# 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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20 views

### 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 ...
16 views

### 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 ...
55 views

### 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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### Why must the non-zero eigenvalues in the Johansen test be between 0 and 1?

Why are the non-zero eigenvalues in the matrix $\Pi$ in the Johansen test between 0 and 1? Why can't they be greater than 1 or less than zero? My lecturer just dropped in that's its because "the ...
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### If all endogenous variables are I(1), and if just two of them are cointegrated, can I incorporate its cointegration in the VAR model?

Suppose a VAR(p) model containing $s$ endogenous variables such that $Y_{t} = (y_{1t}, \ \ldots, y_{st})$. It was verified that, for all $i \in \{1, \ \ldots, s\}$, $y_{it} \sim I(1)$. In addition, it ...
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### How to "derive" and interpret this data generating process for a high-dimensional VEC Model?

I am currently trying to understand the following paper by Smeekes & Wijler (2021) who are proposing an automated estimation procedure for models with a large number of potentially cointegrated ...
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### Determining a variable's order of integration from cointegration results (Engle and Granger) and orders of other variables

If you run a Engle and Granger test with the regression: $$y_t=b_0+b_1x_t+\varepsilon_t$$ and you know that $y_t$ is integrated of order 2, what can you say about the order of integration of $x_t$, ...
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### VAR in levels of differences when series are integrated but not cointegrated?

I have monthly financial time-series data from 2011-present of four stock market indices. I conducted various stationarity tests and found that the series are I(1) processes (stationary only in first ...
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### Dynamic OLS: serial correlation in the residuals

I want to estimate cointegrating vectors between different I(1) time series. I used the R package CointReg to run D-OLS regressions (function CointRegD). The number of lags and leads was selected by ...
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### ARDL cointegration

With ARDL cointegration (the bounds tests approach), why is the dependent variable stated in first differences in software such as Eviews? Best, Lars
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### Why Engle-Granger cointegration test states cointegration between two variables but their trend in time is almost identical?

I have run the Engle-Granger cointegration test in Python between a stock's return and its index return. In this case i have run the test between QQQ returns vs CCMP returns like this: ...
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### Cointegration and Granger causality

Can anyone please tell me whether the existence of cointegration between two series necessarily implies Granger causality between their "first differences"? I'd appreciate it if you could ...
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### I am facing a problem when constructing a SVECM mode with rl!

when using SVEC to construct the model, I just constantly facing the problems: Error in solve.default(infgamma) : system is computationally singular: reciprocal condition number = 5.60627e-21 this ...
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### How to prove that panel series converge over time and that volatility across the series decreases over time

I have multiple daily price series of Bitcoin from several exchanges. I was to test: (1) whether the prices or the spread between the prices decreases over time, and (2) whether the volatility of ...
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### Determining causality between two non-stationary co-integrated time series

I started off using Granger causality test but since the two time series are not stationary and are also co-integrated. Is there another causality test that I can perform which is similar to Granger ...
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### How to interpret Pedroni test results in R?

I'm having trouble understanding how to interpret the results of the Pedroni test of cointegration in panels. I'm using the pco R package. I call the function like ...
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### Multilevel modelling and cointegration, can the two methods be combined?

I am an epidemiologist, but not a statistician. I have a good enough handle on longitudinal multi-level models to push through the material and publish a paper, but my knowledge of all possible ...
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### Johansen test for cointegration - how to find model given test output?

Suppose we are working with three I(1) variables and that the result below is the Johansen cointegration test: Unrestricted Cointegration Rank Test (Trace) Hypothesized No. of CE(s) Eigenvalue Trace ...
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### define the constraints for the 3 cointegrating relationships

I want to do a VECM with the following variable: log(number of international students), log(total domestic enrollment), log(RGDP), dxy, log(labour supply), log(government expenditure on education). ...
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### A VECM in logs or a ARDL in the first difference of logs?

