Questions tagged [ecm]

Error Correction Model

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Help needed with ARDL Bounds Approach

I hope you are doing ok amidst this global pandemic. I'm currently working on this research using the ARDL Bounds approach. My (to a degree self-imposed) "task" is to study the relationship ...
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16 views

Derive Error Correction model

How can I derive The extended version of ECM as follows $$\Delta y_t= \sum_i^{p} \Delta \alpha_i y_{t-i} +\sum_i^q \beta_i \Delta x_{t-i}+\gamma u_{t-1}+e_t$$ I know that ECM can be derived by using ...
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14 views

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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Why is the error correction term equal to the lagged dependent variable in ARDL unrestricted error correction?

Why is the error correction term equal to the lagged dependent variable in ARDL unrestricted error correction? I´m very poor at algebra, so try to explain as simply as possible thanks.
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12 views

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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60 views

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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1answer
284 views

Does Normality of a Time Series imply Stationarity and Viceversa?

I have a theory question which never became completely clear to me. Reading Hamilton (1995) I understod that the stationarity requirement for time series data stands as the normality requirement for ...
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1answer
35 views

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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1answer
38 views

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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1answer
506 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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1answer
145 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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14 views

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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39 views

positive Error correction term, what could be wrong

here is the basic regression: log(Robots per capita)~share of midage+share of older+log(gdp) I obtain good results but all my variables are unit root. So I tried correcting this doing the following. (...
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1answer
32 views

Cointegration in error correction model with only one nonstationary variable

I have three time series variables, two variables are stationary and one is non-stationary. Can we still search for the cointegration and use the error correction model or should I take the first ...
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1answer
64 views

Can an ECM be built such that new regressors enter in Stage 2?

If I have an ECM such that there are 2 cointegrated variables, $Z_t\sim I(1)$, $X_t\sim (1)$, and the equation in levels is $Z_t=a+bX_t+e_t$, $e_t\sim I(0)$, can I add other regressors to the 2nd ...
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106 views

Interpretation of ECM coefficients

Say that we are regressing consumption $C_t$ on time $Y_t$. Furthermore, suppose that both series are $I(1)$ and are co-integrated. Given this, we set up the error correction model (ECM) as follows: $...
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66 views

Queries on Interpretation of Vector Error Correction Model

I am trying to understand the Vector Error Correction (VEC) Model properly. I have been trying to read from several sites, went through the Chapter in Chris Brooks. But with different sources, the ...
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90 views

Cointegration, Error Correction, and ADF test with lags

I am fitting an error correction model (ECM) of two I(1) variables. I'm following the Engle-Granger approach of first finding the cointegrating relationship. So first, I regress one series against the ...
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71 views

Eviews- Error correction estimation using BDM's one-step procedure

I am trying to estimate an equation for the average wage using quarterly data. I want to build an ECM which can bes estimated using Banerjee-Dolado-Mestre's approach to cointegration. So far, I haven'...
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127 views

Error Correction Model (ECM) procedure

I am getting familiar with ECM so I would like to ask for help in order to understand it. My goal is: performing a ECM in a multivariate context. I was reading ECM is part of a Cointegration analisis....
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12 views

Difference of Rates in ECM

I am setting up a model to predict something using Error Correction Model (see pic. to get a general view about the model itself). Some of my $X$ variables are the interest spread between the A and B ...
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36 views

Can I treat the sum of the coefficients of a variable in the Error Correction Model as total short-run effects?

I am working on a project that uses ECM model to inspect the short-run dynamics of money supply (m(t)) to loans (l(t)) since both variables are I(1). Excluding the error correction term, is it ...
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80 views

Cointegration: comparing IRF for the univariate ECT, versus for the multivariate VECM?

Assume we have $k$ I(1) variables, cointegrated of rank $r = 1$. By cointegration, I know that the error-correction term (ECT) is itself a I(0) univariate process. Assume now I am interested in the ...
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41 views

Distribution of coefficient on the error correction term in ECM and VECM

According to statistic academic literature, the cointegration test on coefficient $\alpha$ of the error term included in ECM or VECM does not follow a standard distribution. My question is: If so, ...
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535 views

How to deal with seasonality in cointegration analysis?

I have two time series of daily gasoline prices (1500 observations each) which I suspect to be cointegrated. I aim to find an ECM/Asymmetric ECM/Threshold ECM to investigate possible asymmetries. My ...
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65 views

ECM with different representations

By construction ECM (Error Correction Model) is represented by the following equation: $$\Delta Y_{t}=\psi_{1} \Delta X_{t}-(1-\theta)[Y_{t-1}-\alpha-\beta X_{t-1}]+\epsilon_{t} \ \ \ \ \ \ \ \ ...
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231 views

Engle Granger Error Correction Model - Normality, heteroskedasticity and Autocorrelation tests

I'm building an Error Correction Model using the Engle-Granger approach with the following interest rates data: Observations: 230 Periodicity: Monthly I have the following model: $$\Delta R_t = \...
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255 views

Interaction term in error correction model using

I am having difficulty understanding how to insert an interaction term into my error correction model. I have a panel data across 30 countries over 15 years. I know that the basic error correction ...
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1answer
371 views

VECM in matrix form - explanation

I am wondering if someone can help me with explaining some variables in that VECM equation in a matrix form and checking if my previous assumptions are right about the parameters. So $\varphi$ in ...
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1answer
106 views

Calculating, and plotting, long run effects of dynamic panel models

I am estimating an error correction model of the following form, using panel data where $i$ are countries and $t$ are years: $\Delta y_{it} = \alpha + \phi_1 y_{it-1} + \phi_2 y_{it-2} + \gamma x_{it-...
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3k views

Using a ECM/VECM or ARDL model? Why and How?

