SERVING THE QUANTITATIVE FINANCE COMMUNITY

mnafakh
Topic Author
Posts: 7
Joined: November 29th, 2013, 8:52 pm

### Regression on different frequencies predictors

Hi,I'm looking for regression method which take into account quantitative variables but with different frequencies:- dependent variable : daily frequency- explanatory variables : daily frequency and one having a trimestral frequency (macroeconomic variable) Thanks

Posts: 23951
Joined: September 20th, 2002, 8:30 pm

### Regression on different frequencies predictors

A few suggestions:1) Duplicate the lower-frequency variable across time.2) Interpolate the lower-frequency variable across values.3) Use a Brownian bridge to synthesize random intermediate values of the lower-frequency variable.4) Develop a model of higher-frequency proxies for the lower-frequency variable.Methods 2, 3, and 4 help account for the effects of unmeasured expectations of the intermediate values of the lower-frequency variable. #2 and # 3 are dangerous because they leak information about the future into the model and can't be used in forecasting the dependent variable in a live context (e.g., you don't know the future quarter's value of GDP in order to interpolate or bridge it with the previous value of GDP.)You might also want to analyze the residuals of your regression resorted by time-since-last-measurement both to scope the magnitude of unexplained variance from using the old value and to look at covariance of those residuals with respect to variance of the NEXT observed value of the slow variable.
Last edited by Traden4Alpha on January 28th, 2014, 11:00 pm, edited 1 time in total.

mnafakh
Topic Author
Posts: 7
Joined: November 29th, 2013, 8:52 pm

### Regression on different frequencies predictors

Thank you Traden4Alpha.I will investigate on those trails and will came back to you.I am also investigating on the PLS1 regression, which allows to get round frequencies problems by using PCA procedures (if I understood correctly).One friend told me about :- Tobit regression (but this model aims to describe the relationship between a non-negative dependent variable Y. Given that my dependent variable is returns, I cannot use this regression. Furthermore the model supposes to be in presence of a latent variable.)- GLM regression (but this one is only a generalization of the linear regression (as its name suggests) allowing to seek to express the expected value of the response variable Y as a function of linear combination of explanatory variables. So all our Xi must have a same observations number).Thanks

MHill
Posts: 488
Joined: February 26th, 2010, 11:32 pm

### Regression on different frequencies predictors

I think jamesgin linked a paper about calculating correlations of assets where the values had different and irregular observations.The paper was looking at intra-day correlations of assets, but the principle might apply. Try a search.
Last edited by MHill on January 29th, 2014, 11:00 pm, edited 1 time in total.

mnafakh
Topic Author
Posts: 7
Joined: November 29th, 2013, 8:52 pm

### Regression on different frequencies predictors

Thank you MHill for this paper.If someone have the same problem than mine, those are the links:http://papers.ssrn.com/sol3/papers.cfm? ... 9-2011.pdf

quartz
Posts: 424
Joined: June 28th, 2005, 12:33 pm

### Regression on different frequencies predictors

The terms you're probably looking for are asynchronous and kernel "realized covariance" and "Hayashi-Yoshida" (aka Corsi-Audrino "tick-by-tick"), there's a lot of literature in the area, Andersson just scratched the surface there. Of course my method is the best :-)The other big perspective is that of missing data, imputation, EM algorithm etc. Two notable papers in the direction are Morokoff and Corsi&c again. Best results for more computation.

chocolatemoney
Posts: 322
Joined: October 8th, 2008, 6:50 am

### Regression on different frequencies predictors

Just to clarify: I did not understand how the conversation switched from a regression problem to the covariance matrix estimation.

quartz
Posts: 424
Joined: June 28th, 2005, 12:33 pm

### Regression on different frequencies predictors

QuoteOriginally posted by: chocolatemoneyJust to clarify: I did not understand how the conversation switched from a regression problem to the covariance matrix estimation.Central rule of quantdom: When in doubt, assume normality. Always.

chocolatemoney
Posts: 322
Joined: October 8th, 2008, 6:50 am

### Regression on different frequencies predictors

QuoteOriginally posted by: quartzQuoteOriginally posted by: chocolatemoneyJust to clarify: I did not understand how the conversation switched from a regression problem to the covariance matrix estimation.Central rule of quantdom: When in doubt, assume normality. Always.True. The central rule of quantdom, as it was inscribed on a stone on mount Sinai a while ago.The op mentioned GLM so I suspected he may had something else in mind.Nevertheless, IMO, even assuming normality, covariance matrix estimation and regression are two different problems, with different goals and nuisances. Thanks for posting the links.

quartz
Posts: 424
Joined: June 28th, 2005, 12:33 pm

### Regression on different frequencies predictors

QuoteNevertheless, IMO, even assuming normality, covariance matrix estimation and regression are two different problems, with different goals and nuisances. There's one model, I wouldn't advise turning solution methods into problems themselves, unless one is into nuisances.The least squares solution $a=\overline{y}-b\overline x;\quad b=\frac{Cov[x,y]}{Var[x]}$ with centering gives the isomorphism.