I am studying ECM alone using a book and some parts are not explained.
First, the book advise to test for a unit and for the order of integration of the series. In eviews options are not pretty clear to me :
- What is the difference between level, 1st difference and 2nd difference in the ADF Unit root test ?
Running the test (ADF and intercept) I conclude that my series is not stationary :
Null Hypothesis: LTD_P51S_DHFZ7_CH has a unit root Exogenous: Constant Lag Length: 1 (Automatic - based on SIC, maxlag=13) t-Statistic Prob.* Augmented Dickey-Fuller test statistic -0.874719 0.7939 Test critical values: 1% level -3.475500 5% level -2.881260 10% level -2.577365 *MacKinnon (1996) one-sided p-values. But when using Trend & Intercept it is not very clear that it is not stationnary :
Null Hypothesis: LTD_P51S_DHFZ7_CH has a unit root Exogenous: Constant, Linear Trend Lag Length: 2 (Automatic - based on SIC, maxlag=13) t-Statistic Prob.* Augmented Dickey-Fuller test statistic -2.811152 0.1957 Test critical values: 1% level -4.022586 5% level -3.441111 10% level -3.145082 *MacKinnon (1996) one-sided p-values. Which test should I use ? Intercept ? Trend ? None ?
Also how to test it's order of integration ? I(1), I(2) etc.
Cointegration
Also when you have multiple variables (more than two) in you long term static equation, it is possible that some variable are cointegrated two by two and that you need to run a VECM (from what I have understood).
To test for that I read that you can make a Johansen System Cointegration but I really do not understand all the options (Intercept, trend ; in CE, in VAR etc.) and what they imply, I tried multiple but the results differ greatly.
Thank you.
Best Answer
I'll answer your questions pertaining to cointegration.
1) If the context of your exercise is the forecasting of a particular dependent variable by using a set of independent variables as opposed to jointly forecasting a set of variables, then you want to explore an ECM not a VECM, with the latter one being potentially overkill.
2) In your process of exploring an ECM, you can test for cointegration between your dependent variable Y and a set of independent variables {X1, X2, X3} by testing that the residual obtained after regressing Y on X1, X2, and X3 is weakly stationary. This is the first step of the so-called Engle-Granger two-step process. If the residual is stationary then the variables are cointegrated. Cointegrated relationships, however, need not be unique. The shortcoming of the Engle-Granger two-step process is that it will give you at most one cointegrated relationshpip. If there is a reason why you'd expect there to be more than one cointegrated relationship between Y on X1, X2, and X3, the Johansen method could be appealing because it is able to give you more than one cointegrated relationship, but at the price of switching from a single regression to a vector-based regression (or set of regressions), which could be overkill, if you are looking to forecast one single variable, rather than forecast an entire set of variables. Another reason for staying away from the Johansen method, especially if you are new to the method, is that it will give you potentially erroneous results if the VAR is not specified correctly.
So, if you are forecasting a single-variable, stick with ECM and the Engle-Granger method over VECM and Johansen method, but remember that the Engle-Granger method will give you at most one cointegrated relationship, which is perfectly fine in many if not most situations.
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