Questions tagged [vector-error-correction-model]

VECM stands for Vector Error Correction Model. It is used with cointegrated time series and panel data in finance and macroeconometrics. VECM offers a convenient representation of a cointegrated VAR model as it distinguishes between short-run and long-run (equilibrium) effects.

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Johansen procedure shows cointegration r=1, but ect is not significant?

I have 6 variables, all of them I(1). I tested for cointegration and got a significant result for r=1, so I decided to estimate a VECM. The problem is now that the ECTs of the VECM are not significant....
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Eigenvalues of Johansen Trace Test

I'm currently taking a course in time series and have been struggling with understanding the Johansen trace test. Specifically, the calculation of the eigenvalues for the Likelihood ratio statistic. ...
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Johansen Cointegration Test at Levels or First Differences in a VAR Model

I have multiple variables that I am trying to perform a VAR model with, but all my variables are non-stationary at levels as they fail the Augmented Dickey Fuller test. Having taken the first ...
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VEC model to VAR model transformation in R

I need to transform my VEC model (function VECM() from tsDyn package) into VAR model to be able to estimate Granger causalities. In the first step I need to estimate VEC model. In the second step I ...
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How to impose restrictions on VECM model in R?

Good afternoon! I want to estimate VECM in R and I have a question. Consider an example. I want to estimate a 4-variable VECM model with restrictions: $$ \begin{bmatrix} \bigtriangleup x_t \\ ...
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VECM in R: how to add differenced lags? [closed]

Good afternoon! I want to estimate VECM in R and I have 2 questions: For instance, I want to estimate a model (in vector form): $$ \bigtriangleup y_t = \pi_1 y_{t-1} + \pi_2 y_{t-2} + A_1 \...
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How to approach insignificant coefficients in time series?

Let's say we have an ARIMA model. The series is stationary, autocorrelations significant etc. However, the p-values of the coefficients suggest that the coefficients are insignificant. Now, I've heard ...
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Does a lower AIC imply better forecast RMSE for time series models?

In my application, I am using the VECM function of the tsDyn package in R to fit 4 I(1) processes. Using the Johansen's test, I have identified for 1 cointegrating relationship. I have made use of the ...
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Can second order differences stationary series be estimated via VECM model without considering support from economic theory?

Because some series contain negative raw data, and data is normalized by MinMax. Can VECM be used after second-order difference where the series are stationary? If can, whether the number of lagged ...
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Cointegration equation from VECM with rank=1 is same as OLS result?

In Engle-Granger 2-step ECM model, if there are cointegration relationships then OLS result(1st step) shows a long-run relationship between variables. Short-run relationship is expressed by ECM(2nd ...
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Optimal lag length in VAR/VECM: IC or Residual test?

I read so many answers in here that I should use IC(information criteria) to determine the optimal lag length in VAR/VECM. But also it is important to check the residual of VAR/VECM has no-...
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What is the difference between ECM and VECM?

From what I understood, ECM is for two variables and apply OLS to estimate EC term and VECM is for multi-variables (vector form) and apply VAR to estimate EC term. But as I read other papers, I think ...
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Practical questions about cointegration test

I have a few questions about Johansen's cointegration test. I learnd that all variables must have the same order of integration for cointegration test. Suppose there are 5 variables for one is I(0) ...
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Simplified Version of the Error Correction Model

I have to solve an exercise on Error Correction Models and cointegration, but I'm having a bit of trouble in understanding what I should do. In the previous line, we have concluded that the two ...
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What is the speed of adjustment for two cointegrating vectors?

I have estimated a VECM model in EViews and using Johansen test I obtained that there were cointegration vectors. The output for short-run equation of VECM contains two error correction terms and I ...
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ADF test estimates -0.01 delta, but the p-values are less than 0.05

I am dealing with two datasets of Annual growth Production Cost, and Annual growth Inflation. A lot of problems have arisen, but the most annoying one is referred to integration. At first sight, both ...
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Including dummy variables in VECM using Oxmetrics

I've encountered a problem when doing rank test for an Vector Erro Correction Model using CATS. I'm looking at the relationship between the variables in the Purchasing Price Parity theory, especially ...
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What is the coefficient that shows whether there is a positive or negative relationship between variables in vector error correction models?

