# 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 ...
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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 ...
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 ...
1 vote
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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 ...
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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 ...
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### 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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1 vote
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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 ...
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### 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 ...
1 vote
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### 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 ...
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### 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 ...
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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: ...
1 vote
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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 ...
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### 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 ...
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### 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 ...
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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 ...
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### 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 ...
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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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### 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 ...
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1 vote