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

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Cointegration test results differ for different test specifications (drift, trend, etc.)

I am testing whether stock indices are cointegrated. I have two series representing different indices. Both have been tested and are I(1). When I apply the Johansen test (on eViews), I choose the ...
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26 views

Find cointegrating vectors and loadings from a trivariate VAR(1) equation

I have the following process: $\begin{bmatrix} X_t \\ Y_t \\ Z_t \\ \end{bmatrix} = \begin{bmatrix} 1 \\ 0 \\ 1 \\ \end{bmatrix} + \begin{bmatrix} 0.5 & 0.5 & 0 \\ 0 & 1 & 0 \\ 0 &...
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18 views

Purging dynamics in multiple regression (cointegration)

I was reading Bewley and Yang method to purge dynamics of a multiple regression method as explained towards end of page 4 in this paper. The authors basically state that to remove dynamics from a ...
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1answer
23 views

Example of 2 series correlated but not cointegrated and vice versa

I am studying the time series and only kind of understand correlation vs cointegration. Can someone provide an example of two series that are correlated but not cointegrated, and two that are ...
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1answer
37 views

Error correction term has both positive and negative loadings - is that OK?

I did a Johansen test. The max eigenvalue test resulted in 5 cointegrated variables with contegration rank being 1. The trace test resulted in 5 cointegrated variables with contegration rank being 3. ...
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15 views

Dummy Variables for Structural Breaks in Johansen Test

I am testing two variables for cointegration and after implemeting test for structural break I found there are 2 structural breaks. So, in the Johansen test I need to add dummy variables (following ...
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9 views

Can a cointegrated variable be exogenous in first difference in a VEC model?

If I have a variable C that is cointegrated with both variables A and B separately, can I use it in first-differenced form as an exogenous variable in a VEC model involving A and B?
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Does all variables in a VAR/VEC need to be normally distributed, or only the target variable?

Well? Does all variables in a VAR/VEC need to be normally distributed, or only the target variable? It is very hard to get all of them to meet criteria of normality without deleting too many outliers.
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42 views

VAR lag length vs Johansen cointegration test outcome?

First puzzle: I am taught that the lag order of VECM does not affect the cointegration rank because the lag order is for the differenced regressors. But, I see the contrary: I experimented with sample ...
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22 views

Cointegration test of stationary variables with structural breaks

I am trying to implement test of cointegration (Johansen trace and eigenvalue) between 2 variables that are stationary at first difference but after Zivot-Andrews test of unit root I found they have ...
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19 views

What models for Rahbek and Mosconi method for exogenous variables in VECM?

I'm not very good at algebra, wich caues problems for me when reading econometric articles. Now, I'm reading the Rahbek and Mosconi (1998) paper on how to introduce exogenous variables in VEC models. ...
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32 views

Threshold cointegration

I have a panel data N=45 T=25. Engle-Granger test confirms co-integration between two I(1) variables. I would like to test for threshold cointegration between these two vars. Is there a user written ...
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109 views

Testing for cointegration and building a VEC model

I have 3 variables which are all stationary at 2nd order difference. I want to check for cointegration using the piece of code below. If I run pairwise cointegration analysis then I get these results: ...
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25 views

ARDL bounds testing: model specification and selection

I am performing ARDL bounds testing. In particular, my variables are GDP, renewable and non-renewable electricity, carbon emissions and 2 other control variables, capital and labour. I have seen that ...
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1answer
25 views

R: vector autoregression with penalty for non-cointegrated factors

I can perform a vector autoregression using the "vars" package in R. library(vars) data(Canada) VAR(Canada, p = 2, type = "none") But as I understand it, vector ...
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2answers
46 views

Purpose of the first step in Engle-Granger cointegration test

I have two questions: Why test $u_t$ (see below) for stationarity instead of any other linear combination? And to confirm, if $u_t$ is not stationary does it mean that $x_t$ and $y_t$ are not ...
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30 views

How to impose exclusion restriction on cointegrating vector? R reproducible example

The code given below estimates a VEC model with 2 cointegrating vectors. It is a reproducible code, so just copy and paste into your R console (or script editor). ...
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1answer
49 views

Granger Causality test pre-conditions

I am trying to analyse the causation between individual stock returns and index returns. I have taken the log return values of both stock and index values. Unit root test suggest that the values are ...
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24 views

Intepretation of Eigenvalues in Johansen Test

I am reading this tutorial on how to interpret Johansen Test result http://www.quantcode.com/modules/smartfaq/faq.php?faqid=103 The tutorial indicates that a significant Eigenvalue is required even ...
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21 views

Panel: Estimating cointegrating vector within ECM to test cointegration

In time-series analysis we were taught that one can test for cointegration by estimating an error correction model and testing whether the coefficient estimated to the deviation of the equilibrium ...
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1answer
30 views

Modelling in the presence of multiple cointegrating relationships

I am looking for some clarification regarding multivariable cointegration and what steps I should take to avoid spurious regressions. I am analysing a time series $y$ as a function of independent ...
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1answer
81 views

Is a trend-stationary variable I(1) or I(0)?

I am trying to do cointegration analysis between two variables. I first used the standard Dickey-Fuller and Phillips-Perron tests; they concluded my variables were I(1). I then did cointegration and ...
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29 views

can we use Engle-Granger test for cointegration when I have lags of dependent variable as explanatory variable in my model?

