What is the purpose of the AR Roots graph in Eviews when dealing with VECM?
From EViews 8 documentation:
:AR Roots Table/Graph
Reports the inverse roots of the characteristic AR polynomial; see Lütkepohl (1991). The estimated VAR is stable (stationary) if all roots have modulus less than one and lie inside the unit circle. If the VAR is not stable, certain results (such as impulse response standard errors) are not valid. There will be roots, where is the number of endogenous variables and is the largest lag. If you estimated a VEC with cointegrating relations, roots should be equal to unity."
some times lies at broader of the circles and its still stable or stationary, there are AR root Tables, if you ahve two variables and single cointergation then characteristics polynomial should have one root equal to One
so that means, it does the similar task of checking model stability like done in CUSUM test?
please refer to the following link for a clear explanation on the meaning of the root of any AR process:
http://davegiles.blogspot.co.za/2013/06/when-is-autoregressive-model.html
I am running the Toda Yamamoto model with 4 variable. My basic VAR model with suggested optimum lags is not stable. But when I run the VAR with T-Y approach it is stable. So can I continue with T-Y forecaste...?
I want to make something clear for me. If I have VECM 3 equations and 2 cointegrated equations ( there are also some exogenous variables), is it ok if one dot is on the border of AR roots graph and table shows that one one root equals to 1?
If a time series is stationary, the roots of its characteristic polynomial will lie outside the unit circle. What does that mean?
Imagine you have the following AR(p) process:
y(t) = a(1) y(t-1) + ... + a(p) y(t-p) + e(t)
We can equivalently express this as:
(1 - a(1)L(1) - ... - a(p)L(p)) y(t) = e(t), where L is the lag operator.
let z^k = L(k), then we can express the characteristic equation as:
1 - a(1)z^1 - ... - a(p)z^p = 0
We have parameters a(k), so we can solve this equation for z^k. These are called the roots of the characteristic equation (which are guaranteed to exist by the fundamental theorem of algebra).
If all of the roots of this polynomial lie outside the unit circle (i.e. > 1), then the process is stationary. Eviews shows inverse roots (the reciprocal of the roots). If all inverse roots lie within the unit circle, equivalently, the process is stationary.
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