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process is convert it to a VAR model $$ y_{t} = \left(I+\Pi+\Gamma_{1}\right)y_{t-1}+\cdot\cdot\cdot+\left(\Gamma_{p-1}-\Gamma_{p-2}\right)y_{t-p+1}-\Gamma_{p-1}y_{t-p}+u_{t} $$ find the eigenvalues of … the companion matrix $$ \left[\begin{array}{ccccc} I+\Pi+\Gamma_{1} & \Gamma_{2}-\Gamma_{1} & \cdot\cdot\cdot & \Gamma_{p-1}-\Gamma_{p-2} & -\Gamma_{p-1}\\ I & 0 & 0 & 0 & 0\\ 0 & I & 0 & 0 & 0\\ 0 & …

Suppose we have an m-dimensional VAR(p) model $$Y_t = \Pi_1 Y_{t-1} +\Pi_2 Y_{t-1} +\dots + \Pi_p Y_{t-p} +\varepsilon_t$$ Then the VECM corresponding to this model is $$\Delta Y_t = \Pi Y_{t-1} +\sum_ … But I'm a little confused how the eigenvalues lie between 0 and 1. I have heard that they are the square of the canonical correlations between $\Delta Y_t$ and $Y_{t-1}$. …

First, we will revisit the Vector Autoregressive (VAR) model and its Vector Error Correction Model (VECM) representation: VAR and VECM Models For an $m$-dimensional VAR($p$) model: \begin{equation} Y_t … I still need to read up on how canonical correlation analysis works to understand, but I can see that you will can get $m$ values from performing CCA on $\Delta Y$ and $Y_{t-1}$. …

Building on Why do we need a VECM specification if the I(1) processes are cointegrated? … \end{equation} $$ Here, $z_t'=(y_t,x_t)$, $a'=(\alpha,0)$ and $b'=(1,-\beta)$. I estimate a VAR(1) for the first differences and a VECM, and report the forecasts for $y_t$ for the two models. …

I am considering two time series and I would like to to a VAR regression between them. The ADF test rejected stationarity in only one of them, so the time series would be I(0) and I(1). … Should I consider doing a VAR of the I(0) in levels and the differences in the I(1)? Should I still consider a VECM? …

If you are fairly sure that $Y_1$ is I(1) and $Y_2$ is I(0), take the first difference of $Y_1$ and model $(\Delta Y_1,Y_2)$ using a VAR. … There is no point in using a VECM, as there is no cointegration and thus no error correction term. …

I suggest running at least KPSS in addition to ADF. Not all tests are created equal and some might be more powerful than others, especially in the case of near-unit-root processes. … As regards cointegrated VAR, it makes no sense if you have an I(1) variable and an I(0) variable, but given that you are not sure whether or not this is indeed the case, a Johansen VECM might throw light …

If $d=1$ and there is a single series that is I(1) while the other ones are I(0), you take first differences of that variable and model that together with the other variables using a VAR. … If, on the other hand, the I(1) variables are cointegrated, you model them using VECM; you also include the I(0) variables on the side as in this answer. …

As far as I know, one should consider using the VECM if the multivariate time-series of interest consists of cointegrated I(1) processes. … However, the study did not use the VECM, but estimated a VAR model. One more question: consider two cointegrated I(1) processes. …

For the VECM model, I have selected the lag ($p=1$) using: VAR with variables at level, statistical criterion of AIC, no evidence of autocorrelation or heteroscedasticity in the residuals of VAR, … lag of VECM equal lag of VAR in level minus 1, VECM(0). …

When I run a regression, all variables are I(1), the optimal lag according to SIC is one, and means I should do VECM (1-1=0) the coefficient of the error correction term (ECT) is negative but not significant … My question is: can I do VAR instead of VECM, Should I do VAR of differencs: means in E-views: D(dependent Variable) D(Variable1) D(Variable2) D(Variable3)..and so on. …

Having taken the first difference, they do all become stationary at I(1). I was wondering, do I perform the Johansen cointegration test on the I(0) variables or the I(1) variables. … 2) If I have cointegration present, and my I(0) variables are non-stationary, I should switch to a VECM model? ) …

It looks like you have $x_1$ and $x_3$ being I(1) and $x_2$ being I(2). This is what I would do. Take the first difference of $x_2$ to make it I(1) and call that $y$: $y:=\Delta x_2$. … Second, VECM will not be appropriate as there can be no cointegration between variables that, after the differencing, are at most I(0). …

You have two options (probably a few more, but these 2 are these, I have in my mind): 1.) … With a VAR you can capture season, trend levels. If a VAR in levels is not possible (which would be the case with sales and spendings) use VECM or VAR in differences. …

Suppose a VAR(p) model containing $s$ endogenous variables such that $Y_{t} = (y_{1t}, \ \ldots, y_{st})$. It was verified that, for all $i \in \{1, \ \ldots, s\}$, $y_{it} \sim I(1)$. … 0)$. …