# Questions tagged [cointegration]

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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### What do I need the Error correction model for in the two step Engle Granger approach (bivariate Cointegration)

could someone kindly explain what I need the ECM for in a bivariate Cointegration test? I am currently trying to reproduce the results of Rad et al. (2015): "The profitability of pairs trading ...
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### What is the reason for using log prices in Pairs Trading (Cointegration)?

I was wondering, why some of the research papers on pairs trading (using the cointegration approach) are using log prices to determine the spread of a pair? Why are they not simply using regular ...
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### Understanding Look Back Period

When people say look back period of 6 months, how does that data look like? Are that 6 months of raw data or a weighted average of that data? I am a little confused on how you come up with beta values ...
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### How can one, from regular predictions of high & low prices of a security, their variances and error covariance, construct a trading strategy?

Suppose I have an algorithm that provides a prediction of the daily high and low of some security n periods in the future, a confidence interval for each of these predictions, and the correlation ...
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I've been trying to wrap my head around cointegration. Currently I use the log returns of both stocks A and B, calculate the spread given by: $S = log(A) - n*log(B)$ where $n$ is the Hedge Ratio ...
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### Cointegration and hedge ratio

I've recently been looking into pairs trading through cointegration. So far I've used the log returns of stock A and stock B in a rolling OLS to find the hedge ratio. However, I've noticed that for a ...
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### In Pairs Trading: How can high volatility in spreads be explained when there is a market shock?

In my project I tested a Pairs trading strategy in the US equity market for data of 10 years. These 10 years include the financial crisis (2007-2008). The strategy follows a Cointegration approach. ...
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### Number of observations required for cointegration test

Hopefully a very simple one. I've got two assets daily close prices. How many observations should I use to test for cointegration between these two assets ? Any pointers wuold be great. A
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### Co-integration test on intraday data and day continuation “discontinuity”

I want to implement cointegration test on pairs with intraday data (1min). In order to avoid opening and closing “special” behavior in my statistical computation, I am not taking into account the ...
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### How do we know if cointegration is down to luck?

I have done some analysis of various pairs of tickers on the NYSE. I did a brain dead algorithm to come up with all combinations of pairs and then checked all pairs for cointegration/stationarity. I ...
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### Given a cointegrated portfolio of stocks, how to build a synthetic option position by using the options on the stocks

The setting Let stocks $A$, $B$, and $C$ are cointegrated. Moreover, we know the weights of the cointegrated portfolio (scaled so that the absolute value of the maximum weight is $0.5$): $w_A = 0.15$ ...
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### How to compute returns of a Pairs Trading Strategy with different holding periods?

I am currently working on a project where I am testing a Pairs Trading Strategy based on Cointegration. In this strategy I am considering to trade a couple of hundred stock pairs every day over a time ...
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### Pairs Trading (Cointegration Approach) - Daily Cointegration Test

I have a question regarding the Pairs Trading strategy based on the Cointegration Approach. Most of the papers/literature I found on Pairs Trading using the Cointegration Approach are usually testing ...
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### Calibrating the Ornstein-Uhlenbeck process with an additional parameter

Firstly I find the spread between two cointegrated time-series $Y_t$ and $Z_t$ by finding the best slope parameter $\beta$ in the equation $spread_t = Y_t - \beta Z_t$ (via Cointegrated Dickey-Fuller ...
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### Cointegration where first differences are not jointly stationary

Note: This is a crosspost from this post on cross-validated, where it did not receive an answer. I thought I might have better luck here. I am looking for a rigorous and general treatment of ...
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### What should the look-back period be when calculating Cointegration?

So I am confused as to what the look-back period should be when calculating Cointegration. By this I mean when running for example a Johansen or ADF test, should my look-back period be 6 months?...
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### Should I calculate a spread using stock prices or the ratio?

So I am creating a trading algorithm thats uses cointegration, for a pairs trading strategy. Imagine there is stock A for 100 dollars and stock B for 25 dollars. My questions is when caulcating the ...
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### Pairs Trading: Normalized price series (co-integrated and correlated) always end up diverging

Need some expert advice and suggestions: I am trying out pairs trading or statistical arbitrage (as traders say). But even if two price series are co-integrated (ADF test, Hurst exponent, Ornstein–...
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### Why is OLS based spread not reflective of actual difference?

