Python pandas rolling computations with custom step size

I have a pandas dataframe with daily data. At the last day of each month, I would like to compute a quantity that depends on the daily data of the previous n months (e.g., n=3).

My current solution is to use the pandas rolling function to compute this quantity for every day, and then, only keep the quantities of the last days of each month (and discard all the other quantities). This however implies that I perform a lot of unnecessary computations.

Does somebody of you know how I can improve that?

Thanks a lot in advance!

EDIT: In the following, I add two examples. In both cases, I compute rolling regressions of stock returns. The first (short) example shows the problem described above and is a sub-problem of my actual problem. The second (long) example shows my actual problem. Therefore, I would either need a solution of the first example that can be embedded in my algorithm for solving the second example or a completely different solution of the second example. Note: The dataframe that I'm using is very large, which means that multiple copies of the entire dataframe are not feasible.

Example 1:

import pandas as pd
import random
import statsmodels.api as sm

# Generate a time index
dates = pd.date_range("2018-01-01", periods=365, freq="D", name='date')
df = pd.DataFrame(index=dates,columns=['Y','X']).sort_index()

# Generate Data
df['X'] = np.array(range(0,365))
df['Y'] = 3.1*X-2.5
df = df.iloc[random.sample(range(365),280)] # some days are missing
df.iloc[random.sample(range(280),20),0] = np.nan # some observations are missing
df = df.sort_index()
# Compute Beta
def estimate_beta(ser):
    return sm.OLS(df.loc[ser.index,'Y'], sm.add_constant(df.loc[ser.index,'X']), missing = 'drop').fit().params[-1]     
df['beta'] = df['Y'].rolling('60D', min_periods=10).apply(estimate_beta) # use last 60 days and require at least 10 observations

#  Get last entries per month
df_monthly = df[['beta']].groupby([pd.Grouper(freq='M', level='date')]).agg('last')
df_monthly

Example 2:

import pandas as pd
from pandas import IndexSlice as idx
import random
import statsmodels.api as sm

# Generate a time index
dates = pd.date_range("2018-01-01", periods=365, freq="D", name='date')
arrays = [dates.tolist()+dates.tolist(),["10000"]*365+["10001"]*365]
index = pd.MultiIndex.from_tuples(list(zip(*arrays)), names=["Date", "Stock"])
df = pd.DataFrame(index=index,columns=['Y','X']).sort_index()

# Generate Data
df.loc[idx[:,"10000"],'X'] = X = np.array(range(0,365)).astype(float)
df.loc[idx[:,"10000"],'Y'] = 3*X-2
df.loc[idx[:,"10001"],'X'] = X
df.loc[idx[:,"10001"],'Y'] = -X+1
df = df.iloc[random.sample(range(365*2),360*2)] # some days are missing
df.iloc[random.sample(range(280*2),20*2),0] = np.nan # some observations are missing

# Estimate beta
def estimate_beta_grouped(df_in):
    def estimate_beta(ser):
        return sm.OLS(df.loc[ser.index,'Y'].astype(float),sm.add_constant(df.loc[ser.index,'X'].astype(float)), missing = 'drop').fit().params[-1]
    df = df_in.droplevel('Stock').reset_index().set_index(['Date']).sort_index()
    df['beta'] = df['Y'].rolling('60D',min_periods=10).apply(estimate_beta)
    return df[['beta']]
df_beta = df.groupby(level='Stock').apply(estimate_beta_grouped)

# Extract beta at last day per month
df_monthly = df.groupby([pd.Grouper(freq='M', level='Date'), df.index.get_level_values(1)]).agg('last') # get last observations
df_monthly = df_monthly.merge(df_beta, left_index=True, right_index=True, how='left') # merge beta on df_monthly
df_monthly