Two or more non-stationary variables are cointegrated if there is a linear combination of those variables which is stationary.

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Multicollinearity, variable selection for cointegration testing in ARDL and VECM/VAR frameworks

I have 15 variables some of which are highly correlated. I want to run a cointegration test in the ARDL and VAR/VECM frameworks. Due to the correlation multicollinearity is a big problem; however, I ...
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Johansen panel cointegration [closed]

In situation where the results of the cointegration indicate as follows: @5% critical values None* 0.0007 At most 1 0.3456 At most 2 0.7886 At most 3 0.4333 Can we ...
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41 views

Modelling stationary and integrated time series in one system

I am currently investigating commodities and their impact on the oil price. I have 8 variables of different stationarities $y$ = dependent variable (oil price) is non-stationary I(1); three ...
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28 views

Can negative relationship between X and Y be spurious

Let's assume I have X and Y and both X and Y have positive relationship. In such case in which both series trend in the same direction, we need to test for cointegration to be sure that relationship ...
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Rules of integrated series and balanced regressions

Background There are various rules of linear combinations of integrated series. Let's just consider the $I(0)$ and $I(1)$ cases. For example, if $x_{t} \sim I(1)$, $y_{t} \sim I(0)$, then $ax_{t} + ...
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Varying orders of integration - VAR/VECM model

I am building a VAR model, and have gotten a thorough set of guidelines through a question I asked a little while ago. However, I am left with some questions based on the following quote from Step 3 ...
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Why is cointegration found without unit root?

I'm working on the multiple price series data to look for the long run relationships. DF-GLS tests for unit root are rejected although the series show some trends and seem stationary after ...
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24 views

Johansen cointegration test: interpret the result

I am trying to develop a stationary time series with 6 variables in Matlab. Can anyone tell me whether the 6 variables are cointegrated? The results I got are:
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29 views

VAR and cointegration

I'm facing an issue with this VAR models exercise; I want to know whether I solved it correctly or not. Point a) is easy, we choose $p=2$ since the information criteria has its minimum value there. ...
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102 views

Relationship between cointegrating relationship found via PCA and that found via a Johansen test

Thanks to the explanation given here: PCA on prices or returns I understand how PCA can be used to derive cointegrating relationships. However there is of course another well known method to ...
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66 views

cointegration and correlation

In the following post it was shown by mpiktas that the sample correlation of two I(1) series converge to a random variable. On the other, given two cointegrated I(1) variables the OLS estimator is ...
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53 views

Estimating Cointegration vector

I am learning about the concept of cointegration and I found in various places the following claim about estimating the cointegration vector using OLS which is: Despite the fact that the OLS estimator ...
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56 views

Regression with cointegrated regressors

Suppose that we have the regression model $$Y(t)=\alpha +\beta_1X_1(t)+ \cdots +\beta_nX_n(t)+\epsilon(t)$$ One approach to fitting this model is to use OLS. If the predictor variables ...
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Uncertainties with how to run a VECM for testing the J-curve

I am attempting to test for the existence of a "J-curve" effect (deterioration of the trade balance in the short-term after the depreciation of the currency via more expensive imports, followed by an ...
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23 views

Some, but not all, panels seem to cointegrate

I am trying to estimate the long-run relationship between equity prices and bond default risk measures using a 250*250 panel of firms. There is strong theoretical evidence that there is a relationship ...
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28 views

How should I run a regression on cointegrated variables?

The variables are non-stationary for levels but become stationary for first differences, in other words they are $I(1)$. Also they have been already further checked for cointegration using Johansen ...
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37 views

Cointegration in the short run

I have a very basic question on cointegration; does the term "cointegration" refer to the long run or can we have short-run cointegration, too?
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Log-transforming time series data before cointegration testing

I am testing the cointegration between these variables: Gold Price (Ringgit), Exchange Rate - MYR to USD (Ringgit), Real Effective FX Rate Based on CPI, T-Bill 10 Years Rate, Consumer Price Index. ...
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79 views

Johansen test for cointegration

I am testing for cointegration using the Johansen test. I have seen questions like how to interpret the test results, but when I am interpreting mine I have some doubts. In my results ...
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Contradicting results of a multivariate and pairwise/bivariate Johansens reduced rank test

I was performing Johansen's reduced rank test on a group of 3 commodity price series $X$, $Y$, and $Z$ ($n=3$; lag-length selection based on the SBIC but at least 2; unrestricted constant model (case ...
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52 views

How to interpret lags in cointegration test for constructing the mean reverting series

For bivariate time series cases, the Engle-Granger two step cointegration test is essentially testing the linear combination for a unit root. The format of the error term is thus: $$ y_t - \gamma x_t ...
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Optimizing choice of cointegration coefficient

Testing for cointegration on the linear combination of time series vectors can be done by testing the error term for a unit root. $$y_t - \gamma x_t = \epsilon_t$$ In the bivariate case the choice ...
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32 views

Why might residual series made from the same data but with different variable orientation look so different?

Suppose two time-series vectors. In the process of testing for cointegration, one may calculate the linear combination, AKA the residual series. There is a choice: one can construct the linear ...
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If all hypotheses in the Johansen test are rejected, what is the order of the cointergration?

