What are the three variables? I think you should try using other proxies for the variables.
You appear to have 3 variables
1. price of bitcoin,
2. ethereun (price of ?), and
3. portfol..
A time series is I(0) if it is stationary. A time series is I(1) if it is non-stationary in levels and its first difference is stationary. Thus rather than saying "3 variables are stationary at I(0) and they are at I(1)" you should simply say that the 3 variables are I(1).
The attachment to your question seems to imply that you have tried to estimate an ecm in the first differences of the variables rather than the levels. Check your software manual.
If you have bi-directional causality between the first two variables there is likely to be feedback from the first to the second. (assuming that the first is the price of bitcoin) estimation by ARDL is not valid. Use Johansen.
The stability of your system does not depend on the sign or the magnitude of the coefficient of the error correction mechanism. The stability of your system depends on the entire system consisting of your ARDL equation and the probably VAR-like equations for the other two variables.
More importantly, I do not see how you can get an economic justification for an equilibrium relationship between your three variables. If you look hard enough at any large data set you will find relationships that appear good but are spurious. Your analysis must estimate what is specified by your theory and knowledge of the process.
Have you read Michael Lewis's new book Going Infinite: The Rise and Fall of a New Tycoon" about the antics of Sam Bankman-Fried?
Richmond Addison
my 3 variables are:
portfolio, ehtereum, and bitcoin
Thank you!
John C Frain
Thank you for your answer.
I have not used an ARDL to conduct my sutdies. I have used Johasen then Granger then VECM on Eviews.
And I have run all of my model on the level i.e. original price dataset (only the Granger has been done on return i.e. 1st difference since I am looking for the order of the VECM that takes into account the long-term relationship i.e. returns).
I will have a look at the book right now thank you for that.
But I do not understand how to counter my issues.
Thanks!
@Richmon Addison
By saying procies, do you mean adding exogeneous variables to my model? Thanks!
And also yes you right, my variables are all I(1) i.e. they are not stationary at level but are at 1st differentiate. My bad
Clement Menard
It is not clear what the Portfolio series is measuring. Is it a price series of some portfolio and if so what are the contents of the portfolio? I presume that the other two series are price series. What exactly are you trying to establish?
When I used EVIEWS the t-statistics produced in these circumstances did not have a standard t-distribution. The appropriate way to test the significance of the coefficient(s) on the ecm term is to estimate the model with the relevant coefficient(s) constrained to zero and do a likelihood ratio (or equivalent) test. That said, two of your coefficients will probably be statistically insignificant. I would be more concerned about the small magnitude of the coefficients. The eigenvalues of the companion matrix of the system might be interesting. You might also examine the impulse response functions of the system. Section 7.7 of Lutkepohl gives details of impulse response functions in cointegrated systems.
The methodology of using Granger causality if variables are I(1) an cointegrated is covered in section 7.6 of Lutkepohl (2005), New Introduction to Multiple Time Series Analysis, Springer. Look for the Toda Yamamoto test. The approach using a VAR in first differences is misspecified because it omits the effect of the ECMs.
the Lewis book explains how these markets have been manipulated for a long period. Thus it will be difficult to derive a good theoretical model you can estimate.
If this is part of a term paper or thesis, talk to your supervisor/lecturer. My advice is relevant to a full analysis by an econometrician. If you are not that advanced in your econometric studies you may not be expected to be familiar with this type of analysis. Your supervisor/lecturer is in the best position to give you advice.
John C Frain
Sorry for the unclear structure of my variable.
Bitcoin and ethereum, I have taken the adjusted closing price on yahoo finance
For the portfolio. I have done a markowitz optimisation to determine the weights to put in the 10 first tech firms of NASDAQ index) so there are Apple, Nvidia, ...
It is also measured in closing price. Thank you!
The shortrun dynamic adjustment is not mentioning convergent to the equilibrium also insignificant.
In a VECM model, if CointEq1 (the error correction term) is positive or insignificant, it indicates:
Reevaluate your model for proper specification or cointegration relationships.
Chuck A Arize The eigenvectors or equivalently the characteristic roots of the Companion Matrix of a VECM determine its "stability".
If the roots are outside or on the unit circle ( alternatively if the eigenvectors are inside or on the unit circle then the process is non-stationary but "stable". By stable I mean that it converges to an equilibrium after a shock.
If the roots are inside or on the unit circle ( alternatively if the eigenvectors are outside or on the unit circle then the process is explosive.
It is possible that there is a form of overshooting in one of the equations in a VECM (positive coefficient on the ecm). If the system is "stable" the other equations (including the "short-term" effects) may still restore the new equilibrium.
Your suggestion regarding "incorrect signs" appears on many internet forums. It is not correct.
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