Hi All,
In my world I am looking at Gas vs Power correlations (year ahead contracts not spot). I need to know what is a resonable lower and upper bound correlation estimates. Whether I am using Pearson or EWMA or GARCH all those methods gives a correlation lower and upper bound estimates that varies wildly : when I populate a time series of correlation estimates I find that correlation lies between 0.1 to 0.7. So the correllation through time is very volatile. Is there a way we can incorporate cointegration and ECM to get another sense of what is a more realisitic correlation volatility.
I was guessing to calibrate the ECM and then use it to forecast return for each asset and then use those forcasted returns to asses correlation and correlation's volatility. But not sure if that the best way to evaluate correlation uncertainty (or correlation volatility). Maybe that is the case that I shouln't try to link ECM and any correlation estimators
CoIntegration and ECM to estimated correlation
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 Posts: 815
 Joined: Sun Sep 28, 2008 10:30 pm
Re: CoIntegration and ECM to estimated correlation
Hi,
I don't think your idea to use cointegation and ECM is the right path. Its difficult to see what this will achieve over and above looking at the theoretical standard errors on standard correlation estimates
If you use a rolling window based on a very long historical series the Pearson correlation will not vary much. EWMA estimates will have a volatility that is exactly determined by the smoothing constant, which is your choice. Have you read the material on standard errors of correlation estimates in Section II.3.5.4 and II.3.8.5. I think that is what you need to move on.
I recommend that you forget about trying to use GARCH. This can give very unstable correlation estimates because the bivariate GARCH parameters often lack robustness as the window is rolled over time. You can't even use the standard errors of the parameter estimates to try to imply a standard error for correlation  only for covariance.
When deciding on a methodology, in general, everything depends on the application. So, ask yourself why you need these upper and lower bounds and this may guide you in your choice between Pearson and EWMA standard errors.
Cheers, Carol
I don't think your idea to use cointegation and ECM is the right path. Its difficult to see what this will achieve over and above looking at the theoretical standard errors on standard correlation estimates
If you use a rolling window based on a very long historical series the Pearson correlation will not vary much. EWMA estimates will have a volatility that is exactly determined by the smoothing constant, which is your choice. Have you read the material on standard errors of correlation estimates in Section II.3.5.4 and II.3.8.5. I think that is what you need to move on.
I recommend that you forget about trying to use GARCH. This can give very unstable correlation estimates because the bivariate GARCH parameters often lack robustness as the window is rolled over time. You can't even use the standard errors of the parameter estimates to try to imply a standard error for correlation  only for covariance.
When deciding on a methodology, in general, everything depends on the application. So, ask yourself why you need these upper and lower bounds and this may guide you in your choice between Pearson and EWMA standard errors.
Cheers, Carol
Re: CoIntegration and ECM to estimated correlation
Hi Carole,
Thanks to reply back.
When you say section II.3.5.4 which book are you refering to ?
Also I think the power/gas correlation depends on the state of power/ coal correlation : low level of correl when coal is cheap relative to gas, high level of correl when gas is cheap relative to coal ....its like if power/gas correl would be conditional on the coal to gas prices differentials....and those market forces takes quite some time to develop and materialize (for example, in 2005/2006 gas was very expensive and CSS was < 0, wehreas the CDS was very postive..it took 1.5 year for the gas price to go down and the the CSS to turn positive...
If you have any suggestions to take that into account...:)
Thks again
Cedrick
Thanks to reply back.
When you say section II.3.5.4 which book are you refering to ?
Also I think the power/gas correlation depends on the state of power/ coal correlation : low level of correl when coal is cheap relative to gas, high level of correl when gas is cheap relative to coal ....its like if power/gas correl would be conditional on the coal to gas prices differentials....and those market forces takes quite some time to develop and materialize (for example, in 2005/2006 gas was very expensive and CSS was < 0, wehreas the CDS was very postive..it took 1.5 year for the gas price to go down and the the CSS to turn positive...
If you have any suggestions to take that into account...:)
Thks again
Cedrick

 Posts: 815
 Joined: Sun Sep 28, 2008 10:30 pm
Re: CoIntegration and ECM to estimated correlation
Volume II of Market Risk Analysis, of course! This discussion forum is for readers of my books (and papers)
Re: CoIntegration and ECM to estimated correlation
Dear Professor Alexander,
I am writing you from Turkey, Suleyman Demirel University. I am studying on Cointegration Analysis for G8 Countries and Turkey. I work on stock market indices.
