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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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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Choosing Cross-Sections for Panel Data

I'd like to ask, how do I pick how many and which cross-sections to use for Panel Data analysis? I want to look for cointegration among some variables and run panel VAR/VECM on annual data from 1990-...
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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 ...
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Linear Regression of Two Non-Stationary Series

I am working with two time series that are non-stationary. I would like to regress one to another (Y = Global Temperature Anomalies, X = C02 emissions) to see the relationship. However, I was ...
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VAR or VECM Model?

If I have 4 variables in a model and I want to check for causality between the two variables say X and Y. These two variables are not cointegrated based on Engle-Granger Residual test for ...
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Interpreting the results of the Johansen Cointegration test

This has been asked a few times before, but no answer was in my opinion satisfactory. My test also contains more details than in other question. After using the Johansen test for two time-series in ...
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How to Approach VAR with Stationary Variables

I've got 3 variables and all of them seems to be non-stationary but when I take first differences they are stationary. My aim is to create a VAR with three of them and I'm not sure if I put them as ...
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Unit root testing and cointegration when using first differences

I am working with a panel dataset with N=100 (countries) and T=20 (years) and tested for unit root and found that my data is non-stationary. I therefore conducted the unit root test for first ...
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Cointegration: Long vs Short Run

I am running an ECM model that has one cointegrating vector but two stochastic trends within the cointegration vector ex.(1, -1, 1). Can I use the cointegration vector inside an error correction model ...
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Bivariate cointegration in a multiple regression error correction model

I am new to cointegration and ECM. I have two I(1) variables that I have estimated and their linear combination is I(0) as per the Engle-Granger test. Is it then possible to use this error-correcting ...
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170 views

What is the difference between ECM and VECM and when to chose one over the other?

I hope you can help me concerning the following question. It is mainly about when to use ECM or VECM. Suppose i have two time series of daily stock prices from Company Y and X and regression a ...
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28 views

Co-integration Regression

When running a co-integration regression, can I add other variables quantitative and/or dummy control variables in? If so, do they need to be I(0)?
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First-differences regression of a cointegrating system: forecasting and interpretation

I am working with a time series regression. In particular, both my dependent and independent variables are I(1) and they are co-integrated. I was wondering the following: If I run a regression with ...
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Lag length for a VAR model

I am working on 2 time series Sentiment and Return(from stock). They are daily data excluded weekend. Both are stationary at I(0). Lag lengths for Sentiment is 22 and Return is 2. What lag length ...
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Cointegration/GPH test

I am quite new to R and statistics. I want to test two time series with the GPH test for cointegration. For this I use the package LongMemoryTS and the function gph:...
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Most general definition of cointegration

I am looking for a rigorous and general treatment of cointegration. Unfortunately, many of the econometrics textbooks and papers I have found in this area either place a lot of restrictions on the ...
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(A,B) is cointegrated while (B,A) is not cointegrated

I'm using the Engle Granger Cointegration Method to analyse stocks and do some pairs-trading studies. While some pairs (stock A, stock B) are cointegrated with a p-value < 0.05, sometimes (stock B, ...
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Log - Log Regression in Non-Stationary Cointegrated Time Series

I want to develop the following model: $$\log{Y(t)} = \alpha + \beta_{1}\log{X(t)} + \beta_{2}D(t)$$ where $Y\in\mathbb{R_{\gt 0}}$, $X\in\mathbb{R_{\gt 0}}$ and $D\in\{0,1\}$ is a dummy variable in ...
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What is the range of plausible values of the loading matrix (alpha) in an error correction model?

Assume you have k cointegrated time series $Y$. You want to estimate a VECM and have figured out a suitable lag order p, cointegration rank r and the normalized cointegrating vector $\beta'$. You ...
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108 views

Meaning of two cointegrating vectors in a VECM

Given three I(1) time series, what does it mean to have 2 cointegrating vectors inside the error correction term? As mentioned in the below image, cant we merge ...
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70 views

Getting understand error correction model

I have several intuitive problems with error correction model. I will write below how I understand derivation of ECM model with my queries. Let $I(y_t)=I(X_t)=1$ and consider model : $$y_t=\alpha_0+\...
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(Panel or time series) cointegration including one lagged variable

I have conviction that one of the variables in my vector can affect the rest only if it is lagged. For example, lets imagine a agriculture product which is planted in April of the previous year and ...
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coint_johansen test results

I am running the coint_johansen test (Python) on stock data of 3 different banks. The results im getting are the following: Trace statistics: ...
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127 views

ARDL model as remedy for spurious regression?

Suppose there are two non-stationary time series of integrated order 1. The two time series are not cointegrated. According to conventional econometric theory, "In general, regression models for ...
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102 views

VECM representing an I(0) system?

I am referring to Johansen (1991) where he considers a $p$-dimensional autoregressive process of order $k$ $$ X_t = \sum_{i=1}^{k} \Pi_i X_{t-i} \ + \ \epsilon_t \tag{1}\label{1} $$ written in vector ...
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bounds testing (Pesaran, Shin, and Smith)

This deals with cointegration in the context of Pesaran's ardl models. Specifically it deals with bound testing. It is not clear to me if you have to build an error correction model from your data (...
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Fitting a VAR model with nonstationary data and possible cointegration

I have time series data from multiple realisations (trials) of the same process in the shape (n_trials, n_sensors, n_times) which I would like to fit a vector ...
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187 views

Getting simple ECM Model from VECM in tsa python

Can I get a simple Error Correction Model of the form $$ Y_{t}-Y_{t-1}=\theta _{1}\Delta X_{t}+\theta _{2}(Y_{t-1}-\alpha X_{t-1} - \beta)+\epsilon _{t} $$ using the statsmodels.tsa.vector_ar.vecm....
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Cointegration testing; order of the pantula principle?

In my times series course we learnt about using the Johansen Procedure to determine, if there are cointegrating relationships within a VAR model. My teacher gave us a function to implement it in R. ...
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Cointegration tests, what if Johansen trace and eigenavalue tests disagree?

I have run a both Johansen's trace and eigenvalue test to determine if there is cointegration in my set of variables. But surprisingly they seem to disagree. Specifically the trace test suggests r = 2 ...

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