Suppose I have a number of time series that appear to have exponential growth at similar rates, with errors I believe to be generally proportional to the level of the variable. I believe that one of ...
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### What critical value should you take to test for cointegration at 5% significance in the Engle-Granger residual-based test?

I am trying to test cointegration relationships between several pairs of stocks, two at a time (all integrated of order 1). First I run the linear models yi=a+byj+e1 and then the reverse yj=a+byj +e2. ...
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### choosing which cointegration model to use

I need to run a cointegration test on some foreign exchange rates. I am looking to use the Johansen test. I used to have a Matlab account & the model I used was called H1 & the definition is ...
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### The Lag in johansen test and VECM

For VEC I used the same lag that I used in johansen test and Instead of use the same lag of johansen, my friend did a lag exclusion wald test. Is that correct? can I change it?
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### Interpretation of cointegrating equation

I have big and positive coefficients, so I don't know if it's correct and if it's a problem. I did the Engle-Granger test and found cointegration and did Johansen and found cointegration too.
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### VAR or VECM for I(0) e I(1)

I have 5 series, four nonstationary series and one stationary series.I tested each pair using Engle-Granger (x1,x2),(x1,x3),(x1,x4); (x2,x3) (x2, x4); (x3,x4) and found cointegration only in x2->x4,...
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### Unable to show cointegration between two lagged sine waves with statsmodels cointegration function, why?

When using the statstools cointegration function to test for cointegration with default parameters between two sine waves with a 1 period lag, coint() returns that ...
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### Testing for Cointegration with Dummy Variable (for outlier) in Cointegrating Equation

I have two time series $y_t, x_t$ which are both $I(1)$. I am following the 2-step Engle-Granger approach for testing cointegration between the two series. However, for known reasons, I also want to ...
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### Does the probability of detecting cointegration increase as more collinear variables are considered?

I am scanning for a cointegrating relationship between the asset value of a portfolio and macroeconomic factors. The engle-granger test produces very few significant results when testing for ...
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### can two AR(1) processes be cointegrated

Let $Y_{t}$, for $t=1,2, \dots$ be AR(1) process. $$Y_{t+1} = c_{1} + \phi Y_{t} + \varepsilon_{t}$$ Next, assume that for some $X_{t}$ we have $$X_{t} - \beta Y_{t} = u_{t},$$ where $u_{t}$ is ...
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### Intuition of Condition of (weak) Stationarity in multivariate case

This may be a duplicate. I am trying to get an intuitive idea about the condition for stationarity. I think I got a fair idea of stationarity as a concept (from this and other sources on internet) but ...
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### If $y_t$ and $x_t$ are cointegrated, then are $y_t$ and $x_{t-d}$ also cointegrated?

Assume that $x_t, y_t$ are $I(1)$ series which have a common stochastic trend $u_t = u_{t-1}+e_t$. Particularly, consider the following DGP \begin{align} y_t&=\alpha_y+u_t+a_t \tag{1} \\ \end{...
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### Seasonality and ECM/VECM - Correct seasonality before estimating VECM

I know that for univariate framework, a typical process to deal with seasonality is : detect correct (for instance, withdraw seasonal factors) forecast re-seasonalize the forecasted series (for ...
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### Interpretation of intercept term in ECM

Suppose two $I(1)$ series $x_t, y_t$ are cointegrated. Therefore $\mu_t$ in following equation is stationary: \begin{align} y_t = \beta_0 + \beta_1x_t + \mu_t \tag{1} \end{align} Now consider the ECM ...
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### Heterogeneous panel Granger causality for cointegrated data based on VECM?

I am currently doing a project on the link between transportation and economic growth. Particularly, am interested in the potential heterogeneoua nature of causality relations across regions. However, ...
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### Struggling with some intuitive reasoning when regressing an I(0) variable against an I(1) variable

Say we regress a noisy variable $y_t$ (i.e. $I(0)$) against a non-stationary variable $x_t$ (e.g. $I(1)$) as follows \begin{equation} y_t=\beta x_{t}+\varepsilon_t \end{equation} Then naturally the ...