I'm trying to define and track the spread between two time series (data available here), for the purpose of learning pair trading basics. When running a cointegration test the two series seem to be ...
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### lead lag relationship among futures, options and stock prices

I have the data of past 10 years of NIFTY (the National Stock Exchange of India) stock, futures and options and I want to show the lead-lag relationship (which reacts first, futures, options or stocks)...
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### Understanding output from Johansen Cointegration test

I have a VECM model that Im using to determine the revenues for a firm, based on factors like Interest rates, S&P 500 and company specific variables, as follows: Stage 1: $$z_t= a+ bX_t+e_t$$ ...
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### What value to put in lm() function when testing for cointegration (R)

I'm a CS student working on a financial computing project + have a question regarding cointegration testing using linear regression with the lm() function. https://www.rdocumentation.org/packages/...
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### Johansen cointegration Test for spread generation

I'm using the python statsmodels version of the johansen cointegration test and I'm looking for some advice on how best to generate the spread used within a pairs trading algorithm. For example I've ...
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### Law of one Price and Cointegration relationship

I have a question on the relationship between the law of one price and cointegration of (financial) time series. To set things clear I start with something simple: Suppose there is an unobserved "...
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### Cointegration between prices and dividends. How do I get the following expression?

Actually, I have two questions: 1. Let us assume that expected returns are constant. Then, we have the following expression for how the prices should be determined, provided that the operators are ...
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### Trading 3 stocks X Y Z where X cointegrated to Y, Y to Z, but no other cointegration is available

Suppose you have 3 stocks, say X Y Z. You also know that X is cointegrated to Y using some test (say ADF) and Y is cointegrated to Z. However, no transitivity, and no threesome cointegration ...
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### generalisation of cointegrated stock pair strategies to multiple cointegration

Question: as it is well known, there are strategies to trade pairs of stocks which are known to be co-integrated. See for instance here: https://medium.com/auquan/pairs-trading-data-science-...
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### when a co-integrated times series pair has broken the leash

I have two times series, say $T_i$ and $S_i$ over a reasonably large time window, and I have calculated their cointegration (using python's OLS and Adfuller) . Say that the test has passed with high ...
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### Spot trading: exact mathematical definition of the positions for a portfolio

Let us say that I want to spot trade a portfolio constituted of a pair of two stocks of respective prices (for example in USD) $S^1_t$ and $S^2_t$, and suppose for example that they co-integrate ...
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### Fractional cointegration in R

I'm looking for a package (or some code that anyone has written) that will help me to estimate a VECM for fractionally cointegrated series. I.e. like the ca.jo ...
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### Pairs trading strategy: Portfolio returns and NAV

Currently trying a pairs trading approach using cointegration. Tried both formations: $$log(P_t^A)=log(P_t^B) \hat{\gamma}+\hat{\mu}+\epsilon_t \hspace{0.5cm} (1)$$ P_t^A=P_t^B \hat{\gamma}+\hat{\...
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### Johansen Cointegration Test in R

I know its probably been asked bevor but i just don't get it. I have 2 values (Oil and corn price) and i want to check if they are cointegrated. Bevor that, i have tested if they really are non ...
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### What is the logic of the eigenvectors of the Johanson cointegration test determining hedge ratios?

Reading Algorithmic Trading: Winning Strategies and Their Rationale, Ernie Chan and there is a short section about the Johanson test for cointegration where it is mentioned that the eigenvectors ...
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### If two price series are cointegrated but not correlated, how do I find the hedge ratio?

Mathematically, what is going on here?
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### When constructing a cointegrating series, does choosing the linear regression with the lowest ADF test statistic yield the optimal hedging ratio?

Multiple sources say that you should find the optimal hedging ratio between two stocks in a pairs trade by conducting 2 linear regressions (with each stock as the independent variable), and using ...
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### Are there any papers about cointegration consisting of time series of more than two assets?

Are there any papers about cointegration consisting of time series of more than two assets ? I wonder if there could be any trading strategy for three assets case.
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### Cointegration vs combination of returns

Hi Quantitative Finance, I understand that there are a wealth of pairs trading models out there. Recently, it got me thinking as to why we go through the trouble to find cointegrated pairs while we ...
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I have intuition that cointegration between elements of pair of equities somehow contradicts pairs trading strategies. Because the better is linear fit of the model the less opportunities we have for ...
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### Spurious regression between two futures with the same underlying highly correlated (cor=0.9)

analyzing the correlation between soybean and soybean meal futures in ECBOT, and making a linear regression in R between them I check with an ADF Test that the residuals are not stationary, so ...
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### Looking for materials regarding Pair Trading [closed]

For my master thesis, I wish to work onto Cointegration and Pair Trading. I was wondering if any of you had some scholar/blog material recommendations. Best Regards
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### Why does the presence of cointegration solve the problem of spurious correlation? [closed]

Many of us are familiar with the connection between spurious correlation and its relationship to cointegration. Granger explains in his seminal 1974 paper "Spurious Regressions in Econometrics" how ...
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### How do you decide what time frame you're going to use when testing for cointegration?

I've been fiddling around with different time frames when doing tests for cointegration between two timeseries, and I've realized that the dates that you use for your start/stop of the test will ...