please tell me that how to define the lag length for cointegration test by VAR?
And in all the equations, i have some dummy variables on the right hand side, how should I deal with them in the cointegration test, VAR?
Thank you in advance!

tcfoon
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Re: Method for non-stationay time series data

Postby tcfoon » Tue May 19, 2009 6:37 pm

Dear Coungnh,

First: rice vs oil are not cointegrated while corn vs oil are cointegrated
Just surmise that rice and oil are not cointegrated, while corn and oil are cointegrated over the analysis period. Then, first difference VAR will be used to measure the short run relation between rice and oil, while VECM will be used to measure the short run relationship between corn and oil.

Second: "Deterministic Trend Assumption of Trend"
There are 5 options for you to choose in Eviews and the default will be option 3 that is "intercept in CE". Basically, there are two approaches to ascertain the deterministic trend for Johansen cointegration test. (1) Based on the theory; (2) Based on Pantula's (1989) principle suggested in Johansen (1992) - Oxford Bulletin of Economics and Statistics, 52(2), pp. 169-210. Nevertheless, of course based on the theory will be the best option.

Third: Trace and Eigenvalue tests statistics are contrary
Cheung and Lai (1993) - Oxford Bulletin of Economics and Statistics, 55(3), pp. 313-328 stated that the trace test result should be better, while some research papers noted that Eigenvalue tests statistics is superior to Trace test. Therefore, it is difficult to justify which is the best option if contrary result appeared. Sometime the contrary results may owing to the small sample and also deterministic trend chose problems. Apart from that, you may also try other cointegration approach such as Engle and Granger (1987) and Bounds test developed by Pesaran et al. (2001), then you can compare the results and to the literature. In addition to that, you should read more journal and books in order to solve your problems as also suggested by "trobador".

Fourth: Determine the lag length in the VAR for Johansen's cointegration
First you have to estimate the VAR system including your dummies variables. For your information, dummy variable is an exogenous variable thus you have to locate your dummy variable into the exogenous variables box. Then, all of your estimated endogenous variables (i.e. rice and oil) should be in first differenced form as you would like to determine the lag length of the first differenced endogenous variables [ i.e. D(rice) D(oil) ] in the Johansen's cointegration test equation - VECM. Then in your VAR output, click View/Lag structure/Lag Length Criteria... After you determine the lag structure for your VAR, you have to test the cointegration with variables at level NOT THE 1ST DIFFERENCES. Strictly speaking, the existing critical values for Johansen's cointegration test are not suitable when dummy variable(s) is included. If the dummy variable is not to capture the seasonal effect (seasonal dummy- only exist in the high frequency data, e.g. quarterly, monthly, etc), but is to capture the structural break, then I would suggest you to use Gregory and Hansen (1996) - Journal of Econometrics structural break cointegration test. Unfortunately, you have to write a programme your own or using GAUSS or RATS as this feature is not available in Eviews for this moment.

Finally, I would like to advice you to read more econometrics books. In fact, there are many econometrics books with Eviews applications.

Good luck and hope the above explanation clear your doubt..

Thank you,

Regards,
tcfoon
Last edited by tcfoon on Mon Sep 27, 2010 4:47 pm, edited 1 time in total.

cuongnh
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Re: Method for non-stationay time series data

Postby cuongnh » Tue May 19, 2009 7:24 pm

Dear CF Tang, I do appreciate your kindness and long and clear explanation!

cuongnh
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Re: Method for non-stationay time series data

Postby cuongnh » Wed May 20, 2009 3:44 am

I just did a test on the stationary condition of the residuals (generated from OLS of two variables, I(1)), the result indicated that residual is only stationary at 10% significance level. Anyone helps me to explain what it means?

cuongnh
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Re: Method for non-stationay time series data

