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Questions tagged [cointegration]

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

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Interpretation of Betas and alphas in a VECM

Imagine I set up a VECM where there is only one cointegrated vector among three variables A, B and C and the vector of betas B1, B2 and B3 is (1,-0.25, -0.4) and the alphas a1, a2 and a3 are -0.5, -0....
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Simulate An Error Correction Model with Multiple Cointegrating Vectors

Simulating multiple time series with a single cointegrating vector can be done as follows: $S_t = S_{t-1} - \kappa (S_{t-1} \cdot P-\mu) \Delta t + \epsilon_t\sqrt{\Delta t} $ where the noise $\...
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Connection between cointegration and spurious regressions

My lecturer defines a spurious regression as one in which we frequently reject the null hypothesis, even when the null is true. The null hypothesis is given by: $H_0:$ $\beta = 0$ (Essentially, the ...
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Engle Granger Cointegration test

I am running a model with 3 independent variables. I want to test for cointegration but I have some questions. My dependent variable is stationary I(1) and one of the independent variables is ...
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Granger representation theorem - reverse always true?

The Granger representation theorem claims that a vector error correction model can be transformed into a "common trend representation" (processes share the same stochastic trend) if some criteria are ...
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56 views

Deriving the Cointegrating Equation in a VECM model

I am teaching myself econometrics and I am having trouble understanding how the cointegrating equation in VECM is derived. Lets say we have two variables, Consumption and Income. As I understand it, ...
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Existence of a common term if time series are pairwise cointegrated

Let's suppose that we have $n$ time series that are integrated of order one: $y_t^i\sim I(1)$ for $i=1, 2, \dots, n$ The difference between any two series is stationary: $y_t^i-y_t^j\sim I(0)$ for $...
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Inference in cointegated VAR model

I am estimating the following VAR model: \begin{equation*} x_t = k + A_1 x_{t-1} + A_2 x_{t-2} + \dots + A_p x_{t-p} + \epsilon_t, \end{equation*} where $x_t$ is a vector of variables and notation is ...
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Cointegration (different coefficients using VECM /ca.jo and p-values)

I am trying to get the p-values of my cointegrating vector. I read many questions about it and most of the answers relies on ca.jo funtion from ...
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21 views

Can I use VAR model on I(1) series with cointegration? [duplicate]

I have four I(1) series, and the Johansen test(ca.jo()) shows there is one cointegration. My purpose is to forecast, so I want to compare the forecasting results of VAR and VECM model. Is this ...
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Error Correction Model (ECM) procedure

I am getting familiar with ECM so I would like to ask for help in order to understand it. My goal is: performing a ECM in a multivariate context. I was reading ECM is part of a Cointegration analisis....
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Why do we need a VECM specification if the I(1) processes are cointegrated?

I happened to question the rationale of employing VECM, since some empirical studies like Basu (2017) employed a VAR model to obtain impulse-response analysis. As far as I know, one should consider ...
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1answer
36 views

VAR order in Cointegration Test

I am studying Johansen's Test using Tsay's book (Multivariate Time Series Analysis). The book has given some sample results of function ca.jo in r package ...
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Variance of fitted level of a variable constructed from the fitted difference

I estimated an error correction model for $y_{t}$: \begin{align*} dy_{t+1} & =c(0)+c(1)*dy_{t}+c(2)*(y_{t}-c(3)-c(4)z_{t})\ + u_{t+1} \end{align*} where $y$ and $z$ are cointegrated. Let $\hat{dy}...
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1answer
37 views

Lagged dependent variable with non stationary time series

I'm doing a regression analysis with non stationary time series. If I run the regression the residuals are auto correlated and non stationary. If i add a lag of the dependent variable (the estimated ...
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Testing for (covariance) stationarity specifically (vs. testing for dependence)

I'm using Wooldridge's textbook as my guide for a time-series cross-sectional project. Wooldridge, unlike many, distinguishes between (covariance) stationarity and weak dependence. He says that both ...
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Can I log-transform realized volatility in a co-integration setting

I'm writing my master's thesis and looking to see if there exists fractional co-integration between the volatility of some large stock-indices. My estimates of realized volatility are based on the ...
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Time series has unit root iff integrated of order 1

The wikipedia page for Unit Root says something like "..the stochastic process has a unit root or, alternatively, is integrated of order one..". Are these actually equivalent? Could someone point me ...
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In Cointegration, adf test or for VAR models. What makes difference in having trend + Constant, Constant alone, and non

In Cointegration, adf test or for VAR models. What makes difference in having trend + Constant, Constant alone, and non. in below link http://www.econ.uiuc.edu/~econ508/R/e-ta8_R.html It said ...
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46 views

Regression with non-stationary data

I am doing time series regression (the form I prefer is what SAS calls regression with AR error a form of GLS that runs OLS on the residuals and that has various names in the literature). The problem ...
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1answer
33 views

Like Correlation do we have any measurements in Cointegration

i am new to VEC model We can test for Cointegration using johansen test but like Correlation do we have any measurements or gauge for good Cointergations , Like we say 90% correlation is good and 50%...
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34 views

Intuition behind choosing between versions of Engle-Granger and Johansen cointegration tests

No matter how much I've been searching so far, I haven't found any clear explanation of the logic behind choosing the optimum version of cointegration tests (No constand, with constant, with constant ...
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How can I interpret two outputs in the Johansen cointegration tests

I got two "weird" (for me) outputs of the Johansen cointegration test with two different groups of variables (each group with three endogenous variables). This is the first ...
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Dummy variables in Johansen cointegration analysis

I am doing cointegration analysis (all my macroeconomic series are I(1)). In addition, I want to include in all my cointegration analysis a dummy variable indicating the years where there were ...
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Help with Error Correction Terms (ECTs)?

