Questions tagged [cointegration]

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

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R: Johansen test for two variables

I am trying to replicate work from this paper, specifically examination of the rationality of inflation and inflation expectations when both series are non-stationary I(1). I need to apply Johansen ...
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Panel Cointegration when some individual series in the panels are stationary

I'm studying a few panels which are comprised of series, of which some seem to be stationary. This conclusion was reached after using the CIPS test (Pesaran, 2007) as well as ADF and PP Fisher-type ...
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Significance of parameter on cointegrating vector

I have been reading Section 6.2 (page 96) of this manual, where a procedure called "fully modified least squares" is discussed, and was developed on a paper of Phillips and Hansen (1990) . ...
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How to prove that cointegration tests between two time series are invalid in the presence of structural breaks in both time series?

How to prove that cointegration tests on $two$ time series are invalid in the presence of structural breaks in both time series? Wouldn't the presence of a structural break in all the time series ...
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Testing cointegration in a VECM with autocorrelation?

I have four I(1) (monthly) variables. AIC is used to determine the number of lags. A VECM is estimated by ML-method and the Eigevalues imply that there are two cointegrating vectors. Now the problem ...
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Non-stationary time series data and OLS regression (with controls)

I am using 2000-2020 quarterly data and want to test if an appreciation of the real exchange rate leads to a decrease in manufacturing output of a country. However, my data seems to be non-stationary ...
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Constant in Cointegrating Relationship

If I had a cointegrating relationship $c_t = \beta_0 + y_t$, is there a difference between the interpretation of $\beta_0$ and the interpretation of the constant estimated in a simple static ...
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How powerful is cointegration test?

I am performing Engle-Granger cointegration test on my data as below ...
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Johansen procedure shows cointegration r=1, but ect is not significant?

I have 6 variables, all of them I(1). I tested for cointegration and got a significant result for r=1, so I decided to estimate a VECM. The problem is now that the ECTs of the VECM are not significant....
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Eigenvalues of Johansen Trace Test

I'm currently taking a course in time series and have been struggling with understanding the Johansen trace test. Specifically, the calculation of the eigenvalues for the Likelihood ratio statistic. ...
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Update cointegration vector

Hello everyone and thanks in advance for your interest. I have a time series of length T, and I compute the cointegration vector though the Johansen's methods over one section of the series itself, ...
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Johansen Cointegration Test at Levels or First Differences in a VAR Model

I have multiple variables that I am trying to perform a VAR model with, but all my variables are non-stationary at levels as they fail the Augmented Dickey Fuller test. Having taken the first ...
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Regression of a time series difference

Suppose $x(t)$ and $y(t)$ are two time series. I regress $y(t)$ against $x(t)$, and obtain $$y(t)=ax(t)+b+z(t) $$ for some regression constants $a, b$ and residue $z(t)$. Define $\Delta u(t):=u(t+1)-u(...
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Help Johansen test interpretation for co-integration confirmation

I have run following test ...
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Cointegration test; model with different number of explanatory variables

I have run an ADF test on the residuals of an ARDL and a DOLS model to test for cointegration. I have 3 explanatory variables and 1 response variable. When I run the ADF test on the residuals on both ...
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How to impose restrictions on VECM model in R?

Good afternoon! I want to estimate VECM in R and I have a question. Consider an example. I want to estimate a 4-variable VECM model with restrictions: $$ \begin{bmatrix} \bigtriangleup x_t \\ ...
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VAR with trend-stationary variables

I'm currently trying to estimate a VAR with 3 variables - consumption, investment and a credit spread. I have inspected the variables and run ADF tests to determine that they are in-fact trend-...
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VECM in R: how to add differenced lags? [closed]

Good afternoon! I want to estimate VECM in R and I have 2 questions: For instance, I want to estimate a model (in vector form): $$ \bigtriangleup y_t = \pi_1 y_{t-1} + \pi_2 y_{t-2} + A_1 \...
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Cointegrated regression with stationar

For several years, I have been thinking about cointegration regression involving stationary variables as explanatory variables. I am looking for comments on whether the following procedure is ...
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Logit with non-stationary predictors

I have a logit with two predictors that are I(1). Can I meaningfully test for cointegration between the predictors. If so, what would I save for the logit? I am assuming that cointegration between the ...
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Stationary in levels I(0), three variables -- cointegration test?

After running ADF-tests and kpss-test I find that the variables are stationary without drift and trend. I have two questions: Is it the correct use of terminology to say that they are not integrated, ...
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Can the cointegration coefficient be negative?

I am trying to understand the cointegration coefficient, $\gamma$. In the following case, $$P_{A,t }- \gamma P_{B,t}= \varepsilon_t$$ where $P_{A,t}$ and $P_{B,t}$ are the prices of the assets A and B ...
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Expectation of a first difference of I(1) stationary?

I have a simply but still challenging question (at least to me). My question boils down to the following, if the first differences $\Delta y_t$ of an I(1) process is stationary, is then also the ...
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Cointegration equation from VECM with rank=1 is same as OLS result?

In Engle-Granger 2-step ECM model, if there are cointegration relationships then OLS result(1st step) shows a long-run relationship between variables. Short-run relationship is expressed by ECM(2nd ...
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Negative coefficient on the error correction term in an ECM

Why should $\beta_2$ in the error correction model, $(Y_t – Y_{t−1}) = \beta_0 + \beta_1(X_{t−1} – X_{t−2}) + \beta_2(Y_{t−1} + (–\beta_3)X_{t−1}) + u_t$, be negative? I cannot locate any clear ...
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What is the difference between ECM and VECM?

