Regression on small values I am working on a problem to predict a stock's returns with a certain set of features.
The problem which I am facing is that when I try to predict the stock price itself, the models capture the trend very well and the R-Squared scores are closer to 1.
But, when I try to predict the daily returns of the stock (a pct_change on the Stock Price), my values are not able to capture the trend, and the R-Squared scores go negative (sometimes even beyond -1).
I know that a workaround for this would be simply to predict the stock prices and then do a pct_change() on the predicted price (which captures the trends in daily returns accurately). However, I want to know as to what I could do to improve my current models with the dependent variable being the returns themselves as opposed to the Stock Price.
My hunch is that this could be because the daily returns themselves have a lower values (the average returns for my stock turn out to be about ~0.0002) whereas the stock prices themselves have somewhat high values (average stock price over 90 days ~ $30).
But, I believe that the models should still work well enough. My independent variables also have a range between -1 and 1, and they have a positive correlation with the stock's returns and the stock's price.
What could I do to overcome this issue?
Thanks!
 A: Lot's more data and trading capital.
If I understand you right, you want to predict prices at, say P(t+1) based on today's price at P(t).  The problem is that any time series like stock prices there is a natural correlation from today today's price and tomorrow's: much like weather, the best estimate for tomorrow's price is today's price likely with a but of drift.
The problem with this is that it gives a false sense of security.  In cross-sectional data a high R-squared gives you a sense of what you have accomplished.  Usually one looks at both the "adjusted R-squared" (which is, loosely, the R-squared once that serial correlation is removed or accounted for.  Hence, we try to predict the amount by which tomorrow's price can be estimated today, and that ideally captures the "real" R-squared - not one boosted by serial correlation.  One would also look at the t-statistic on the "growth per day" to make sure it is statistically sound.
One thing that should not matter is the size of the typical variables.  you could laser-measure movements in the Hoover dam measured in thousandths in a millimeter based on the weight of the water in the lake as measured in quadrillion pounds.  All of the scaling should be irrelevant, it just gives you more accurate or intuitive results.
