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12 votes
Accepted

Does Chan use the wrong state transition model in his Kalman filter code?

In addition to getting the right transition model for the Kalman filter, the main obstacle to optimizing filter performance is to implement an optimal initialization. I use an iterative approach to ...
Amanda G.'s user avatar
  • 361
8 votes
Accepted

What is the reason for using log prices in Pairs Trading (Cointegration)?

I'm assuming that the paper you're referring to uses the Engle-Granger test for cointegration. The standard test procedure checks for unit roots in the residuals of a linear regression. It is a "...
databento's user avatar
  • 2,518
7 votes

Looking for materials regarding Pair Trading

Here is a literature list from my masters thesis on stat arb. Lederman, J., (1996). Market Neutral: Long/Short Strategies for Every Market Environment, 2. – 3. lpp. Gatev, E., Goetzman, W. N....
Artem Korol's user avatar
6 votes

Imposing Restrictions on Cointegrating Vectors, R example

I know this was asked almost two years ago, but I thought I'd answer the question. It appears that the H that you want to estimate is identical to the values you received from the Johansen test, ...
Cameron Pfiffer's user avatar
5 votes

What is the reason for using log prices in Pairs Trading (Cointegration)?

This is for better linearity/normality in the QQ plot at the tails, which as both @noob2 and @rkr allude to, give a better fit and hence better properties for normalizing the residuals with z-scoring ...
Katie's user avatar
  • 304
4 votes

Are there any papers about cointegration consisting of time series of more than two assets?

Technically, if you do PCA on the yield curve (live dangerously!, do it in levels), the first two PCAs are nonstationary. The third is questionable. Note that this is a perfectly valid way of looking ...
NBF's user avatar
  • 1,078
3 votes

Trading 3 stocks X Y Z where X cointegrated to Y, Y to Z, but no other cointegration is available

Assuming we are talking about Pearson correlation, then we may apply the triangle inequality. Let $\rho(X,Y)$ denote the correlation between $X$ and $Y$. Then, $(1-\rho(X,Z))^{1/2}\le (1-\rho(X,Y))^{...
Joseph Zambrano's user avatar
3 votes
Accepted

What is the logic of the eigenvectors of the Johanson cointegration test determining hedge ratios?

Necropost. I know, but this article helped me some time ago. https://georgemdallas.wordpress.com/2013/10/30/principal-component-analysis-4-dummies-eigenvectors-eigenvalues-and-dimension-reduction/ The ...
Anonymous's user avatar
  • 415
2 votes

How to determine ratios for mean-reverting basket

In a recent paper - Cointegration and Relative Value Arbitrage by Binh Do and Robert Faff, the issue of relative value arbitrage with three stocks is addressed. On page 27 they formulate the ...
MGL's user avatar
  • 516
2 votes

Interpretation of Johansen cointegration test in R

Johansen test estimates the rank (r) of given matrix of time series with confidence level. In your example you have 2 time series, therefore Johansen tests null hypothesis of r=0 < (no ...
Nod Ulus's user avatar
2 votes

Cointegration on prices or difference of prices

Precisely because differences in prices and log-returns are often stationary, cointegration cannot be done for them. By definition, stochastic processes $X(t)$ and $Y(t)$ are cointegrated if neither ...
stans's user avatar
  • 272
2 votes

Are there any papers about cointegration consisting of time series of more than two assets?

The Johansen test can be used to test for cointegration among $n$ assets. https://en.wikipedia.org/wiki/Johansen_test The original paper: Johansen, Søren (1991). "Estimation and Hypothesis Testing ...
RRG's user avatar
  • 1,024
2 votes
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when a co-integrated times series pair has broken the leash

You have estimated a cointegration relationship between $T_i, S_i$. $$ T_i=\hat{\beta_1}+\hat{\beta_2} S_i + \hat{u_i}$$ For each new observation $(T_{new},S_{new})$, replace to the existing ...
alexbougias's user avatar
  • 1,426
2 votes

What should the look-back period be when calculating Cointegration?

As the comments suggest, there is no definitively 'gold standard' of lookback periods for such thing, especially if the underlying distribution appears to be stochastic. I understand where you're ...
Hamish Gibson's user avatar
2 votes
Accepted

Calibrating the Ornstein-Uhlenbeck process with an additional parameter

It's difficult to follow parts of your question because of the notation. Throughout your formulas, I'm not sure where $X_t$ is an input to your regression and $X_t$ is what you've defined as spread. ...
Mild_Thornberry's user avatar
2 votes
Accepted

How to compute returns of a Pairs Trading Strategy with different holding periods?