From what I understood, ECM is for two variables and apply OLS to estimate EC term and VECM is for multi-variables (vector form) and apply VAR to estimate EC term. But as I read other papers, I think ...
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Practical questions about cointegration test

I have a few questions about Johansen's cointegration test. I learnd that all variables must have the same order of integration for cointegration test. Suppose there are 5 variables for one is I(0) ...
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Stationarity test - What is wrong with this timeseries?

Following is a timeseries for which I want to test for stationarity. Visually, this timeseries looks stationary as the price is fluctuation between $22.6 and ...
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Simplified Version of the Error Correction Model

I have to solve an exercise on Error Correction Models and cointegration, but I'm having a bit of trouble in understanding what I should do. In the previous line, we have concluded that the two ...
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Interpretation of Cointegration Test Results

I ran the Johansen Cointegration Test and "Phillips & Ouliaris" Cointegration Test on the past 7 years of data of Oil Futures (BZ=F), Gold Futures (GC=F), Gold ETF (GLD), and Silver (SLV)...
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What is the speed of adjustment for two cointegrating vectors?

I have estimated a VECM model in EViews and using Johansen test I obtained that there were cointegration vectors. The output for short-run equation of VECM contains two error correction terms and I ...
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ADF test estimates -0.01 delta, but the p-values are less than 0.05

I am dealing with two datasets of Annual growth Production Cost, and Annual growth Inflation. A lot of problems have arisen, but the most annoying one is referred to integration. At first sight, both ...
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What type of Chart is best to display for which of the 2 Data effects the Spread more at a given point?

For 2 Variables of Data, i have taken a Spread between them. Spread = Data A - Data B. I want to display inside of a Chart, Which Data has more of an Effect when the Spread changes. For Example, if ...
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What is the coefficient that shows whether there is a positive or negative relationship between variables in vector error correction models?

I am trying to estimate the long-run and short-run relationship between variables. Based on the Johansen cointegration analysis it was concluded, that there is one cointegrating relationship. The next ...
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Analyzing relationships in 5 time series (cointegration)

I don't have a dependent variable in this case. 5 time series correspond to 5 different sections of the same company. I want to analyze the relationships between the sections based on these 5 time ...
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Vector error correction models and order of integration

I am trying to estimate VEC models for three variables in different regions. So, using each region's data I am estimating a different VEC model. Mostly, series are I(1) and co-integrated. To have ...
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Why does the prediction of a VAR dgp diverge from the test set?

I'm working on a multivariate data set consisting in 44 observations (which have to be splitted: the first 34 observations are in the training set, the remaining ones in the testing set) of 9 ...
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Estimating cointegrating equations in VEC models

When using the Johansen MLE procedure to estimate a VEC model, is it true to say that the cointegrating equations are estimated simultaneously with the other parameters of the VEC model? Meaning ...
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Cointegration with Multiple Structural Break in R

I am trying to find cointegrated stocks in S&P 500. I have data on all the 500 S&P stocks from 2000 to 2021 which includes multiple structural breaks. I am doing the analysis in R. Currently I ...
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Panel Data Short-Run & Long-Run estimators

Hello kind folk of crossvalidated, It would seem that I need your help once again. I have some data in panel format, which I really shouldn't get too specific about. The aim is to find the short and ...
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Gonzalo's cointegration DGP

I am trying to reprogram the data generating process from Haug (1996) which follows this equation: Parameter a1 can take values (0,1); a2 is fixed at value 1 and their purpose is to set exogeneity or ...
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R Packages urca and aTSA yielding different values of the test statistic

I am testing for the cointegration of 2 series in 2 ways: 1) by obtaining the residuals from the regression of one on the other and conducting an ADF test on the residuals (using package urca); and 2) ...
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Is a random walk cointegrated with its own lag?

Can a random walk, or more broadly a unit-root process, be considered cointegrated with its own lag? E.g. if $y_t=y_{t-1}+u_t$ with $u_t\sim$ i.i.d., then $y_t$ is I(1), $x_t:=y_{t-1}$ is I(1) and ...
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Cointegration testing: is there any relation between maximum lag length and the order of integration?

I have some time series and i have to check if they are cointegrated, testing each possible couple. I have understood that the best way to go is, firstly, to verify the order of integration of all the ...
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Panel ARDL Bounds steps?

I hope you are doing well. I need a little help. Can you please mention the steps for the ARDL Bounds test for cointegration and then causality - the panel data version, not the time series one. If ...
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Help needed with ARDL Bounds Approach

I hope you are doing ok amidst this global pandemic. I'm currently working on this research using the ARDL Bounds approach. My (to a degree self-imposed) "task" is to study the relationship ...
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Cointegrated panel data but stationary regressor

I have a panel with 50 years and 97 countries. I plan to do cointegration with a methodology which requires all regressors to be I(1), but one of them is actually I(0). I looked at individual ...
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Can a linear combination of an I(2) and I(1) variable be I(1)?

I have two variables; log household credit and log real GDP. I use the Augmented Dickey Fuller test following Dolado 1990's testing procedure (https://ideas.repec.org/a/bla/jecsur/v4y1990i3p249-73....
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Time series: Combining trended and periodic series

I have a set of strongly trended time series that are cointegrated (and I think heteroskedastic), and a a strongly periodic but not obviously trended variable that seems to explain some of the ...
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VECM coefficients and equations

I am building a macroeconomic model using VECM. I have a dataset divided into training and testing set and I am forecasting the future values of y. I performed all the testing and I want to get the ...
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