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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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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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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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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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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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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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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106 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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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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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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How should I treat a binary variable for VAR/VECM?

I have a binary variable (2 values) and I plan to implement a VAR/VECM model. The model aims to focus more on how a change in this binary variable affect the other variables in the system rather than ...
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Is logged data considered level data?

Hi I'm new to VECM/VAR models. I read that we can use VECM when data is non-stationary at level but some form of cointegration exists. By "level" does it mean it has to be the raw data? Or ...
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Hypothesis testing on cointegration vector

I am studying cointegration theory in time series using online resources. As per https://www.econometrics-with-r.org/16-2-ooiatdfglsurt.html DF-GLS test is implemented in the package urca can be used ...
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Is the Python Johansen cointegration test trustworthy?

I'm trying to learn how to do Johansen's cointegration test. I am using the Python's "statsmodels.tsa.vector_ar.vecm.coint_johansen". I have run 10 tests, each with 5 series. All series ...
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What's the relationship between cointegration and linear regression?

If two non-stationary processes are cointegrated, that means a linear combination of the two processes are stationary. In a simple linear regression, we have the model form: $y = b_0 + b_1x + e$ If ...
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How to correctly pre-whiten time series

I'm trying to find cross -correlation between two-time series and as it so happens, they are auto-correlated(2), nonstationary and co-integrated. As I read about them, it appears that pre-whitening ...
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What is the use of cointegration?

From what I have briefly read, seems like cointegration is used to determine if there is a statistically significant relationship between two unit root processes (as opposed to spurious correlation). ...
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1answer
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Question about latent variables in Co-integration Regression

I have a question about cointegration regression models as follows: Is it common to have latent variables or regressors with measurement error in the cointegrating regression model? Is it highly ...
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Bivariate Cointegration Test using Johansen Test

I am currently working on my final thesis on the subject of pairs trading and have to carry out a large number of cointegration tests. The reason for this is that I want to compare 100 foreign shares ...
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Relationship among futures, options and stock prices [closed]

I have the data of past 10 years of NIFTY (the National Stock Exchange of India) stock, futures and options and I want to show the lead-lag relationship (which reacts first, futures, options or stocks)...
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What is the right model structure for spike-and-diminish feature?

I am asked to build a model for detecting anomalies/monitoring the usage of some machines. The x-axis is time in minutes, and the y-axis is the resource usage of a machine (you can think of something ...
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Is there such a thing as a Vector ARDL model? ARDL (AutoRegressive Distributed Lag) vs VAR (Vector AutoRegressive)

Question 1: I am confused with the difference between ARDL and VAR. If VAR only allows for modelling of I(0) variables and variables are required to have the same lags in the model (i.e. each equation)...
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Co-integration test using aTSA package in R

I am learning more about co-integration test. I would like to compare two series: one that has the return and the other one that has a price. I used the aTSA package, and got the following result: <...
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Understanding the output from the Johansen Cointegration test in R

I have a VECM model that Im using to determine the revenues for a firm, based on factors like Interest rates, S&P 500 and company specific variables, as follows: Stage 1: $$z_t= a+ bX_t+e_t$$ ...
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38 views

Should I use a ARDL if I have more than one cointegrating relationship?

I have a four time series variables. They are a mix of I(0) and I(1) variables. There is also more than one cointegrating relationship among the variables. If there is more than one cointegrating ...
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Looking for the right model of non-stationary asset market variables

I need help finding an appropriate model given the below criteria. Objective: to derive fitted value for front-month gold futures prices (dependent variable) based on cross-asset market independent ...

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