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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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Is stationarity or co-integration of order one needed for Time Series regression models?

After reading Chapter 7 Time Series Regression Models of a well-known excellent book Forecasting Principles and Practice by Hyndman & Athanasopoulos, it struck me that there is no mention of the ...
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Non-stationary time series: what are the advantages of doing analysis in levels instead of differences?

Suppose we want to analyze some non-stationary time series, x(t) and y(t). For simplicity, assume they are I(1). We can analyze them in levels (using cointegration tests) or in differences. What are ...
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Seasonality in ECM: Controlling Within the Model (e.g., Adding Dummies) vs. Outside the Model (e.g., Seasonal Adjustment)

When running an Error Correction Model (ECM) with seasonal data, two main strategies are typically considered (for example here and here): Incorporating seasonal dummies within the model to control ...
An economist's user avatar
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Engle-Granger cointegration test critical values

I am conducting the Engle-Granger cointegration test on a system of three time series: logged spot exchange rates, logged domestic price index, and logged foreign price index. I would like to use ...
Pavel Filip's user avatar
1 vote
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Estimating VAR of differences of potentially cointegrated variables

What are the possible issues, if any, of estimating a standard two-dimensional $VAR(p)$ of $I(0)$ variables that are first differences of $I(1)$ variables whose potential cointegrating relationship ...
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VAR regression between I(1) and I(0)

I am considering two time series and I would like to to a VAR regression between them. The ADF test rejected stationarity in only one of them, so the time series would be I(0) and I(1). I understand ...
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Outputs of Granger causality and FEVD are opposite of each other

This is regarding cointegration or VAR analysis of bivariate systems. The Granger causality will either say that instrument 1 (say fund) and instrument 2 (say index) are either not Granger causing ...
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Does cointegration test of exogenous variable with Y variable make sense when doing ARIMAX/SARIMAX?

The cointegration test between two time series variable is generally relevant from my understanding when you are performing a regression model. In terms of ARIMA model the approach is straightforward ...
Sayooj Balakrishnan's user avatar
2 votes
1 answer
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Cointegration and trend stationarity

Cointegration relationship is typically studied with integrated time series (that is, difference stationary time series) and when they have the same order of integration, it is possible that you find ...
Johannes Konrad's user avatar
4 votes
1 answer
50 views

The eigen values of Johansen's cointegration procedure

Assume a K dimension VECM model for cointegration analysis $$\Delta y_t=\Pi y_{t-1}+\Gamma_1\Delta y_{t-1}+...+\Gamma_{p-1}\Delta y_{t-p+1}+u_t$$ The Johansen approach for maximum eigenvalue test or ...
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Interpreting the VECM: which variable corrects towards which one?

I am trying to understand the vector-autoregressive error correction model, but I am having a hard time understanding the error correction part. Imagine that we have a VAR(1) model of 2 dimensions: $$\...
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cointegration tests for time series

To test cointegration relationship for multiple time series, one usually writes the VAR(k) as $$ \Delta y_t = \Pi y_{t-1} + \sum_{j=1}^{k-1}\Gamma_j\Delta y_{t-j} + e_t $$ See, e.g., https://www.uh....
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Prediction based on new data in the tsDyn package [closed]

I decided to use the tsDyn package to build the model and precision the values. The argument for this package (I previously worked with urca, vars) was the ability to make predictions based on new ...
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Interpreting an estimated bivariate VECM

I have used the tsDyn package in R to estimate a VEC model for the data in the graph, and I am unsure about my interpretation of the output. ...
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Granger causality does not imply a pair of integrated time series are cointegrated: an example

If a pair of integrated time series $\{X_t\}$ and $\{Y_t\}$ are cointegrated, at least one of them must Granger-cause the other. Is the converse also true? I guess not, but I am struggling to come up ...
Robert H.'s user avatar
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Mincer-Zarnowitz test with cointegrated time series

The Mincer-Zarnowitz test of forecast optimality regresses forecast errors $e_{t+h|t}$ on the forecasts $\hat y_{t+h|t}$, $$ e_{t+h|t} = \gamma_0 + \gamma_1\hat y_{t+h|t} + u_t \tag{1} $$ or in ...
Richard Hardy's user avatar
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Panel data cointegration test: Package pco in R, how to interpret output from pedroni99 function?

