Time-series Regression

Discussion on Quantitative Methods in Finance
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oiac
Posts: 11
Joined: Fri Mar 04, 2011 4:54 pm

Time-series Regression

Postby oiac » Mon Apr 02, 2012 4:27 pm

Thank you for your answers to my previous (related) questions.

I am working on multivariate time series regression of daily market data.
Typically looking back 360 d.

I have tested for colinearity and use PCA where this is an issue.
I have looked for information remaining in and heteroskedasticity in the residuals
but have found no evidence of either. I have looked at forecasting error.

I run test-downs and have tried step-wise regression (using the F-stat) to select my independent data.
Typically my Rsq are low (of order 1 %) and my adjusted RSq can even be negative.

Can you make any suggestions, or give any advice, for starting out with non-linear regression
on market data? I am very wary of over-fitting but cannot believe that an RSq of approximately 1 - 3 %
is of any use and have run out of ideas other than misspecification of the model as linear.

Many thanks.

coalexander
Posts: 815
Joined: Sun Sep 28, 2008 10:30 pm

Re: Time-series Regression

Postby coalexander » Sat Apr 07, 2012 10:12 am

Hello

Sorry for delayed reply, I've been very busy recently.

Yes, R^2 are very low, that's worrying. If you can get more data that might help...360d is not much. Or, using a non-linear relationship may help...do scatter plots of Y against each X and see if there are obvious non-linear relationships.

What are pairwise correlations corr{Y,X_i}? If they are very low, maybe its the theory that is wrong -- there simply isn't a relationship between Y and these X variables anyway.

Best wishes, Carol

oiac
Posts: 11
Joined: Fri Mar 04, 2011 4:54 pm

Re: Time-series Regression

Postby oiac » Tue Apr 10, 2012 2:12 pm

Dear Carol,
Many thanks for your very useful response.

The correlations between the independent variables and the dependent variable are low - absolute values of order 0.01 to 0.1.
In fact some correlations between the independent variables are much higher. Given this it is not surprising that I cannot
see structure in the plots of each independent variable vs the dependent.

I am surprised by this though as it is a commonly held belief in econometrics that my variables are related - perhaps not at the sampling frequency I am using.

Am I correct in assuming that if my correlations are so low that trying different non-linear regression techniques is more than likely a waste of time?

Thanks again,
Oiac

coalexander
Posts: 815
Joined: Sun Sep 28, 2008 10:30 pm

Re: Time-series Regression

Postby coalexander » Tue Apr 10, 2012 6:11 pm

Yes, unfortunately....may getting different data (different frequency, longer period?) would help.

Carol

oiac
Posts: 11
Joined: Fri Mar 04, 2011 4:54 pm

Re: Time-series Regression

Postby oiac » Wed Apr 11, 2012 9:53 am

Thank you for your help.
Oiac


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