I am trying to estimate the long-run and short-run relationship between variables. Based on the Johansen cointegration analysis it was concluded, that there is one cointegrating relationship. The next ...
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Vector error correction and impulse-response functions only when error correction terms are negative?

I have used VEC models with two variables and have estimated impulse-response functions (IRFs)from them. I am testing two theories, and each variable is the dependent variable for a corresponding ...
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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 ...
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Include exogenous variable in both level and first-difference

I am wondering if I could include, in a VECM, exogenous variable in both level and first-difference, such as : $\Delta X_t = \alpha \beta^{'} X_{t-1} + \Delta X_{t-1} + Y_t + \Delta Y_t + U_t$ Is ...
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Stationarity condition for a vector error correction model

Consider $n$ time series stored in an array $y_t = \begin{pmatrix} y_{1,t} \\ \vdots \\ y_{n,t} \end{pmatrix}$, assumed to follow a vector error correction model: for some matrix $\alpha \in \mathcal{...
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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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Intercept in 2nd-stage Error Correction Model (ECM) regression -- yes or no?

When doing a two-step ECM regression, do we add an intercept in the 2nd stage regression? I've seen course notes that add an intercept in the ECM, but some do not, so I'm confused if I should include ...
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What is the intuition behind orthogonalized Impulse-Response Funtions?

Daer All, I have a questions concerning IRFs (impulse-response-functions) in a VAR Framework. More specifically it is about orthogonalized IRFs. My general understanding is that IRFs in a bivariate ...
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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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VECM terms of variables

I have estimated a VECM model of 4 endogenous variables and 3 exogenous, before solving my model, I would like to introduce another variable (endog, let's say (X)) which is calculated with a formula ...
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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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Choosing VECM or VAR

I am currently investigating the relationship between S&P 500 Spot and Future prices. Thes series contains daily closing prices of the past 4 years. Checking the residuals via a regression of the ...
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State space representation of VECM-GARCH

Can someone help me write a state-space representation for the VECM-GARCH model to estimate the time-varying parameters using Kalman Filtering in Matlab? I am struggling with specifying the GARCH ...
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Estimating Moving Average Impact Matrix after running VECM

How to estimate moving average impact matrix after running VECM model in R? It is given as $ \hat{\beta_c}( \hat{\alpha_c}$ $\hat{\Gamma}$ $\hat{\beta_c}$)$^{-1}$ $\hat{\alpha_c}'$, where $\alpha$, $\...
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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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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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Can a restricted VECM be expressed as two ARDL equations?

I'm currently working on a model where I have two variables that are cointegrated. The issue is that, whilst they are cointegrated (based both on intuition and tests), the relationship is lag-heavy. $...
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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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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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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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Stepwise Regression for VAR or VECM Models

I'm doing an analysis of integrated price series for two different types of crude oil. These crudes are priced off a differential to a main type ("marker"). I built an exogenous variable ...
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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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Covariance matrix computation VECM, Lutkepohl (2005) p.287

In Lutkepohls book "New introduction to multiple time series analysis" (2005) on p.287 is outlined how to calculate your estimated parameters $[\hat \Pi,\hat \Gamma]$ sample covariance ...
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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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VECM - Impulse reponse function - statsmodels - AttributeError: 'lr_effects'

I am using statsmodels version '0.11.1'. I am trying to sum cumulative effects of using the impulse response function derived of a VECM, but I am getting an AttributeError regarding 'lr_effects'. As ...
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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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Good resource on ECMs/VECMs?

I am trying to understand ECMs and VECMs and what the relationship between a regression model with stationary residuals or time series errors. Is there a good website/book that goes into the ...
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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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Granger causality over VECM (unknown possible problem in data)

I have data with 4 variables GDP, foreign debt, export (all in nominal values), and exchange rate. Each of those are I(1) (the difference is stationary). The four variables together are cointegrated ...
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