I have a panel dataset and I want to test cointegration between 2 variables. I cleaned the missing values and set my data frame as required but I don't know and can't find how to interpret the outcome ...
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Johansen cointegration, VAR, VECM

I do have a question regarding Johansen's cointegration, VAR, and VECM model estimation. I would like to analyze the relationship between two variables using these methods. My dataset consists of 4 ...
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Cointegration in quantile regression

I used quantile regression for my research. My variables were significant but my pseudo r was low. So I tested for cointegration. All my variables are I(1) and when I run the models with raw (...
Helpplease's user avatar
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How to find cointegrating vectors

How to find cointegrating vectors and how many vectors could there be if $e_t\ $, $p_t\ $ and $p_t^\ast\ $ are cointegrated? $ e_t\ =\ p_t\ -\ p_t^\ast\ +\ v_t $ $ p_t\ =\ p_{t-1}+\ u_{2t} $ $ p_t^\...
Aella's user avatar
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Trade-offs when building VAR models

I am trying to build my first VAR model, consisting of three time series, for forecasting and have gotten quite far. I have made all the tests and comparing models indcluding different lags, different ...
Johanna W's user avatar
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1 answer
165 views

Unit root test and cointegration

maybe someone can help me with my data. I analyse how macroeconomic indicators affect stock index. For this analysis I prefer VAR model.In my case data of all variables are non-stationary - I have ...
Laura_777's user avatar
3 votes
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Johansen test: why testing for the algebraic multiplicity of 0 and not for the nullity?

From what I already know about the Johansen test, it tests the rank of the VAR matrix (in error correction form) through steps testing whether every eigenvalue is signifincantly different from 0 (...
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Johansen test accepts first null hypothesis but would reject last one

Suppose that we perfrom a Johansen test over three I(1) variables that give us these results through the maximum eigenvalues statistic: as you can see, we accept the null hypothesis in the first step ...
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Cointegration $p$-value and VECM loading forces show low correlation

After having read about VEC model (VECM), I thought that cointegration and VECM loading forces were strongly, not to say numerically correlated. I thought that the more we have cointegration, the less ...
Jerem Lachkar's user avatar
1 vote
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135 views

R ecdet in ca.jo() [closed]

I am experimenting with the ca.jo function of the urca package and I am getting confused about the ...
Les's user avatar
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Uniqueness of cointegration coefficient

Let $A_t$ and $B_t$ be $I(1)$ processes and assume that they are co-integrated i.e. there exists $\beta$ such that $A_t - \beta B_t$ is $I(0)$. Woolridge's Introductory Econometrics text (5th edition, ...
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Correct cointegration p-value by sample size?

I have several time séries couples from which I compute cointegration p-value, then sort these couple by that p-value, starting from the lowest (for further VECM analysis on the top 100). All couples ...
Jerem Lachkar's user avatar
5 votes
1 answer
214 views

VECM: alpha is a 0-vector? cointegration rank = $k$ even though $X_t$ is I(1)?

I'm trying to wrap my head around the VECM model by doing some simple examples. In this exercise I'm taking the log prices of 2 assets, A and B. These prices are clearly not stationary, for example <...
Hiperfly's user avatar
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Forecasting VECM model ( Python and R )

I'm working on an academic project. The aim is to forecast some cointegrated time series. I retrieved the data from 2008 to 2018 of the observations of 30 time series. I performed a unit-root test to ...
andreat's user avatar
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ACF/PACF of my residuals from the cointegration model shows a perfect 1-lag autocorrelation?

I'm performing a cointegration test + OLS regression on 2 assets' prices. If I check the correlogram of the model residuals (training set, but also happens with the test set residuals) it looks like ...
Hiperfly's user avatar
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1 answer
34 views

Need help in panel data tests and steps

Greetings! I am analyzing the impact of climate change of wheat crop across 4 districts for the last 30 years. It is imperative to check the stationarity of the panels. I performed LLC and IPS tests. ...
Khan Bahadur's user avatar
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335 views

How to calculate the mean and standard deviation of a time series spread?

I am just starting anew in econometrics, and am presently trying out statistical arbitrage, specifically cointegration. I have stochastic time series data for variables A, B. Engle-Granger testing is ...
ken4ward's user avatar
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1 answer
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Johansen Cointegration test in Python (statsmodels)

I have three time series df['a'], df['b'] and df['c'] which I want to test for cointegration ...
Harry's user avatar
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How to deal with non normality of residuals in VECM?

