You can find a good overview here:
Seasonal Anomalies by Ziemba, W.; Dzahabarov, C.
This chapter is a survey of seasonal anomalies. Ziemba has been
involved in the re- search and trading of such anomalies as the
January turn-of-the-year effect since 1982. His research plus that of
other academics plus the very useful practitioner ...
As Chris already wrote in his comments: your
description is not complete. But I would suggest to
write a simple loop over your data matrix. There is no
need for working with zoo/xts while doing these
I use your sample dataset and call it data0.
time0 <- index(data0)
assets <- colnames(data0)
data0 <- ...
In my humble opinion, the most volatile day during the week should be monday, since it is the day that incorporates the greater number of information that are still not incorporated by the price, but I never tested by myself, so, as you suggested monday-to-monday returns should be different from tuesday-to-tuesday.
The literature suggests different solution ...
Including a seasonal independent variable represents a problem similar to including one with serial correlation or attempting to fit a misspecified model. Namely, you're attempting to describe a non-linear relationship using a linear model. Using it as is, your estimates are likely to be biased, and your confidence intervals smaller than appropriate.