I have some questions about the correction and error terms of the VECM model. I have a system with 10 variables and 3 vectors of cointegration according to the Johansen test. For each dependent ...
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Hypothesis testing for a known parameter value vs. for an estimated parameter value

I will motivate this question with 2 examples: Cointegration coefficient known vs. unknown The expectations theory of the term structure of interest rates establishes that the cointegration ...
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Cointegration: comparing IRF for the univariate ECT, versus for the multivariate VECM?

Assume we have $k$ I(1) variables, cointegrated of rank $r = 1$. By cointegration, I know that the error-correction term (ECT) is itself a I(0) univariate process. Assume now I am interested in the ...
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1answer
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What is an overall procedure for cointegration test?

I'm working on a set of macroeconomic variables form 1992M01 to 201407. They are PPI, CPI, industrial production, stock price index and exchange rate. I know that I should run a cointegration test for ...
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45 views

How do you estimate long-run coefficients from ARDL bounds test?

Can anyone explain this to me in simple english without too much complex algebra please? Hw and why etc. Thx
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41 views

Determining if two time series are cointegrated

I'm currently working on a problem where I am given that $\epsilon_t$ is a series of independent draws from a N(0,1) distribution $w_t$ is another series of independent draws from a N(0,1) ...
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Properties of Cointegration

Suppose Xt , Yt and Wt are all I(1) scalar series. a) If Xt and Yt are cointegrated and Wt and Xt are also cointegrated, then are Yt and Wt necessarily cointegrated? b) Suppose that Xt , Yt and Wt ...
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Eviews : How to test for cointegration in the right way

I am studying ECM alone using a book and some parts are not explained. First, the book advise to test for a unit and for the order of integration of the series. In eviews options are not pretty clear ...
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Reducing number of time series in VECM

I am exploring using VECM for several time series that are all I(1). However, I am hoping to avoid a model that is too large and was wondering if there is any way I can filter out several variables ...
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Is it possible to combine cointegration with interrupted time series analysis?

I will describe my question with the following example. Imagine I have 3 series that are cointegrated and there is another that is a policy variable. This policy variable is I(0) and was ranging ...
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Phillips-Ouliaris test in R by po.test

Phillips-Ouliaris Test is a cointegration test, and in my understanding it should be commutative. That is, the test result for series x and y and the test result for series y and x should coincide. ...
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440 views

Why are the critical values in coint_johansen in statsmodels in Python so different from the ones in ca.jo in urca in R?

When i run the same johansen test across Python and R I get very different critical values. If I normalize the two columns in <...
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How to deal with seasonality in cointegration analysis?

I have two time series of daily gasoline prices (1500 observations each) which I suspect to be cointegrated. I aim to find an ECM/Asymmetric ECM/Threshold ECM to investigate possible asymmetries. My ...
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1answer
130 views

Unit Root - Real Interest Rate

I want to find out whether the real interest rate of different countries are non-stationary. The real interest rate is defined as the difference between the nominal interest rate and the inflation ...
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65 views

Cointegration vs regression of differences

I have a small number I(1) time series (under 10) that are cointegrated. I would like to create a forecasting model and my choices are either cointegration or regression of differences. I understand ...
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281 views

Grouping similar time series (clustering, cointegration)

I have a number of time series' that I am effectively trying to understand which are similar and which can be grouped together. I have some idea of what should be grouped with each other but I am also ...
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Johansen Cointegration with daily data

I'm performing the Johansen cointegration analysis with daily data, and will extend my analysis with an MGARCH model. My dataset comprises of bond indexes and oil futures it spans 9 years. Using AIC/...
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Johansen test - full rank however variables are I(1)

I have a situation in which my Johansen cointegration test results indicate a full rank, rejecting both that there is no cointegrating vector as well as that there is at most one. I am working with ...
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1answer
192 views

VAR model for first differences (not a good idea?)

I have read from couple of slides in the internet that if I have two $I(1)$ processes, it’s not a good idea to simply take the differences and include them in a VAR model, as then one might lose ...
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Johansen test R - long term relationship covariance

I have two time series which are I(1) and co-integrated. I would like to make long term forecasts for one of the time series, given an assumed fixed value for the other. I used the Johansen test (ca....
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1answer
37 views

Co-integration for processes integrated of order zero

I read that two (or more) time series that are integrated of order 1 (or higher) can be co-integrated. I have three time series, and all three of them are stationary processes. Can they be co-...
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I(2) and I(0) cointegration

I have 23 time-series in my data set, one (interpolated) series is found to be I(2) and the rest are I(0). Is it correct to take the maximum order of the integration for the group as 2? Will Johansen ...
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Computing half life from alpha matrix in Cointegration Analysis - Johansen test

This post suggests that we use eigen values to determine the half life of reverting to mean : https://quant.stackexchange.com/questions/2076/how-to-interpret-the-eigenmatrix-from-a-johansen-...
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Cointegration vs high cross-correlation in pairs trading

My econometrics professor once said that “trading two cointegrated series is a profoundly different thing than trading two highly correlated series”. What was he referring to and what are the ...
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209 views

Interpreting the names used in the output of Johansen test in package urca in R

Here is a snippet from an example in the package urca:- ...
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39 views

Regression of cointegrated variables, serial correlation

I have a response variable $Y$ and a series of predictor variables $X_1, X_2, ... X_n$. All are $I(1)$. I found that $Y and X_1, X_2, ... X_n$ are cointegrated. To estimate coeffcients of $Y ~ X_1,...