Cointegration is often used in statistical abitrage as a way to identify how to combine some tradable instrument to obtain a *mean reverting* one.

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Specifying integration level of time series [closed]

Following model was estimated on 200 observations. How to specify the level of integration of $X_t?$ In brackets there are standard errors and p-value of Breusch-Godfrey test is also shown. ...
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How to interpret the eigenmatrix from a Johansen cointegration test?

I ran a Johansen cointegration test on 3 instruments, A B and C. The results that I got are: ...
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How to interpret results of Johansen Test?

I have two time-series a & b. The objective is to find out whether two series are cointegrated or not. I am using Johansen Test in R to find this out. I am using urca package of R. Here is the ...
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What does the cointegration coefficient represent in pairs trading when cointegrating log stock prices?

In Pairs Trading by Vidyamurthy, on page 83 (and throughout the book), the author describes an elementary example of trading with log prices. The long run equilibrium of the basic portfolio is given ...
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optimal look back period for cointegration analysis on daily prices

I'm running some cointegration tests on 2 stock pairs and was wondering, generally speaking, what would be the optimal look back period to test considering I am using daily prices and the average ...
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1answer
93 views

Pair trading based on cointegration - equity line

I'm preparing a project at my Uni where I have to make a simple pair trading strategy using cointegration between two stocks. I'm stuck on the equity line calculation. I have prepared opening and ...
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Interpretation of Johansen cointegration test in R

I am using urca package of R for Johansen Cointegration test in 2 stocks datas( A and B. My question is very elementar, but have cause some problems for me. How I interpret the critical values, for ...
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2answers
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Johansen test on two stocks (for pairs trading) yielding annoying results

I hope you can help me with this one. I am using cointegration to discover potential pairs trading opportunities within stocks and more precisely I am utilizing the Johansen trace test for only two ...
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2answers
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How to select optimal look back period for statistical arbitrage?

Is it possible to estimate the optimal look back period for OLS from which we test if residuals are stationary? Almost all papers that I read use random look back periods of 100 days, 252 days, 500 ...
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Cointegration Test: Residual is stationary but not random?

I am testing cointegration relationship on various pairs of stocks by this following these steps. Test for I(1) on a pair of stocks, says X and Y, using Dickey-Fuller test. If both time series are ...
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1answer
813 views

Johansen Cointegration Test

I just performed a Johansen Co-integration test on two stocks. The results I get are: ans = r0 r1 t1 true false I am using Matlab. Can ...
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johansen cointegration test eviews interpreation

I am not sure whether i am interpreting the cointegration test correct. This is the test result : Because of the probability of the test i understand that my series are cointegrated of order 2. ...
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1answer
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Cointegration tests: how do you accurately test the necessity of time trends in the Johansen and Engle-Granger Test?

Is there a correct and up to date procedure? I just run the equation in VEC form and test the significance of the time trends? What are the possible problems that I should be aware of?
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After finding the pair, what next?

Had a question on how do I go about doing pairs trading. I have found some cointegrated stocks. Now the question is what next. From what I understand if two pairs are cointegrated, the distance ...
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62 views

Cointegration and variance of time series

Given that $X_t , Y_t$ are two cointegrated random processes, what can we say about the relationship between variance of the two increments $var(X_{t+h}-X_t)$ , $var(Y_{t+h}-Y_t)$ for a given ...
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Alternative ways to understand time-varying comovement between two time-series?

I have been looking into ways to better understand how the dependencies/correlations/etc between two time series can vary over time. I first thought about using a Kalman/particle filter over a ...
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1answer
121 views

matlab interpretation of johansen cointegration test

I need some help understanding the results of Johansen Cointegration test run on MATLAB. I am quite new to econometrics and do not fully comprehend what MATLAB has come up with. I would be really in ...
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1answer
93 views

Different ways to identify a co-integrated series?

I have been reading and trying out stuff until I am totally confused and back to square one. Could someone please explain the difference between the two methods suggested below? Suppose I have 10 ...
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45 views

Interpreting Johansen co integration test

I am a little new to econometrics. Please pardon me for this silly question. I was running a Johansen cointegration test on two time series using the econometrics toolbox provided by James LeSage for ...
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3answers
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Dou you have an example of implementing Engle-Granger 2-step cointegration?

Does anyone know where to find an example of implementing Engle-Granger 2-step cointegration? Python's ideal, but any language will do. I've skimmed and read many articles, but understand little ...
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4answers
578 views

Variable Selection in factor models

Let's say you have a dependent variable and many independent variables. What are the preferred metrics for sorting and selecting variables based on explanatory power? Let's say you are not concerned ...
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Interpretation of Cointegration results, pValues and t-Stat

This is a follow up to: Cointegration results interpretation validation? I ran another Engel Granger Test on a pair, The results I get: ...
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1answer
236 views

Cointegration results interpretation validation?

Here is how I am interpreting results of a Johansen Cointegration Test and Engel-Granger Test for A and B. The results:(Using matlab) ...
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What is the intuition behind cointegration?

What is the intuition behind cointegration? What does the Dickey-Fuller test do to test for it? Ideally, a non-technical explanation would be appreciated. Say you need to explain it to an investor ...
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2answers
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Need help on cointegration

I tried to test stock pairs for pairs trading. There are two questions I am not sure. I am not using ADF to test the log difference between two stocks. But I also see people using Johansen test. ...
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1answer
2k views

How do different methods and techniques used in pairs trading compare?

