# Tagged Questions

Two or more non-stationary variables are cointegrated if there is a linear combination of those variables which is stationary.

6k views

### Time series 'clustering' in R

I have a set of time series data. Each series covers the same period, although the actual dates in each time series may not all 'line up' exactly. That is to say, if the Time series were to be read ...
441 views

### Does a cointegration model exist for irregularly spaced time series?

It isn't clear to me how to calculate cointegration with irregular time series (ideally using the Johansen test with VECM). My initial thought would be to regularize the series and interpolate ...
415 views

### Resources for learning about spurious time series regression

"Spurious regression" (in the context of time series) and associated terms like unit root tests are something I've heard a lot about, but never understood. Why/when, intuitively, does it occur? (I ...
119 views

### Does zero correlation between 2 differenced series implies no cointegration between original series?

The question is related to this one. In this question @mpiktas gives an answer on why checking correlation is not enough but the answer doesn't seem completely correct to me for the following reason: ...
2k views

### What is the correct procedure to choose the lag when performing Johansen cointegration test?

When preforming Johansen Cointegration test for 2 time series (the simple case) you need to decide the lag you want to use. Doing the test for different lags return different results: for some lag ...
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### How to know if a list of prices are mean-reverting?

I have two historical price lists with the following columns data - price Now i have to create the ratio between the prices of these lists: list A: 01/01/2011 10.50 list B: 01/01/2011 ...
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### What does that mean that two time series are colinear?

I am familiar with the concept of cointegration. But I hear sometimes people talking about colinearity (or collinearity) for time series. A set of points is collinear if they are on the same line. ...
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I have read that PP unit root is often used in economy. Is it sensible to do both tests (PP & ADF) or is PP test enough?
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### Are two identical time series cointegrated?

I wonder if two identical time series are cointegrated. Can anyone shed some light on this? Thanks
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### Cointegration-based feature selection

I have a basket of time series (stock prices). I want to find the N (fixed or not) time series that will best replicate the basket in the sense that combination of them will be best cointegrated with ...
365 views

### A doubt about the cointegration tests

I'm doing Phillips-Ouliaris Cointegration test with po.test function inside tseries library. I have a simple question about the "cointegration". When i do PO test I get the p-value result but I ...
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### How to choose number of lags for Zivot unit root test?

The fUnitRoots package considers lag=2 as the default value in the urzaTest() function (Zivot & Andrews unit root test), ...
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### Interpretation of an integrable time series of an order zero

REF: http://en.wikipedia.org/wiki/Order_of_integration What is the interpretation/intuition behind a time series integrable of order 0? I am reading something on cointegration and this is not yet ...
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### Relationship between cointegration and causality in a VAR/VECM model

I am asking myself how cointegration and causality are related in a VAR/VECM model. Suppose you have two $I(1)$ variables in your 2 dim VAR process which are cointegrated, so there is one ...
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I want to figure out how to read the cointegration relation between 5 cointegrated variables. I present the results down here with r=number of cointegrated equations is 3. Variables are normalized ...
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### How to check if a time series is I(1) in R?

I'm testing the cointegration of two time series of stock prices using adfTest from fUnitRoots, but first I need to check if the series are I(1). How can I check if a time series is I(1)?
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### How to test model misspecification using Johansen test?

There are three misspecification tests that I would like to perform on my model for a Johansen test before continuing with the cointegration tests themselves. Following Johansen's advice in ...
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### Cointegration and correlation

Based on real data (e.g. spot and futures prices of an index) if two series are correlated in the long run (e.g. strong positive significant correlation) it does not mean that they are cointegrated. ...
88 views

### Cointegration structure

I have two time series that I am investigating, acc and amb, the time frequency is daily data. They are both non stationary, as evidenced by the follows: ...
110 views

### Help for Johansen cointegrating vectors test

I used the Johansen cointegrating procedure to see how many cointegrating vectors are available in the long run and obtained ONE cointegrating vector from Maximum Eigenvalue statistic and FOUR ...
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### Computing (lagged) correlations (or similar) between multiple time-series from a VECM or its levels-VARM

Ok, after trying to find a way to get all lagged and non-lagged - correlations from multiple time-series (behavioral series with length around 180) I've confined myself to the following: I have ...
119 views

### Is is correct to compare t-statistics of different pairs of cointegrated timeseries?

I am testing for cointegration all the pairs from a set of 100 stocks. I run an Ordinary Least Square Regression on each pair and then I test for the existence of unit roots in the residuals. I am ...
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### Structural shifts

I am using the R programming language to analyze the cointegration of 5 data sets. I have determined that the series share 3 cointegrating vectors after taking structural shits into account following ...
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### What are Pu and Pz in the Phillips & Ouliaris cointegration test?

