I am calculating a high-frequency beta. For example I have 90 days of data of the S&P and GOOGLE and I have 10-minute percent returns for each instrument. Each day has 34 10-minute percent returns so my data set is 2 vectors that are both 3060 in length (90 days x 34 10-miunute percent returns each day) = 3060 data points for the S&p and 3060 data points for GOOGLE.
Next in R I run a regression
reg= lm(google~snp) # both the google and snp vector have lenght = 3060 summary(reg)
My question is that sometimes I get low R-squared for the regression. Is this expected...should/can anything thing be done about it?
I know beta is usually done using daily data NOT 10-minute data but even with daily data sometimes the r-squared is low. What is the significance of beta with a low r-squared?