I was going through the paper of Avellaneda (2008) on stat arb and I found it interesting that he uses asset returns vs. their respective ETFs to compute the s-score. I am wondering if anyone has ...
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1answer
201 views

Simulate non-stationary time series with cointegration

how can I simulate/generate two non-stationary time series (with unit root) so that they can be also cointegrated (using R or Matlab). Thanks in advance.
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1answer
180 views

High correlation will help detect spurious regression over cointegration?

I'm analyzing two financial time series with Johansen method. A high Correlation coefficient using the Pearson method will help me to detect spurious cointegration models to avoid? If this is not ...
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1answer
109 views

Replicating the short part of a long-short trade using inverse ETFs

I devised a pair trading strategy going long XXX and short B*YYY. B is the quantity of shares of YYY I need to short. The problem is I can’t go short on YYY, but there is an inverse ETF for YYY ...
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cointegration applied to Portfolio Construction & Risk management

There are all sorts of applications of cointegration to generating alpha on mean-reverting timeseries: comparing spot vs. futures, bond spreads, identifying mean-reverting residuals, etc. But there ...
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1answer
477 views

What is the correct procedure to choose the lag when preforming 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 lag levels returns different results: for some ...
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359 views

What's the practical difference between the Johansen vs Engle-Granger tests for cointegration?

For the two-variable case, what are the practical differences between using the Engle-Granger procedure versus the Johansen test for cointegration? Is one universally more powerful than the other? ...
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229 views

Co-integration constraints of coint(X,Z) given coint(X,Y) and coint(Y,Z)?

The Augmented Dickey-Fuller Test can be used to measure how well ranked certain pairs are against others for co-integration. So then say we have a known co-integration between ...
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2answers
3k views

Cointegration tests

I'm trying to figure out how to perform cointegration tests in R between 2 time series. I'm using po.test from the package ...
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277 views

pairs trading or long short strategy given volatility of the stocks

Suppose I have 2 stocks and the only thing I know about them is their volatility and that they cointegrate. Let's say vol of stock A is 25% and B is 20%. Will I be able to find a hedge ratio only ...
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ADF test in R yielding perfect cointegration. How is this possible?

I am using the famous conintegrated pairs tutorial to just different stocks for cointegration. The adf.test yeilds perfect cointegration, which I feel must be incorrect. Here is why: When I run ...
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1answer
179 views

Trend in Cointegration relationship

I was estimating a long-run relationship of exchange rate and purchasing power parity. The residual of the long-run relation which should be $I(0)$, but it is only $I(0)$ when I introduce trend in ...
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1answer
2k views

Cointegrating relationships - Johansen in R

I read the posts, How to interpret results of Johansen Test? and How to interpret the eigenmatrix from a Johansen cointegration test? But still I am quite confused by the output. I have a project with ...
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498 views

How to determine ratios for mean-reverting basket

Suppose I have a basket of 3 securities A, B, and C. I believe that the basket is cointegrated and I want to create a mean-reverting trade. I fit the model: ...
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1answer
642 views

R Outputs from Johansen test. Linear combination still not stationary?

I am trying to see if house price is cointegrated with interest rate, per capita income and rental vacancy rate and got the following output from ca.jo in R: ...
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1answer
369 views

Stepwise Cointegration

This is more of a general question at this point, but if my thought process makes sense I will follow up with an R implementation. I have read a number of papers on cointegration analysis for pairs ...
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609 views

Philips-Ouliaris test for cointegration

I'm trying to implement cointegration tests using the R urca package. I've figured out the Johansen test (ca.jo), but I'm having trouble with the Philips-Ouliaris test (ca.po). I have two questions: ...
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1answer
346 views

Using cointegration to prove that a long-short strategy is market neutral (in CAPM sense)

I am trying to prove that a long-short strategy invested according to the cointegrated relationship from Engle-Granger's. So essentially I'm trying to show that the return $r_{XY}$ of the portfolio (X ...
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Modelling long run relationship between dividend and earnings

I am working on a paper where I have to model the long run relationship between earnings and dividends. I have downloaded the raw data from shillers website. I have converted the series to ...
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1answer
629 views

Pairs trade CDS contracts using cointegration

Recently I have looked at some sovereign CDS spreads (of the Nordic countries to be precise) and have tested for cointegration in the levels (i.e. untransformed) and logs of the spreads. Tests ...
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Cointegration trading: Ignoring pairs that aren't economically related

Cointegration trading question What's the state of the art when it comes to choosing proper subsets of stocks/assets where cointegrating relationships aren't ignored as (likely to be) spurious? For ...
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4answers
2k views

Are two identical time series cointegrated?

I did cointegration test on two identical time series, and the result shows that they are not cointegrated, but intuitively, I think they are. Can anyone share some thoughts on this? Thanks!
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1answer
597 views

Meta-view of different time-series similarity measures?

While I spend most of my StackExchange time on MathematicaSE, I'm in the business and follow the questions and answers on this site with great interest. Recently questions like the following (and ...
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How are correlation and cointegration related?

In what ways (and under what circumstances) are correlation and cointegration related, if at all? One difference is that one usually thinks of correlation in terms of returns and cointegration in ...
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Two prices pass the cointegration test but there is a trend. How to check stationarity?

Below is a spread built with two ETFs that pass the cointegration test i.e. Adjusted Dickey Fuller, adfTest(type="nc") in R's fUnitRoots with a p-value < 0.01. The red line is the trendline. What ...