## Dickey Fuller for Multiple Regression Models

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econochoice
Posts: 13
Joined: Fri Jun 05, 2009 1:55 am

### Dickey Fuller for Multiple Regression Models

Dear All,
I am stuck with removing non-stationarity and the transformation of the original model variables.My problems are below:
1.Can I use ADF for multiple regression at all
2.If yes then how can I put different differenced series in the original model of 5 variables.The corresponding cases /respondent data would not tally if I take different differences for its variables like income, performance,experience (supposing they all have non-stationary series)
3. How should I transform the series that got stationary at 2nd difference ? Please give an example how to make the new variable in this case

My original model to be estimated is as below:

V=a+b1x1+b2x2+b3x3
b=coefficients
x=variables
I am told that stationarity has to be removed from all the series that I want to use in my multiple regression

tcfoon
Posts: 54
Joined: Fri May 15, 2009 4:33 am

### Re: Dickey Fuller for Multiple Regression Models

Dear Econochoice,

1. I am told that stationarity has to be removed from all the series that I want to use in my multiple regression

The above sentence mean each variables in you multiple regression model must be stationary. Granger and Newbolds (1974) and Phillips (1986) have pointed out that the regression results may be spurious (nonsense) if the estimated variables are non-stationary and not cointegrated. Therefore, someone asked you to ensure that the estimated variables are stationary, otherwise take the d time of differencing to make it stationary.

2. Can I use ADF for multiple regression at all?

For me the above question is not clear, but I assumed that you would like to ask whether Augmented Dickey-Fuller (ADF) can be applied to multiple (multivariate) variables instead of univariate. Literally speaking, yes the ADF for multivariate is known as Johansen cointegration test, but as I see that your intention is only to analyse the multiple regression. I suggest you to apply the univariate ADF test that is available in Eviews - Quick\Series Statistics\Unit Root test. If the variables are integrated of order one, I(1) process, then run the multiple regression with the first differencing variables.

3. You just type this "genr dy2 = d(y,2)" in the Eviews command window to generate the second differencing variables.

In addition, you could also read some Introduction to Econometrics, Applied Time Series Econometrics books.

Thank you,

Regards,
tcfoon
Last edited by tcfoon on Mon Sep 27, 2010 4:50 pm, edited 1 time in total.

econochoice
Posts: 13
Joined: Fri Jun 05, 2009 1:55 am

### Re: Dickey Fuller for Multiple Regression Models

Hi Mr.Tang,

I am really grateul to you for the help.I have seen many books but I am in a better position after seeing your message.
As for my confusing question No.2 I try to simplify it:

1) ) If I have to use different differences I(1) for one series and I(2) for another variable/series will it be fine to put these differenced variables in my original model ?

2) Second : how would I interpret the model

Y=a+2.5L+3.1M+5P
Where as per differencing say L=I(1), M=I(0) and P=I(2)
The normal OLS interpretation would be :
One unit change in L would cause 2.5 unit change in Y and so on.But here we are having differenced variables.
I'll be grateful

tcfoon
Posts: 54
Joined: Fri May 15, 2009 4:33 am

### Re: Dickey Fuller for Multiple Regression Models

Just interpreted as if d(L) increase by one unit, on average the Y will increase by 2.5 unit.

econochoice
Posts: 13
Joined: Fri Jun 05, 2009 1:55 am

### Re: Dickey Fuller for Multiple Regression Models

Thanks again Sir,
So what in a nut shell is that each variable with a different difference I(1), I(2) or I(0) can be used together in a multiple regression model.Secondly the variables would be interpreted as , a unit increase in differenced(L) would result in 2.5 unit increase in Y.Then if L is Price the government should increase the price by 1 unit to get 2.5 additional units of output (The term "Differenced" in d(L) would not make any difference in interpretation)? Am I right ?

tcfoon
Posts: 54
Joined: Fri May 15, 2009 4:33 am

### Re: Dickey Fuller for Multiple Regression Models

In the beginning someone comment your work and asked to check the stationarity for each variables in the regression model. If your data is a time series, stationarity is vital. Why?? The time series literature stated that the regression results may be spurious if the estimated variables are non-stationary. For this reason, you have to run the regression with stationary variables, I(0). Since, you observed that the order of integration for each series is different, thus you have to transform (i.e. differencing) the variable until stationary. If price is I(1), then change of price may interpreted as inflation. NO, the d(L) would make a different interpretation with the L term. One more thing I would like to inform you that the Y (dependent variable) must be stationarity as well.

econochoice
Posts: 13
Joined: Fri Jun 05, 2009 1:55 am

### Re: Dickey Fuller for Multiple Regression Models

I am getting more clear with each response from your side.This is really commendable.

You said" If price is I(1), then change of price may interpreted as inflation. NO, the d(L) would make a different interpretation with the L term." so what would be the new interpretation? and interpretation of the other variables with I(1) and I(2)

I wish there was a book or tutorial with step by step instructions till final interpretation.I am producing one such tutorial with screen shots so that people like me can benefit.If you like I can send it to you and you can improve it and put it on some website.

>> One more thing I would like to inform you that the Y (dependent variable) must be stationarity as well.