I want to check for cointegration test using Engle-Granger test for my model which is of the form: y= y(-1) + y(-2) + x1 + x2 + x3 Is Engle granger test suitable for such cases.
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31 views

Replicate cointegration rank statistics using a 9 variable VAR(2)

I am trying to replicate Tables 3 and 4 from the paper "A Long Run Structural Macroeconometric Model OF the UK" by Garratt et al (2003). Using the Akaike criterion the authors decide to proceed with ...
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30 views

Conflicting cointegration results due to different lags in Johansen procedure

I have been using two different models for cointegration: Johansen's test and ARDL (autoregressive distributed lag). I guess this example could be extendent for other cointegration models as well. I ...
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43 views

Cointegration Restrictions

If there are two I(1) series that are not cointegrated, why could it be that if I create a VECM and impose restrictions implying that they are cointegrated, that I cannot reject this restriction ...
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71 views

Model residuals pass stationarity test, but Durbin–Watson test fails

I have a OLS model that I try to prove it has cointegration between two regressors and the dependent variable. The model fits well, with a very high R-squared. The residuals don't seem to be ...
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44 views

Testing the expectations hypothesis in eviews (term structure)

I am testing the Forward Rate Unbiasdness Hypothesis (FRUH) in eviews using t-bills, and have so far found the spot rate and forward rates to be cointegrated using the Johansen test. This is the first ...
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41 views

panel cointegration Westerlund test Pedroni cointegration test

My data is non stationary.So in order to check for cointegration i used westerlunds test but it showed not cointegrating relationships. But on doing a Pedronis cointegration test,it shows that there ...
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14 views

Making series cointegrated if they are not cointegrated?

I am fairly new to pairs trading. I was looking at a couple of series and testing whether they were cointegrated to see if I could apply a pairs trading strategy to them. I tested the series for ...
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44 views

Johansen Test - Full rank but variables are not I(0)

I have a model of four implied exchange rates which are based on stock prices denominated in two currencies. They should all be cointegrated based on the law of one price. Each of the series is ...
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1answer
76 views

Why can't I get rid of serial correlation in lag length selection?

I'm doing a statistical study based on the USD price of Bitcoin, including explanatory variables like Google Trends data, Dollar strength, stock exchange etc. Setting up a VAR in levels for lag ...
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1answer
53 views

Counterintuitive impulse responses in a SVAR model, why?

I did a study with structural vector autoregression (SVAR model) corresponding to the IS-LM model (a macroeconomic model). I have four variables that are I(1). I have fitted the SVAR model to the ...
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16 views

how do we interpret cointegration results?

I don't know how to interpret cointegration results? I only done unit root test and trace and maxeigenvalue interpretation but don't know how to find negative and positive relation between the ...
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1answer
58 views

What is the difference between cointegration and the VECM?

What is the difference between cointegration and the vector error correction model (VECM)? I applied cointegration test and found long run association between variables, so should I apply VECM?
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41 views

Assistance with methodological procedures for (panel data) [investment/GDP]

I am attempting to see the relationship between FDI and Economic growth. So my two variables are FDI and GDP growth (I am also not opposed to using GDP per capita). My data is panel, as I am using 59 ...
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79 views

How can I represent exogenous I(0) variable in VECM / Cointegrating relationship?

So I am doing an econometric study on Bitcoin's USD price. As an exogenous regressor, I have the total number of bitcoins in circulation (nbtc). The graph looks like this: This variable is: ...
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35 views

VECM for 2 stationary and 1 integrated series

I am carrying the Johansen test on 3 time series variables and eventually estimating a VECM. 2 of my variables are stationary while the other one is nonstationary. I have a few doubts: Do I need to ...
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37 views

Choosing lag length for VAR

I've got 2 questions about this. I'm fitting a VAR in levels in order to select lag length for Johansen cointegration tests. All my data are in natural logarithms. 1) All my variables are I(1) except ...
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36 views

Granger causality and Wald test in multivariate non-stationary case

I have a list of market indices (like 20 indices) and want to analyse which indices are the most important for prediction of CDS of a company. Most of the time series are I(1) processes. I was using ...
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32 views

Cointegration test with I(1) and I(0) variables

I have four variables, three of them are I(1) and one of them is I(0). I'm using STATA as my software. Can I use Johansen's test to check for cointegration? I understood that all variables should be I(...
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94 views

Should multicollinearity problem be looked into while doing cointegration?

Multicollinearity and Cointegration is not the same thing however, if the series actually move together in the long-run i.e. are cointegrated wont they also be collinear making e.g. Autoregressive ...
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13 views

Query regarding cointegrating vector and cointegration rank

Respected Group Members In VECM, what is the difference between cointegrating vectors and cointegration rank. Do they mean the same thing. If I have three variables (n=3) and getting 2 cointegrating ...
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113 views

Lag order selection in error correction model (ECM)

I am building an Error Correction Model for monthly price data ($X, Y, Z$). I am deliberately using an ECM and not VECM and apply a two step approach (estimating cointegration relationship first, then ...
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53 views

Cointegrated Data Proc Panel SAS

I have data that are co-integrated. I am using a Proc Panel data in SAS in order to run regression analysis. Obviously running the panel regression of one data over a related co-integrated data causes ...
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1answer
162 views

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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81 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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38 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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37 views

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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113 views

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 ...