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

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VECM, positive loading coefficients of EC terms?

I am looking at two very similar time series (correlation is about .997) - two commodity price series. Johansen coint. test indicates 1 coint. relationship for case 1 (no trend and no intercept) and ...
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1answer
43 views

Help understanding how the cointegration equation for VECM models are derived

I am learning about Vector Error Correction Models from Sean Becketti's "Introduction to Time Series using Stata". While I know how to run the Stata commands to estimate the VECM, I have no idea why ...
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23 views

Vector autoregression (VAR)

In a VAR I use two price-variables which are co- integrated. Is that a problem, the literature is somewhat mixed? With three lags there are no problems with serial correlation between them ...
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1answer
18 views

Johansen's test of cointegration on a subset of variables

I am trying to find cointegrated relationships between N variables. However it could be possible that only M of them are cointegrated where M < N. If I use standard Johansen's test on N variables ...
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1answer
106 views

Test for cointegration between two time series using Engle–Granger two-step method

I am seeking to test for cointegration between two time series. Both series have weekly data spanning ~3 years. I am trying to do the Engle-Granger Two Step Method. My order of operations follows. ...
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71 views

Johansen Test in python

How to get the trace statistics from the Johansen test for cointegration in python. Also, i tried to search it myself on google, found the following website ...
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56 views

Estimation of VECM via ML and OLS

Take a vector error correction (VECM) model: $$\;\;\;\Delta y_t=\Pi y_{t-1}+\Gamma_1\Delta y_{t-1}+...+\Gamma_{p-1}\Delta y_{t-(p-1)}+\varepsilon_t$$ where $\Pi=\alpha \beta'$ and each row of ...
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40 views

Question on Stationary & Cointegration Test (Augmented Dickey Fuller & Engle Granger test)

I'm performing the stationary and cointegration test on stock prices. What I'm confused is 1) the difference between ADF stationary test and ADF cointegration test. 2) Also, in ADF stationary test, ...
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41 views

How to interpret standard errors and t-values in error-correction terms?

When estimating a Vector Error Correction (VEC) model in EViews, the resulting output always shows the error-correction terms together with standard errors and t-values for the included variables, and ...
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91 views

Modeling an I(1) process with a cointegrating I(1) and an I(0) variable

A colleague says that estimating the following time series model is statistically sound: $$y_t = \beta_0 + \beta_1 x_{1t} + \beta_2 x_{2t} + e_t$$ where $y_t$ is nonstationary $I(1)$, $x_{1t}$ is ...
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109 views

OLS versus ML estimation of VECM

A vector error correction (VECM) model has an equivalent vector autoregression (VAR) representation. (VECM) $\;\;\;\Delta y_t=\Pi y_{t-1}+\Gamma_1\Delta y_{t-1}+...+\Gamma_{p-1}\Delta ...
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35 views

Cointegration with dummy variables?

Let's say I'm interested in the relationship between poverty (measured by some continuous variable) and different types of financial reforms (which are dummies). Given this does it make sense to ...
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47 views

Engle Granger Matlab Cointegration

I am struggling in the interpretation of a cointegration test I did on 2 stocks. I would be grateful if you could eventually tell me if I am wrong somewhere. So I am trying to analyse the ...
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21 views

cointegrated vectors in continuous time

I am working on a problem where I am looking at two cointegrated stocks and their associated stochastic differential equations (SDEs). I have read a lot of the papers on cointegration, but they all ...
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1answer
70 views

Understanding $O_p$

One thing I feel like I have never mastered is the concept of $O_p$ convergence and how to use it. I understand the basic idea and what bounded in probability means, but I always have a hard time ...
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23 views

cointegration analysis for different level stationary series

I have a data set of of three variables: imports, exports and GDP. The import variable is I(1), but the export variable is I(1) only for constant and constant and trend but not for none. Similarly, ...
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1answer
98 views

Cointegrated Vector ARMA (CVARMA) Model vs. Dynamic Factor Model (DFM)

Two questions regarding the equivalence (or lack thereof) of vector error correction model (VECM) cointegrated vector ARMA model (CVARMA) and dynamic factor model (DFM): Can every VECM CVARMA be ...
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49 views

Maximum lag length in cointegration?

I've got two conflicting answers when I search the internet for my question. Since cointegration is sensitive to maximum lag length, it is important to choose maximum lag length wisely. According to ...
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35 views

Cointegration verses GMM in dynamic panel data

I would like to know the situations under which one prefer cointegration over GMM or GMM over cointegration in panel data. Review of literature suggests that cointegration is usually applied when T ...
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30 views

Is it appropriate to run the Error Correction Model on data which are not I(1)?

I have intraday data (frequency = 1 min.) for 6 stocks and 1950 observations per each time series. I checked stationarity for the level data and first difference and it appears that: 5 stocks's ...
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43 views

VECM “goodness of fit” in R

I'm using ca.jo in R to perform the Johansen test on a given dataset. I obtain my VECM coefficients, cointegration rank, etc. However, it does not seem to give any notion of "strength of ...
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31 views

Running an AR(4) model based on engle-granger cointegration results

I have the below results based on the engle-granger test for cointegration, where the dependent and independent variables themselves are not stationary. The results show that null (process is not ...
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VECM Diagnostic Test

I have got few questions about VECM and cointegration test. Basically I conducted a cointegration test on two time series (spot vs forward price) by using the Johansen procedure. The results suggest ...
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39 views

What does “degrees of freedom” mean in the context of cointegration?