Postby cuongnh » Wed May 20, 2009 3:57 pm

Dear Friends, in the book: New Direction in Econometric Practice" by Charemza and Deadman, there is one part says about the two-step procedure (by Engle-Granger) page 132-133:
There are two equation 1 (1) and 2 (2) (It is difficult to type the equation form in this web, so I uploaded as attachments).
First estimate (1) by OLS and test for stationarity of the residuals. Second, if this is not rejected, estimate (2) replacing beta by its previously computed OLS betahat. Now the condition of the identical order of cointegration for the varibales in (2) is met. deltay_t, deltax_t and (y_t-1 - betahatx_t-1) are all I(0), and consequently, provided the model is properly specied, epsalon_t-1 is also I(0).
As I understand is replacing betahat obtained from (1) with beta in (2) before estimate (2) using OLS. Is that right? I dont understand quiet well that expression.
Attachments
equation 2.JPG
equation 2.JPG (15.53 KiB) Viewed 36219 times
equation 1.JPG
equation 1.JPG (18.33 KiB) Viewed 36222 times

cuongnh
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Re: Method for non-stationay time series data

Postby cuongnh » Wed May 20, 2009 5:55 pm

I come up with this VAR test results:
Vector Autoregression Estimates
Date: 05/21/09 Time: 09:51
Sample (adjusted): 3 441
Included observations: 439 after adjustments
Standard errors in ( ) & t-statistics in [ ]

PRICE POIL

PRICE(-1) 1.057410 0.423231
(0.05141) (0.39235)
[ 20.5663] [ 1.07871]

PRICE(-2) -0.111388 -0.272600
(0.05049) (0.38529)
[-2.20616] [-0.70753]

POIL(-1) 0.001533 0.900535
(0.00685) (0.05231)
[ 0.22361] [ 17.2167]

POIL(-2) 0.002547 0.082144
(0.00677) (0.05164)
[ 0.37642] [ 1.59075]

C 0.472657 -1.194631
(0.13036) (0.99482)
[ 3.62565] [-1.20085]

DRICQ -0.151957 0.984769
(0.06375) (0.48647)
[-2.38370] [ 2.02433]

DTHS 0.153278 -0.759206
(0.07473) (0.57030)
[ 2.05097] [-1.33123]

SDMEP 0.002680 -0.002714
(0.00072) (0.00553)
[ 3.70094] [-0.49115]

SDVXB 0.005242 -0.005884
(0.00101) (0.00774)
[ 5.17000] [-0.76051]

R-squared 0.991419 0.992563
Adj. R-squared 0.991260 0.992424
Sum sq. resids 46.63310 2715.568
S.E. equation 0.329316 2.513021
F-statistic 6210.422 7173.493
Log likelihood -130.7536 -1022.899
Akaike AIC 0.636691 4.701136
Schwarz SC 0.720427 4.784873
Mean dependent 15.35982 86.84279
S.D. dependent 3.522514 28.87290

Determinant resid covariance (dof adj.) 0.577947
Determinant resid covariance 0.554493
Log likelihood -1116.389
Akaike information criterion 5.168058
Schwarz criterion 5.335531

I dont know how to interprete well this result. But I think the "poil" does not explain changes in "price" since the t-stat is too low (poil = price of oil; price = price of rice). Could someone help me to confirm this?

cuongnh
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Re: Confirmation of cointegration results

Postby cuongnh » Thu May 21, 2009 1:51 am

Dear, could someone help me to confirm this? In the cointegration result (attached file), which coefficients, Normalized cointegrating coefficients or Adjusted coefficients, should I use for my conclusion? And also, please help to explain me how to understand the values of: Price, 1.000000 (in Normalized cointegrating coefficients) and DPrice, -0.057076 (in Adjusted coefficients).
Result of cointegration indicates that there is one cointegration relation. Thank you very much!
Attachments
newpicture6.jpg
newpicture6.jpg (44.44 KiB) Viewed 36175 times

tcfoon
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Re: Method for non-stationay time series data

Postby tcfoon » Thu May 21, 2009 2:49 am

Dear Coungnh,

From your questions I suspect that you are loss. In fact, I am also confuse of what you are trying to do? Initially, your posting is for Engle and Granger (1987) cointegration test, follow by error-correction modelling, then VAR estimation output, after that the normalised cointegrating vector from Johansen's cointegration test. Please write down your questions properly in order for me to understand your problems. Before that, please organised your questions and write down what is your research objective and what methodologies your are going to employ? I will lend my hand if plausible.