The result of the Johansen test is confusing to me. I have two time series and I'd like to test if they are cointegrated. However, in the Johansen test (performed by the function ...
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Interpretation of results from Johansen's co-integration test

I am not able to interpret the following result output for gretl for co-integration: Rank $\ $ Eigenvalue $\ \ $ Trace test $\ \ $ p-value $\ \ $ Lmax test $\ $ p-value 0 $\ \ \ \ \ \ \ $ 0.032753 ...
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25 views

Questions about cointegration and error correction model

I am confused about cointegration and error correction model. I gather that, if two variables are cointegrated, they are related. Is the condition for two variables $X_t\sim~I(a)$,$Y_t\sim I(b)$ to ...
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Null distribution of $F$-statistic in small samples with (co-)integrated time series

A fellow economist proposed an idea for dealing with significance testing in a time series model in a small sample. I doubt its validity, but I have trouble thoroughly disproving the approach. Could ...
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Can any sort of conclusion be made about the cointegration of $B, A$ given the cointegration test statistic of $A, B$?

It can be shown that, generally, the cointegration test statistic of $A, B \ne B,A$. I believe this to be true for all cointegration tests, so the particular test used is, perhaps, irrelevant. ...
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If time series $A, B$ and $A, C$ are cointegrated, is $B, C$ also cointegrated? And with similar confidence?

While I am interested in the general case, let's consider the case of three series. So, suppose time series $A, B, C$. If I can show that $A, B$ and $A, C$ are cointegrated with a test statistic $\ge ...
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43 views

Interpretation of VAR results on R

I am trying to run VAR on the first differences of XLE and Brent futures. Prior to this I have already tested that the series in levels are I(1) and are not cointegrated. Below are my results using ...
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panel co-integration test between debt and gdp

Is is statistically valid (possible) to test for panel co-integration and causality on a multi-country panel dataset between the series [Log(GDP per capita)] and [Log(Debt per capita)]? And does it ...
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Which test to apply if variables are a mixture of I(0), I(1) and I(2)?

I have annual data with 25 observations. 1 dependent variable and 4 independent variables. I used to methods to test stationarity. First I de-trended data and used ADF test and found out that all my ...
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Understanding of the specification of the Johansen Cointegration test in R

I've just started getting into cointegration testing in R using the "urca" and "tseries" packages last week and am still very confused about the different arguments, despite having read the manuals. ...
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233 views

Interpretation of results using Johansen and Engle-Granger 2-step Cointegration tests

I am trying to test for cointegration between two series that based on qualitative reasoning, should be cointegrated. They are the prices of XLE ETF (XLE US equity) ...
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Level or Diff data for lag selection criteria?

I am doing granger causality for oil price and exchange rate using Eviews. I would like to ask if my data is stationary after 1st diff for both variables after using unit root test, then should i use ...
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Signs on independent variables change in VECM results

I am estimating a VECM model and it was determined by the trace tests that there are two cointegration equations. From this, I proceeded to estimate the β under this restriction that provides the ...
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Engle-Granger cointegration testing with a structural break

I have two series of daily close prices for UN and UL from 01/02/2002 to 12/31/2002. Both are for Unilever Co. When I conduct the Engle-Granger cointegration test, the MacKinnon $p$-value is high, ...
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87 views

Unit Root Test - Order of Integration (Johansen)

Let's assume we have 2 variables and test each of them for a unit root with the ADF test. When plotting the data, we can see that it has some up/down movements but is overall clearly trending upwards. ...
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64 views

Engle-Granger Test with I(1) - Gretl

I do have data with 4 variables that are rather trending upwards. They are mostly stationary at level, but only when I include a constant and trend into the ADF unit root test. They are not ...
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79 views

Cointegration test between a stationary and non-stationary time series

I would like to determine if there is any association between two time series. One of the time series is stationary, the other is not stationary. In this scenario does a cointegration test make sense ...
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How do I project multi-population's mortality with R?

During this period, I’m writing my thesis about Longevity Basis Risk and I need any advice about multipopulation mortality model with R. Now, I know the new package “StMoMo” (by Doc.Villegas and ...
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Johansen cointegration test: which of 5 models?

I have 4 variables (GDP, export, industrial production). I found that the variables are nonstationary in level but stationary in their first differences. I conducted the Johansen test and got this ...
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Johansen Cointegration Test [duplicate]

I do have a question regarding Johansen Cointegration test. After checking my time series variables with ADF, PP and KPSS, I conclude that my time series is non-stationary at level but stationary at ...
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Interpretation of Engle-Granger Cointegration Test (Gretl)

How would you interpret following result from running the Engle-Granger cointegration test in Gretl: ...
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77 views

Consider structural breaks in VECM

I am implementing a VECM, which should also take two structural breaks into account. I am using the function ca.jo from the "vars" package in R and include the ...
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79 views

Testing Restrictions on Beta (long run coefficients), R example

The code given below estimates a VEC model with 4 cointegrating vectors. It is a reproducible code, so just copy and paste into your R console (or script editor). ...
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Cointegration and long run restrictions

Below is a typical output from a 5 variable VECM model with 4 cointegrating vectors with $r-1$ restrictions on each equation. Therefore, the top part of the output is a diagonal matrix by default. For ...
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Cointegrating vectors/equations

I am experimenting with 5 variable co-integration model via simulations. Below are output of cointegrating vectors from two different data sets. As you can see there are 4 long run equations in each ...
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Time varying cointegrating equation

I am estimating a rolling cointegration model and saving the parameters of the long run equation for trend analysis. I wonder if it is possible to estimate time varying parameter VECM using Kalman ...
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Intepret results from Johansen (cointegration) test

I have 3 variables ( GDP, exportation, indstrial production). i found that variables are non stationnary in level but stationnary in their first. difference.i made the johenson test, i must choose ...