I recently read a paper where the author says they used cointegration "with two degrees of freedom". What does degrees of freedom mean in this context?
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34 views

Cointegration between two stationary processes

I have two stationary time series. I would like to check for cointegration between them. Does this make sense, and can I just use Engle-Granger Test (two step) for Cointegration for this?
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1answer
31 views

Stationary processes I(0) cointegration, does it make sense?

I'm looking at two time series and I would like to determine how they move together. They both are however stationary. Would it make sense to test for cointegration? Linear relationship between both ...
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219 views

Getting cointegration vectors using Johansen method

I'm trying to understand better Johansen method so I developed an example 3.1 given by the book Likelihood-Based-Inference-Cointegrated-Autoregressive-Econometrics where we have three processes: ...
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Inference from a sometimes-random time-series

Let's say we have two cointegrated time-series, $Y_{1}$ and $Y_{2}$, and I want to assess the causal impact of $Y_{1}$ on $Y_{2}$. There is good reason to think that both variables are influenced by a ...
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228 views

Interpreting vecm result with 4 cointegrating equations

I have performed Johansen cointegration test and the result shows that I have more than one cointegration for all my models. Below is the cointegration test result for one of my models (I have 6). ...
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69 views

Interpreting the Johansen cointegration test output

I am running the Johansen cointegration test using 2 non-stationary time-series, as suggested by the literature. The output I got is the following: ...
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2answers
106 views

Why does ca.jo has a minimum lag order of 2?

I am trying to use urca library to do cointegration test, and its function ca.jo, which conducts the Johansen procedure on a given data set. I think a lag order of 1 is possible for a cointegrated ...
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30 views

Long-run cointegration and I(2) variables

I'd like to run a test for long-run cointegration of two time series: CO2 emissions/capita and energy use/capita in China. My data includes 23 observations for years 1990-2012. Now as far as I know I ...
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106 views

Why is there a need to do OLS regression of VECM?

I am trying to use the R package urca. It has functions cajorls and carools, which do OLS regression of restricted and unrestricted VECM respectively. Both functions take in the VECM estimated using ...
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590 views

Cointegration - same thing as stationary residuals?

So I'm aware that cointegration means there is some linear combination of the set of variables that is stationary. So, if you do a regression and find stationary residuals, can you just immediately ...
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57 views

Time Series Econometrics: Cointegration methods for series with mixed degree of integration

I am performing a time series analysis on dataset ranging from 1974-2008. I have performed Augmented Dickey Fuller tests and Phillips Perron tests to check the stationarity/ order of integration of my ...
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1answer
27 views

Explanation of order of integration in the context of cointegration

Please explain the meaning of 'order of integration' when talking about cointegration. An explanation with some examples would be great.
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213 views

structural breaks in time series using matlab

in a plot of my time series there is clearly visible that there is structural break, but I have to find the exact date. I want test this with the chow test. Although I understand how to perform this ...
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clarification Johansen cointegration matlab

To my understanding the Johansen cointegration test, will test first if the time series have zero cointegrations, if rejected, the Johansen test will test for one cointegration, if rejected, it will ...
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38 views

Transforming time series of different time horizon to stationary

I have a list of monthly time series data with different time periods and different order of integration. I want to transform them all to stationary and a same time period. I noticed that the order ...
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1answer
36 views

Test statistic distribution in a cointegrating regression

Let's assume I have a simple cointegrating regression of the type $$y_t=\beta_0+\beta_1x_t+\varepsilon_t$$ $y,x$ are $I(1)$. If testing the OLS residuals I find that $y$ and $x$ are cointegrated, ...
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Is there a way to “regularize” the Johansen cointegration test?

I'm using a Johansen cointegration test to check for cointegration among a large number of time series. I've found that while the eigenvectors look great in-sample, the cointegrating relationships ...
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41 views

Johansen's cointegration test and multicollinearity

Which variables to use when running Johansen's cointegration test? levels or the differenced? How can I better detect and avoid multicollinearity before running Johansen's cointegration test?
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112 views

Pairs Trading: What statistics to use for analysis of Cointegration using ADF Test?

I have just begun to study Pairs Trading strategy as a part of my assignment for an internship. My purpose is to analyse any two stocks/commodities for possible co-integration. I made a VBA code where ...
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what if I know my time series are cointegrated over a long period but not over a short period?

I am regressing time series on time series. I have tested for cointegration on the entire time sample (3 years) and the series are cointegrated. I need to make a rolling window of regressions (to ...
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cointegration with time trend and binary variables

I have an equation composed of one explained variable and three explanatory variables, which are all non-stationary. Is it possible to add for the equation another two variables: a time trend and a ...
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1answer
63 views

How to test if time series are not cointegrated?

Is there a test whose null hypothesis is that time series are cointegrated? There are lots of tests whose null is no cointegration. How can I calculate a p-value for the null that two series are ...
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21 views

High correlation will help detect spurious regression over cointegration?

I'm analyzing two financial time series with Johansen method. A high Correlation coefficient using the Pearson method will help me to detect spurious cointegration models to avoid? If this is not ...
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how to do conditional forecasting with cointegration model?

I'm confused about multistep forecasting from VECM model for 2 cointegrated series. The model is pretty simple, in error-correction form: $$ \Delta x_{t+1} = \alpha_1 (y_t - \beta x_t -\beta_0) ...
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99 views

What's the practical difference between the Johansen vs Engle-Granger tests for cointegration?

For the two-variable case, what are the practical differences between using the Engle-Granger procedure versus the Johansen test for cointegration? Is one universally more powerful than the other? ...
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174 views

Where can I find ADF test library or source code from c#

I would like to test for stationarity in cointegration. I intend to use an augmented dickey fuller test. However, I need one for c# - either a library or the source code. Or is your have source in a ...