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

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R: fractionally cointegrated vector autoregressive model with error correction

I can find packages for VECM (vars,urca, tsDyn) but I cannot find: fractionally cointegrated vector autoregressive model with error correction (FVECM). There is a package in MATLAB that deals with ...
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1answer
53 views

Confusion about cointegration for AR(M) model

I have a question regarding the concept of cointegration. Does the concept of cointegration apply to any model? Or it only applies to OLS? For example, I fit an autoregressive error model, AR(M) ...
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84 views

Panel regression and unit roots

I am trying to figure out how to alter my panel regression in a case where unobserved heterogeneity exists and one (or both) of the variables are I(1) processes (or in other words contain unit root). ...
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19 views

Testing for cointegration given a priori restrictions

I have a time series variable $y_t$ which I forecast $h$ steps ahead. I do that a number of times using a rolling window so that I collect a total of $T$ forecasts which form a time series ...
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17 views

Relation between raw and central moments

This question arose when reading Johansen's likelihood-based inference in cointegrated VAR models, the 2009 reprint, page 146. I will do my best to make my post self-contained. Let $Z_{0t}=\Delta ...
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1answer
20 views

Cointegration of two $I(0)$ plus $T$

I have two series that are $I(0)+T$, and I wonder if I can consider cointegration relationship between them. $x$ is $I(0)+T$ and $y$ is $I(0)+T$. The Johansen test tells that $x$ and $y$ are ...
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1answer
39 views

Stationarity requirements of using regression with ARIMA errors - ROUND 2

Referring to this Post: What are the stationarity requirements of using regression with ARIMA errors for inference? I would like to seek a confirmation of the below practice: The situation is as ...
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1answer
29 views

analysis after Gregory-Hansen cointegration test

I have two time series which fail E-G cointegration test over the whole sample, but G-H cointegration test indicates the presence of cointegration when regime shift is allowed. Can I set up a dummy ...
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39 views

Cointegration ratio using R for pair trading [closed]

I am hoping to do pair trading using R. To do that, I have to calculate the cointegration ratio between the two stocks. How can I obtain this cointegration ratio using R? For example, I am going do a ...
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14 views

Johansen test with ARCH and non-normality

I am testing a cointegration between two variables using Johansen test and VECM framework (2 variables, optimal lag length selected by AIC/BIC/HQC on VAR). Johansen test indicates existence of 1 ...
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41 views

Timeseries forecasting (Cointegration)

I am trying to forecast commodity price fluctuations in a small dataset. The data I am using is here . Does my data have seasonality and Trend? Can someone explain me how to decide that? If my ...
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25 views

Unit root and cointegration in Panel Data

What should I do when I found out that my variables are stationary in first differencies? Should I estimate model in differencies? How unit root is related with cointegration? Thx for answers.
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1answer
38 views

Are linear processes stationary?

I am reading Soren Johansen's book on cointegration and I'm wonder about the following definition: Definition 3.1. A linear process is defined by $Y_t=\sum_{i=0}^\infty C_i\epsilon_{t-i}$, $t=0, ...
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1answer
72 views

How to test for serial correlation and ARCH effect in R package tsDyn?

I recently started playing around with the tsDyn package for R and successfully used it to estimate a bunch of VEC models and print their impulse responses (IRF) and error variance decompositions ...
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16 views

Interpretion of results in the Johansen Procedure

I get the following output from a VECM with two variables (produced by ca.jo function in vars package in ...
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1answer
52 views

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
85 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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35 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
24 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
418 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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242 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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1answer
89 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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1answer
85 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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1answer
98 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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2answers
192 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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153 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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1answer
43 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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80 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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27 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
71 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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29 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
117 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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1answer
70 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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43 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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36 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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57 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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43 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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77 views

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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1answer
42 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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1answer
45 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
35 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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1answer
411 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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29 views

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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366 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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78 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
118 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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44 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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1answer
115 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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2answers
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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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65 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 ...