I would like to ask you two questions.
Firstly, I read your articles and I understand, for Johansen Cointegration procedure it is better to use the raw price data instead of returns. Is it same for the unit root tests we do before cointegraton test, I mean do we have to use indices price data or can we also use return or log data of indices for Dickey Fuller and Phillips Perron.
Secondly stock markets’ trading time is not synchronous; we may use weekly data as a solution. But I also have daily data. In order to make the analysis with a higher frequency, can we use daily data? If yes, how? (Tokyo Stock Exchange and the other stock markets do not have synchronous trading time) Or doesn’t it matter the trading time differences according to the following sentences?
“With cointegration, we work with actual prices and not price returns. When we refer to a time series as stationary we mean that it is a stochastic process whose joint probability distribution does not change with respect to time. Mean and variance are constant irrespective of time.
In contrast, correlation is sensitive to time. Simple lag effects will change the correlation.
An example would be if one were examining the correlation between the prompt month of NYMEX Henry Hub natural gas returns and the Prompt+1 month returns on a daily basis. If one shifted the daily analysis from today to today 1, the correlation would most likely change. However, the cointegration will not change.
Correlated time series will move together while cointegrated time series will trend to a common spread. Correlation tells us nothing about the long term relationships between time series. Correlation is taken relatively short intervals; cointegration is over a longer period of time.”
A Briefing on Cointegration
By Warren Murdoch
http://www.riskadvisory.com/news/newsar ... ration.htm, (13.03.2013)
Best regards,
Turan KOCABIYIK
I am writing you from Turkey, Suleyman Demirel University. I am studying on Cointegration Analysis for G8 Countries and Turkey. I work on stock market indices.
I would like to ask you two questions.
Firstly, I read your articles and I understand, for Johansen Cointegration procedure it is better to use the raw price data instead of returns. Is it same for the unit root tests we do before cointegraton test, I mean do we have to use indices price data or can we also use return or log data of indices for Dickey Fuller and Phillips Perron.
Secondly stock markets’ trading time is not synchronous; we may use weekly data as a solution. But I also have daily data. In order to make the analysis with a higher frequency, can we use daily data? If yes, how? (Tokyo Stock Exchange and the other stock markets do not have synchronous trading time) Or doesn’t it matter the trading time differences according to the following sentences?
“With cointegration, we work with actual prices and not price returns. When we refer to a time series as stationary we mean that it is a stochastic process whose joint probability distribution does not change with respect to time. Mean and variance are constant irrespective of time.
In contrast, correlation is sensitive to time. Simple lag effects will change the correlation.
An example would be if one were examining the correlation between the prompt month of NYMEX Henry Hub natural gas returns and the Prompt+1 month returns on a daily basis. If one shifted the daily analysis from today to today 1, the correlation would most likely change. However, the cointegration will not change.
Correlated time series will move together while cointegrated time series will trend to a common spread. Correlation tells us nothing about the long term relationships between time series. Correlation is taken relatively short intervals; cointegration is over a longer period of time.”
A Briefing on Cointegration
By Warren Murdoch
http://www.riskadvisory.com/news/newsar ... ration.htm, (13.03.2013)
Best regards,
Turan KOCABIYIK

 Posts: 815
 Joined: Sun Sep 28, 2008 10:30 pm
Re: CoIntegration and ECM to estimated correlation
Hi
I don't think you have quite understood the nature of cointegration and unit root tests. They are always done on integrated series, but returns are not integrated they are stationary. You can use price, or log price. Your choice.
Even weekly data (usually taken on Wednesday) are not synchronous. The error is less with weekly data than it is with daily data. At the daily frequency you need to find synchronous data somehow.
I agree with the broad nature of the comments made in the quote, even if I would perhaps have chosen lightly different wording in some place,
Hope this help, Carol
I don't think you have quite understood the nature of cointegration and unit root tests. They are always done on integrated series, but returns are not integrated they are stationary. You can use price, or log price. Your choice.
Even weekly data (usually taken on Wednesday) are not synchronous. The error is less with weekly data than it is with daily data. At the daily frequency you need to find synchronous data somehow.
I agree with the broad nature of the comments made in the quote, even if I would perhaps have chosen lightly different wording in some place,
Hope this help, Carol
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