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This answer depends on the $X^i$ Before jumping on to the solution it should be answered that are $X^i$ traded in the market? i.e. are the returns on these available in the market (Size/Momentum portfolios, ETF returns) or are these economic variables like CPI, Inflation etc. If it is the former i.e. traded assets then we can do the time series regression ...

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First of all, the only one way to compute factor betas is to use the linear regression model, as suggested by John in the 1st comment. There is not other way to get them. You can get it by simply using excel through the Data Analysis package or using the relative command/code in other statistical command; in Stata, for instance, the command regress gives as ...

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It's really important to vectorize operations as much as possible when working with big data in R when speed is a consideration. The code below is an example of multiple regression performed on a matrix with 1000 rows and 10000 columns with the independent variables of interest in each column. The same 5 covariates are also controlled for in every model. It ...

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In the chapter that deals with NMF of the book "Programming collective intelligence" , the author did NMF on several stock trading volumes and found some comovement. I googled a little. This did NMF on 40 chinese stock close prices. This developed A variant of nonnegative matrix factorization for Stock Trend Extraction. Another google found this also did ...

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I am not sure if I have correctly understood your problem. But, as you want to detect the market sentiment (bear/bull), you imply that there is extra information in the market that is not included in the stock prices yet. You should then rather use a collective factorization on (on-line) news monitoring, in order to detect previously unknown topics, as you ...

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