First year finance student here, I am reading some anomaly papers and find that most papers predict weekly, monthly or quarterly returns despite CRSP or OptionMetrics are in daily frequency. What's the reason for that?
Why most empirical asset pricing papers do not predict daily returns?

(Almost) infinite trading cost if you work with daily data in practice
After all, momentum strategies that rely on monthly rebalancing are criticised for their trading cost. Given that most strategies (factors) rely on some accounting variables that are only updated every three months at best, there's no need to pay for daily rebalancing...

noise
What does that mean? Returns at daily frequency are more subject to noise?
Yes. Suppose there is some true underlying price p*_t, which is a martingale, and you observe p_t = p*_t + eps_t. Now consider the observed return over j periods,
r_{t,t+j} = p_{t+j}  p_t = r*_{t,t+j} + eps_{t+j}  eps_t
where r*_{t,t+j} = p*_{t+j}  p*_t is the true return.
the measured return is thus equal to the true return plus noise with variance equal to 2*var(eps). The variance of the signal, r*_{t,t+j}  i.e., the thing you really want to measure  is going to be proportional to j. Errors in the prices you observe will therefore contribute a constant amount of variance to the observed returns, while the signal component, r*, will contribute a variance that grows with the horizon.So if you use monthly returns, the signaltonoise ratio is 21 times higher than for daily returns.

come on bro
you need to give some time for the market to make a response to shocks, news, or information
Compustat is collected by fiscal year with firms having different reporting time
I do not even understand what you mean. Look at fama's method: fiscal year t's characteristics to predict calendar year t+1's returns (there is no difference between you collecting the whole year's daily or monthly returns and add them up within the year). Fama only looks at the return's oneyear response. Whether that predictability reverses is another issue.
if you're asking timeseries predictive regressions like why when you regress returns onto many years' lagged PD you would find strong predictability and why when you regress returns onto several months' lagged volatility you wouldn't find any predictability, then this is still a puzzle that awaits you to solve

noise
What does that mean? Returns at daily frequency are more subject to noise?
Yes. Suppose there is some true underlying price p*_t, which is a martingale, and you observe p_t = p*_t + eps_t. Now consider the observed return over j periods,
r_{t,t+j} = p_{t+j}  p_t = r*_{t,t+j} + eps_{t+j}  eps_t
where r*_{t,t+j} = p*_{t+j}  p*_t is the true return.
the measured return is thus equal to the true return plus noise with variance equal to 2*var(eps). The variance of the signal, r*_{t,t+j}  i.e., the thing you really want to measure  is going to be proportional to j. Errors in the prices you observe will therefore contribute a constant amount of variance to the observed returns, while the signal component, r*, will contribute a variance that grows with the horizon.
So if you use monthly returns, the signaltonoise ratio is 21 times higher than for daily returns.This analysis is a good example of the time averaging fallacy.

come on bro
you need to give some time for the market to make a response to shocks, news, or information
Compustat is collected by fiscal year with firms having different reporting time
I do not even understand what you mean. Look at fama's method: fiscal year t's characteristics to predict calendar year t+1's returns (there is no difference between you collecting the whole year's daily or monthly returns and add them up within the year). Fama only looks at the return's oneyear response. Whether that predictability reverses is another issue.
if you're asking timeseries predictive regressions like why when you regress returns onto many years' lagged PD you would find strong predictability and why when you regress returns onto several months' lagged volatility you wouldn't find any predictability, then this is still a puzzle that awaits you to solveMy time series regression shows that global warming predicts a rising stock market. JF idea anyone?

This analysis is a good example of the time averaging fallacy.
No, the distinction is the exact point. The timeaveraging fallacy is due to the fact that returns are not serially correlated, so that an innovation to the return won't be undone over time. But when there is measurement error in prices, that in fact does produce serial correlation  it induces an MA(1) term.
Obviously it's possible for there also to be measurement error in the returns themselves, but it's very hard to come up for a story why that would happen (not to mention the fact that the implications for observed valuations are counterfactual). Things like bid/ask bounce will create errors in prices, not returns.
Comments like yours are why I find 90% of my conversations with finance people frustrating and tiring. The quality of the knowledge of finance people about their own data is far lower than that of economists about theirs.

There are quite a few seminal papers predicting daily returns, mostly market returns. Daily crosssectional predictability is 1) hard to execute considering the cost; 2) full of noise and the result might simply be spurious or from overfitting; and 3) mostly lean towards smallcap stocks.

Yes. Suppose there is some true underlying price p*_t, which is a martingale, and you observe p_t = p*_t + eps_t. Now consider the observed return over j periods,
r_{t,t+j} = p_{t+j}  p_t = r*_{t,t+j} + eps_{t+j}  eps_t
where r*_{t,t+j} = p*_{t+j}  p*_t is the true return.
the measured return is thus equal to the true return plus noise with variance equal to 2*var(eps). The variance of the signal, r*_{t,t+j}  i.e., the thing you really want to measure  is going to be proportional to j. Errors in the prices you observe will therefore contribute a constant amount of variance to the observed returns, while the signal component, r*, will contribute a variance that grows with the horizon.
So if you use monthly returns, the signaltonoise ratio is 21 times higher than for daily returns.I love how you write that "p*_t is a martingale" but don't define your filtration properly. So is a "monthly" participant just going to observe a sequence of month end prices, and ignore the daily data? Clearly, the filtration generated by {day 0, day 1, ..., day 30} is bigger than the filtration generated by just {day 30}. A martingale with respect to the latter, is not a martingale with respect to the former.
Ignoring all that stochastic analysis stuff, your measurement error assumption makes no sense. Are you literally telling me  of all things  prices of publicly traded stocks are recorded with error? Especially at the daily level?
Finally, before screaming on how finance people are dumdums, perhaps you should think closer on the stochastic properties of time series data. There are many reasons why finance academia prefers monthly over daily data, but "measurement error" is definitely not one of them.