For your information,[ Enders, W. (2004) Applied Econometric Time Series. 2nd Edition, John Wiley & Sons: USA ] is one of a potential book that you could refer to.

Thank you,

Regards,
tcfoon
Last edited by tcfoon on Mon Sep 27, 2010 4:48 pm, edited 1 time in total.

cuongnh
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Re: Method for non-stationay time series data

Postby cuongnh » Thu May 21, 2009 3:14 am

Thank you for your suggestions. In fact, I am trying to reach the results of the research, I have to present in early Jun. I was really confusable myself of what I am doing. However, my questions were not in right order, I have reason for that. Let me clear all of your questions:
Objective of my research is to see the relationship between price of rice and price of oil (explanatory variable).
I put questions relating to VAR, since at that time there is no cointegration equation in my Johansen cointegration test (it is said that, if two variables I(1) are not cointegrated, VAR is used); furthermore, my another question on VAR is to know how to define lag length by using VAR for the Johansen cointegration test. Today, I tested the Johansen cointegration again (with the suggested lag length by using Lag lenght Criteria in VAR window), and supprisingly test denotes one cointegration equation. That is why I try with VECM (it is said that, if two variables I(1) are not cointegrated, VECM is preferred).
I do things as I learnt from textbooks and other sources. Since I have 4 commodities (including rice) to test with oil prices for relationships, thus I have to do it separately 4 times. If, in any case, there is not any cointegaration equation (by Johansen cointegration test), I am going to use VAR; and if yes, I will use VECM to check also the adjustment of speed of deviation from the long run. However, I cannot interpret by myself the results of VAR and VECM.
I hope that make sense to you. I really need your helps since I have to complete it as soon as possible. It is bad that I am sometimes very confusable. Thank you for your willingness.

tcfoon
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Re: Method for non-stationay time series data

Postby tcfoon » Thu May 21, 2009 4:43 am

Dear Coungnh,

1. "If the variables are not cointegrated, then VAR is used"
The answer is NO. This is because the used of VAR will produce bias result if the estimated variables are not cointegrated. Therefore, if the estimated variables are not cointegrated, the first differenced VAR should be estimated if the variables are integrated of order one, I(1).

2. Lag length determination for Johansen's cointegration test with Eviews.
As noted in the Eviews6 User Guide II page 368, "the lags are specified as lags of the first differenced terms used in the auxiliary regression, not in terms of the levels." Therefore, when you determine the lag length for Johansen cointegration test, you should run the VAR with first differenced variables. Alternatively, you may run the VAR with the variables at levels, then subtract the suggested lag length by one (1), for example, if the level VAR suggested that 3 lags is the best, then you should use lags 2 for your Johansen's cointegration test. Caution: You must use the variables at levels when running the Johansen cointegration test.

3. The interpretation for the first differenced VAR and VECM if the variables are cointegrated
In fact, VAR just like the standard regression model, so you just interpret the results as usual. The estimated coefficients refer to the short run relationship between dependent variable and the independent variables. 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.
The different between first differenced VAR and VECM is merely the one period lagged error-correction term (ECT) derived from the cointegrating vectors. As you known that the coefficient of the ECT refer to the speed of adjustment to the equilibrium if the system expose to shock and the significant of the ECT coefficient represent the long run causality. In fact, you can run the error-correction model (ECM) and also the first differenced VAR manually with Eviews the "make equation" feature

From my point of view, you should read some basic econometrics book first and don't restrict yourself to Johansen's cointegration only. There are some simple cointegration test that suitable for bi-variate system such as Engle and Granger (1987). The step is easy (1) Estimate the regression (i.e. price of rice and price of oil), then save the residuals. (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). If test statistics reject the null hypothesis of no cointegration, meaning that the variables are cointegrated, then proceed to estimate your ECM, otherwise estimate the first differenced VAR system.

I think these should be clear for you and you should also consult the experts in your university / organisation to polish your basic econometric knowledge.

Thank you,

Regards,
tcfoon
Last edited by tcfoon on Mon Sep 27, 2010 4:49 pm, edited 1 time in total.


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