I have a couple of question regarding the use ECM/VECM and Johansen test for cointegration.  In my model (6 variables), I have only one variable that is Stationary in its level, the remaining five ...
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1answer
52 views

How to rearrange formula - Error correction models

I am studying a time series subject but I am really struggling with the maths. Could someone please help me get from the first equation to the second equation? Apparently it has been reparameterised ...
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2answers
73 views

Is there any reason why one cannot create a time series from variables calculated from regressions on cross sections?

I am asking this question as the textbooks that I have don't specifically address the topic of creating a time series. If you have an answer, or even links to articles that I can research myself, it ...
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268 views

confusion about error correction model

I came across the following model in an internal paper: $∆y_t=\beta (\mu-y_{t-1} ) +\kappa(x_{t} -\alpha y_{t-1} ) +\epsilon_t$........................(1) In this the first part : $\beta(\mu-y_{t-...
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1answer
500 views

Contemporaneous regressors in the Error-correction Mechanism

I am estimating an Error Correction Model using the two step approach. In the usual form the ECM second-step regression includes lagged first differences of independent variables $X_{1}, ..., X_{k}$ ...
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176 views

ECM with fixed effects in a long-run equation

I would like to make a simple estimate of regional GDP. Predicted values of GDP on country level are available, so I was thinking about using these values and create a simple model. Simple linear ...
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1answer
1k views

Autocorrelated residuals in ARDL and/or ECM

When there is an issue of autocorrelation in an ARDL or ECM model, are we allowed to use AR(1) to correct for the problem? What is the difference between ARDL model and ECM model?
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76 views

Error Correction Model for p=1?

When building an Error Correction Model, is there any point in keeping p=1? I see a lot of equations where there t is influenced not only by t-1 but also t-2. If I only have t-1, is it useful at all ...
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1answer
3k views

Interpretation of the Error Correction Term as time to correct

I have the following question that I haven't managed to find a satisfying answer. In an Error Correction Model (assuming that all its assumptions hold): $$\Delta y_{t} = a + b(y_{t-1}-\hat c-\hat kx_{...
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83 views

Level variables along with differenced variables in ARDL / Error Correctional Model

I am running an ARDL model, I have both levels and difference variables. I know for sure that the difference variables should be included in the ECM but should I include the level variables as well?
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216 views

Panel: Estimating cointegrating vector within ECM to test cointegration

In time-series analysis we were taught that one can test for cointegration by estimating an error correction model and testing whether the coefficient estimated to the deviation of the equilibrium ...
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1answer
1k views

Does using difference transformation lead to bias? (Levels vs differences regression)

Consider the model estimated in levels (also assume this is the true population model): $$y_t = x_t\beta + e_t$$ As usual we have the dependent variable $y$, independent $x$, the error term $e$, and ...
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1answer
3k views

Sign of adjustment coefficient of error correction term in VECM

I am modelling the relationship between stock prices and 6 macroeconomic variables using Vector Error Correction Model(VECM). It turns out that 6 out of seven adjustment coefficient are positive. Does ...
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1answer
1k views

Long-run elasticities in an ECM estimation

I am reading a paper (Stockhammer, Onaran and Ederer, 2011) which estimates the effects of GDP, profits and the interest rate on investment in an ECM form. I am quoting the relevant part of it: The ...
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2k views

Lag order selection in error correction model (ECM)

I am building an Error Correction Model for monthly price data ($X, Y, Z$). I am deliberately using an ECM and not VECM and apply a two step approach (estimating cointegration relationship first, then ...
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606 views

Questions about cointegration and error correction model

I am confused about cointegration and error correction model. I gather that, if two variables are cointegrated, they are related. Is the condition for two variables $X_t\sim~I(a)$,$Y_t\sim I(b)$ to ...
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Visualising ECM model

I'm presenting an error correction model to a somewhat non-technical audience and want to make as much of the presentation as possible visual. Does anyone have any tips or hints that could be ...
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633 views

Estimation of a VECM model

I am attending a time series econometrics course and I am working on VECM models. We have learnt that to estimate a VECM model we should use Engle-Granger two-step procedure but I have not understood ...
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1answer
2k views

Econometrics - Relationship between cointegration and ECM

I'm pretty new to econometrics and I've been taking a class at university which uses the book "Econometric theory and methods" by Davidson and MacKinnon. It's a pretty good book but there's one thing ...
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1answer
1k 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 ...