A more appropriate approach is to sum your PNL each day across all of your positions and calculate the return for the book as a whole (assuming I understand your question correctly). Return should be ...
user42108's user avatar
  • 2,272
2 votes

Cointegration between crypto markets

There is likely an issue with the missing candles in your data. Whilst you have made steps to ensure that the data is equal length for your test, it is quite possible that these two series' timestamps ...
Hamish Gibson's user avatar
2 votes
Accepted

Critical values of trace statistic of Johansen cointegration test for arbitrary number of I(1) variables

Based on the paper STATISTICAL ANALYSIS OF COINTEGRATION VECTORS (Johansen, 1987), I derived the following solution which gives a good approximation of the critical values: Let $c(f) = f \rightarrow 0....
md0101's user avatar
  • 63
1 vote

generalisation of cointegrated stock pair strategies to multiple cointegration

Chapter 2 of the Applied Quantitative Methods for Trading and Investment may be useful. You can download the excel file from the companion website. Here is the link and the Download link is at the ...
Magic is in the chain's user avatar
1 vote

Cointegration and Ratio Pair Trading

No. In the above equation, you mentioned the spread as the ratio of prices and not of log prices. Also, you verified the spread's cointegration using $A - \gamma \cdot B$ and not $A/B$ as the input ...
Varun's user avatar
  • 31
1 vote

Cointegration and Ratio Pair Trading

If I want to trade the spread, should I model the OLS as $ln(A)=−γ⋅ln(B)+ \epsilon$? It depends on how you define your spread. If you used log return as spread then use log return in OLS also. If you ...
numerairX's user avatar
  • 609
1 vote

If two price series are cointegrated but not correlated, how do I find the hedge ratio?

To find the hedge ratio you can run the Johansen Cointegration test and the eigen-vector corresponding to the largest eigenvalue would give you the hedge ratio, you can see with a bit mathematical ...
Dhruv Mahajan's user avatar
1 vote

If two price series are cointegrated but not correlated, how do I find the hedge ratio?

If two price series are cointegrated, you can run the linear regression to calculate the hedge ratio. The linear regression is in the form: $$y = \beta X + \epsilon$$ where, $y$ is the dependent ...
vibhu_singh's user avatar
1 vote

When constructing a cointegrating series, does choosing the linear regression with the lowest ADF test statistic yield the optimal hedging ratio?

You are right that it is a "very arbitrary procedure". More charitably it is a "hack" that gives a practical solution without addressing the fundamental issue. The very fact that when you do an OLS ...
Alex C's user avatar
  • 9,382
1 vote

Cointegration vs combination of returns

The reason we look for cointegration is to find some long-term relationship between levels of prices. When you use the returns, you are seeking a relationship between first differences, which are ...
Cameron Pfiffer's user avatar
1 vote

What does the cointegration coefficient represent in pairs trading when cointegrating log stock prices?

It should mean market values (instead of shares). You can see this more obviously by creating an "artificial stock" (stock C) which price equals the price of stock B divided by 10,000 (same ...
Jason Huang's user avatar
1 vote

Simulate non-stationary time series with cointegration

Simulate Random Walk Series We can now simulate a random walk series in R as shown below: RW <- arima.sim(model= list(order = c(0, 1, 0)), n=200) We can plot the newly generated series as well ...
Muhammad Jawad's user avatar
1 vote

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

Neither. This question and its references suggest that the Philipis Ouliaris (1990) test is a significant improvement over EG ADF and JCT. Given the automation, you should probably run all three ...
d8aninja's user avatar
  • 111
1 vote

cointegration applied to Portfolio Construction & Risk management

Cointegration really shouldn't be a risk relationship. It's a sort of equilibrium pricing relationship. If you take a bunch of prices/yields and regress them in levels, you are looking for a 'fair ...
NBF's user avatar
  • 1,078
1 vote

How do you decide what time frame you're going to use when testing for cointegration?

If the data generating process was fixed over time, you would choose the longest available data sample for cointegration testing -- because a larger sample yields higher power for the test. If the ...
Richard Hardy's user avatar

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