How to interpret R-square trend?

[DennisLe]

Hi all,

Appreciate if you could help me with these questions.

When I calculate beta between a stock vs an index. R-square represents how much the index returns explain the stock price returns.

However, if I see a declining/increasing trend in RSQ (Beta could stay unchanged), how could I interpret that trend now?

Now if I calculate RSQ for all index members, sum them together and see a trend, what is the implication from the trend there?

Thank you.

Dennis

[PGStats]

Beta, I guess is a linear regression slope. Members, I guess are stocks that make up a market index (a weighted sum). What is RSQ?

[rainxi]

My guess is RSQ represents R-Square. 

Did you include more independent variables into or exclude some variables from the model? That may cause the change  in R-Square. 

Are you trying to measure the relationship between variables or to do forecasting?  R-Sqaure measures the goodness-of-fit. If you would like to evaluate the forecasting performance, you may want to do out-of-sample test. Here is a good paper 

L. J. Tashman, “Out-of-sample tests of forecasting accuracy: an analysis and review,” Int. J. Forecast., vol. 16, no. 4, pp. 437–450, 2000.

http://www.sciencedirect.com/science/article/pii/S0169207000000650

Thanks,

Rain

[DennisLe]

Yeah, sr I didnt make it clear. RSQ is R-Square.

Totally aware of the concepts but I got some troubles interpreting the results here.

I'm doing 1 factor analysis only so I do not use many variables.

Definitely I want to do forecasting. The issue here is, if I do rolling regression day by day and see a declining trend in R-square. That seems to indicate that my independent (even though the index is not that independent) variable has less and less power in predicting the future price. Hence, what I can think of is, waiting to see when R-square is trending up to decide to reuse the model again.

Thanks for sharing the paper. I'll take a look.

In the meantime, hope someone could help clarify the sum of R-square trending issue.

Dennis