I agree and that would change the interpretation again.You can help.

guero303030
Posts: 14
Joined: Sun May 24, 2009 4:28 pm
Location: Laredo, Texas
Contact:

### Re: Dickey Fuller for Multiple Regression Models

Dear eviews,
you guys are great and I am very appreciative.
To follow up on doing the Dickey Fuller Test, I had a question. When doing the DF unit root test, this is where my ignorance comes in, I am trying perform a test where I regress delta y(change in y) on y(t-1), actually I am doing it on the "delta" r3 = c - r3 t-1 . It is a wooldridge example that I am doing so I can learn to do a unit root test on my paper. I don't know how to create delta in eviews? Is there a command for delta or do I have to create a series? Would it be going to object/new equation/ and then put in (y - y t-1) to create a new series(it doesn't let me do it). Any help would be much appreciated. Thanks again, Guero303030 Did you use forum search?
Posts: 1518
Joined: Thu Nov 20, 2008 12:04 pm

### Re: Dickey Fuller for Multiple Regression Models

You are looking for the difference operator. See the Time Series Functions section of the help file and manual for details:

Code: Select all

`d(Y) 'means Yt - Yt-1`

guero303030
Posts: 14
Joined: Sun May 24, 2009 4:28 pm
Location: Laredo, Texas
Contact:

### Re: Dickey Fuller for Multiple Regression Models

sorry, I did my homework and found exactly what you answer. You guys have a very helpful forum. thank you. guero303030

tcfoon
Posts: 54
Joined: Fri May 15, 2009 4:33 am

### Re: Dickey Fuller for Multiple Regression Models

Dear Econochoice,

For I(1) process, If L is price then the first difference of L = D(L) is interpreted as inflation. If Y is income, then first difference of income may interpreted as growth. The interpretation is that if inflation increase by one percent, on average the economic growth will increase/decrease by XXX percent and holding other factors is constant.

For I(2) process, DD(L) may be interpreted as growth of inflation (which is the growth of the growth), if growth of inflation increase by one percent, on average economic growth will increase/decrease by XXX percent.

Sometime the transformed variables is meaningless, but is to comply the statistical require only. From my point of view, the magnitude or the size of the parameter is not very important issue compared to the sign of the variables. If we aware of the fact that, when we interpret the coefficient we must mention the statement "holding other factor is constant" either in front or at the end of the sentence. The statement of "holding others factor is constant" or also known as Ceteris Paribus is irrational in the real world. Lutkepohl (1994) - Econometric Reviews pointed out that in the real world nothing is constant, thus direct interpretation of the coefficient may be incorrect. In this respect, obtain a correct sign should be focus on instead of the interpretation of the coefficients. For example, if the coefficient for computer price is -1.04, conventionally we may conclude that if the price of computer increase by one unit, then the demand for computer will reduce by 1.04 unit, holding other factor is constant. In practice, are you sure that the demand for computer will reduce by exactly 1.04 unit or 1.00 unit if the price of computer increase by one unit? Of course NO and the most useful indication for -1.04 is the negative relationship. One thing we affirm is that when the price of computer increase the demand for computer will reduce but we are not sure by how many unit computer will reduce.

If you want to make your research more valuable and interesting, you may consider cointegration, Granger causality, impulse response function and variance decomposition analyses.

Thank you,

Regards,
tcfoon
Last edited by tcfoon on Mon Sep 27, 2010 4:51 pm, edited 1 time in total.

Shijaku
Posts: 1
Joined: Tue Sep 08, 2009 12:58 am

### Re: Dickey Fuller for Multiple Regression Models

Hi guys
I was following your discussion and I guessed that you were saying that in runing a Multiple regression in eviews by OLS Model the variables should be in level or in first/second differences. I have run a ols model on OLS method and I have put the variables in level. I found them significant but in the cost of serial correlation, which I remove by applying a lag methods. I do not know whether I am right or I should have put them in the stationarity form.

All the best to you guys. I appreteate your anwser.

Gerti

lardie2345
Posts: 1
Joined: Sat Dec 18, 2010 6:31 am

### Re: Dickey Fuller for Multiple Regression Models

Hi,
I am trying to test for stationarity in a multivariate series. I used the ADF test to test individual variables and found some independent variables to be non-stationary when integrated at level but stationary when integrated of order one. My question now is that can I continue to run the multivariate regression using OLS by inputting the I(1) independent variables as first differences and leaving the I(0) variables as they are?

Also, what if the dependent variable is also stationary at I(1), can I apply first differences or do I have to test for cointegration or use Johansen?

Thank you

dealsfe
Posts: 5
Joined: Sun Apr 10, 2011 7:17 am

### Re: Dickey Fuller for Multiple Regression Models

to lardie2345

if all variables are I(1), you should use level values, if variables are different integrating order, you should equal them by integrating order.

Flora
Posts: 1
Joined: Sat May 28, 2011 1:17 am

### Re: Dickey Fuller for Multiple Regression Models

Hi,
Kindly, tell me how to enter the fourth difference of variable Yt (variabel which is integrated of order 3) in the eviews..
thanks a lot.