Does anyone know how to handle non normality of residuals in VECM? I have tried transforming the data into log, exp, and Box-cox but nothing has changed. Any suggestion will do. Thank you.
Anne's user avatar
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How to deal with VECM with a different structural break for each time series?

I am modelling a VECM with structural breaks. I am following Joyeux (2007) way of doing it with dummy variables, including the different trace and eigenvalue stats for cointegration with structural ...
Anne's user avatar
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1 answer
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Investigating the presence of unit root in the following $X_t$

I am given a model and need to calculate the unit-root of $X_t$ but it seems that there is no unit-root. The model is given: $X_t = (x_{1t},x_{2t})'$ $$\Delta X_t = \alpha \beta ' X_{t-1} + \epsilon_t ...
user avatar
1 vote
0 answers
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What is the role of Panel Cointegration Analysis in Estimating Long Run Effects for ARDL models?

I am estimating some panel ARDL models, and wanted to ask where the value add comes from with cointegration analysis. From what I've read, one can estimate long-run effects using an ARDL in levels as ...
Thomas Simpson's user avatar
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1 answer
282 views

Python statmodel coint doesn't give the same p-value as adfuller on OLS residual

According to Eagle and Granger (1987), if I have 2 time series y1 and y2, we can test their cointegration with the p-value of an ADF stationarity test performed on the OLS residual. Though, when ...
Jerem Lachkar's user avatar
1 vote
0 answers
76 views

Forecasting accuracy of VECM using train and test

I am forecasting using VECM and I plan to do it on train and test split data. My data is 132 monthly observations. My VECM is lag 3 with unrestricted constant. All diagnostic test are passed. I plan ...
Sandy's user avatar
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246 views

Interpretation of VECM results when the variables are swapped as response variable

I have two variables, which is Tomato farmgate price and retail price. When I use VECM, both variables are endogenous. However, there can still be a response variable (ex. when you put the variable ...
Niah's user avatar
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Johansens Cointegration test - VARselect output showing all Lag 1's

I am running a cointegration test on 4 input variables over 1 year and when I run the VARselect it outputs: ...
Niall Jenkins's user avatar
1 vote
0 answers
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Regularize variables for Johansen coinegration

I am looking into applying the Johansen cointegration procedure to variables of very different scales, going from units to tens of thousands. I use log(prices) but the scale difference is still very ...
StatArb's user avatar
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1 answer
322 views

Interpretation of the trend variable in the cointegrating equation of VECM (VECM Case 4: Unrestricted trend)

I am doing VECM of prices of meat. This one result confuses me. This one shows that P_F and P_R has a positive relationship. This can be interpreted at 1% of P_R is 0.18% of P_F. However it also shows ...
Ashlley's user avatar
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2 votes
1 answer
484 views

ARDL Model in First Differences For Non-Cointegrated Time Series?

I would like to regress $Y_t$ on $X_t$. I have concluded that the series are each $I(1)$ and not cointegrated. I am curious as to if I can still use an ARDL model to capture any possible long-term ...
Anthony's user avatar
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1 answer
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Johansen test - r studio , "ect1" "ect2" etc

Can someone explain to me the result of this test? I am not sure what the ect1, ect2, etc. mean. Output ...
Enzo Marques's user avatar
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67 views

The cointegrating equation in VECM changed sign when I added a trend in the deterministic regressor

I am studying the cointegration between retail prices of pork. In an economical theory this should have a positive relationship. However, when I tested for cointegration using Johansen in Eviews, it ...
ash's user avatar
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Johansen cointegration test for ECM model

I'm dealing with the Johansen cointegration test before running an ECM model. I cannot figure out which type of test execute: with/without constant, with/without trend, ... How can I choose the ...
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213 views

How to specify a VAR model in R with non-stationary, stationary, and trend-stationary variables?

I have a multivariate time series and I want to estimate a VAR model. I tested for unit roots with the ADF and KPSS test and concluded that some variables are non-stationary, while others are ...
Mina's user avatar
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1 vote
1 answer
314 views

Engle-Granger approach to cointegration, and use of other integration tests

The Engle and Granger define two series as cointegrated, if they are integrated, but a linear combination of the two series exist, which is stationary. To estimate the cointegrating vector (i.e. the ...
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