I see the type parameter for Phillips & Ouliaris Cointegration Test in the urca package that should be Pz or Pu. I read the details, but I don't understand what ...
257 views

### Did I find a bug in the tseries or urca packages?

I'm trying the functions to check the cointegration of a matrix. I'm using Phillips & Ouliaris Cointegration Test The function in tseries package is po.test and ca.po in urca The results with ...
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### About the stationarity of a sine wave

I generated two sine wave time series and want to check the stationarity of them. (1) The first time series is short. kpss.test() thinks it is stationary. ...
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### Linear combination of processes yielding higher order of integrarion

Is it possible to have an integrated random walk process by linearly combining finite number of random walks? Is it possible to have a random walk process by linearly combining I(0) processes? ...
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### Lagged Exogenous Variables in VECM with R

Looking to estimate a VARX(p,q) type VECM in R if possible. I'd like to estimate a VECM with p lags (lags relative to the level, not diff of the vars) on the ...
166 views

### Why use vector error correction model?

I am confused about the Vector Error Correction Model (VECM). Technical background: VECM offers a possibility to apply Vector Autoregressive Model (VAR) to integrated multivariate time series. In the ...
488 views

### Cointegration testing with a dummy variable

I have the model: $y_t = \alpha + \beta_1 x_t + \beta_2 D_t x_t + \epsilon_t$ With $y_t$ and $x_t$ as $I(1)$ processes, and $D_t =1$ during a large financial crisis, $D_t = 0$ during non-crisis ...
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### Testing two I(1) vectors for a relationship

Suppose I have two I(1) time series X and Y, and I want to know whether X and Y are "related" (for some definition of "related"). The standard cointegration approach defines relationship as ...
865 views

### How to interpret ADF-test optimal lag model reduction?

I was looking at howto figure out the optimal lag order for an ADF-test when I came across this PPT presentation. There are two examples of a ADF-test model reduction, one on p23 and one on p36. I ...
259 views

### Johansen cointegration test with stationary variables

Journals and books about the Johansen cointegration test suggest that only I(1) variables should be put into a cointegration test. However many journals modelling economic growth and inflation use two ...
154 views

### Putting stationary variables through Johansen procedure

Is it okay to feed $I(0)$ variables into the Johansen procedure? I've read three sources that seem to state that this is not what you're supposed to do. However, whenever I've done this, I notice that ...
367 views

### Vector error correction model

I am working on finding the relationship between equity, gold, crude oil, and currency value. I used the Johanson cointegration test. Trace test indicates 4 cointegrating equations at the 0.05 level. ...
184 views

### Isn't a test for cointegration the same as testing for heteroskedasticity in the residual error terms?

Testing for cointegration tests to see if the residuals from a regression between the two variables is a stationary process. So wouldn't a test on those residuals for heteroskedasticity be the same ...
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### Cointegration but no Granger-Causality found

I have found Cointegration based on Engle/ Granger and Johansen. However, Granger-causality is rejected for both variables. How is that possible? According to theory, if x and y are I(1) and ...
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I'm using the URCA package in R to test for cointegration by Johansen's method. Can anyone tell me what the weights (loading ...
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### How to tell if the relationship between time series variables changes over time?

Lets start out by saying that I'm a novice with statistics. I'm looking to analyze the relationship between Return on Sales (ROS) and Asset Turnover (TAT) over time to see how they impact firm ...
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### How can I perform a familywise error rate correction for Johansen cointegration tests?

I want to test multiple possible cointegration relationships with the Johansen cointegration test. I'm currently using the urca package in R with the ca.jo test. I was going to use the Bonferroni ...
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### PCA of cointegrated variables

In Optimal Hedging Using Cointegration, C. Alexander, 1999 (http://www.icmacentre.ac.uk/pdf/cointegration.pdf), page 3, footnote #2: [...] a PCA of cointegrated variables will yield the common ...
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### Constructing a VECM with a mix of I(0) and I(1) variables

I've been using the Johansen Procedure to check and correct for cointegration in my model, by estimating a VECM instead of VAR. But now I want to estimate a new model, in which I expect the same ...
192 views

### Johansen's $\Pi$ is full rank except variables are non-stationary

I have two variables. They're both $I(1)$ even when I fit constant and trend terms into the ADF test. The $p$-values for the stationarity tests are around 0.5 so it's not a marginal case. However, ...
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### Is is ok to use credit spreads to account for a drop in time series for vector error correction model?

I am doing a time series analysis on a quarterly basis from 1990 to the third quarter 2012. Some of the time series had a drop in 2008 because of recession then resumed upwards. This drop is rather ...
162 views

### Difference between unrestricted VECM and restricted VECM?

What's the difference between an unrestricted and a restricted VECM? I believe a hint lies within the cajorls()[1] function of R language's ...
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### Non parametric cointegration test in R

I am not very comfortable with the (parametric) assumptions made in cointegration analysis. I have recently found that there is a way to carry out nonparametric conintegration analysis (a google ...
140 views

### How does regression with and without intercept followed by test of stationarity affect cointegration test?

For a simple 2 variables (say X and Y) cointegration test, how does it affect our analysis, if we perform regression on X and Y with and without the intercept, and then test the spread for ...
193 views

### Fractional integration and cointegration with R

I am currently reading about fractional integration in the context of error correction models. Does anyone know of a package in r that has a function for Sowells maximum likelihood estimator of d?
I was reading about cointegration (page 5) and it said "If a linear combination of combination of a set of $I(1)$ variables is $I(0)$, then the variables are cointegrated." Does this mean ...