Как я могу создать скользящую регрессию для почти 500 фондов и сохранить параметры?

Question

У меня есть ежемесячные данные о возвращении около 500 средств. Я оцениваю с помощью al oop для каждого фонда линейную модель (факторная модель, но это не имеет значения). После этого я хочу сохранить различные параметры, такие как константа (альфа), R квадрат и c. в отдельном векторе. Теперь у меня есть 2 проблемы:

1.) Как я могу адаптировать эту функцию, чтобы линейная модель оценивалась не по всему временному ряду, а только, например, с 1999 по 2007 гг.

2. Я хочу оценить ту же линейную модель, что и выше, используя скользящую регрессию (перекрывающееся окно -> 3 года, затем t + 1). Тем самым всегда нужно оценивать 3 года.

У кого-нибудь есть идеи, как я могу это реализовать? Важно, чтобы я сохранил соответствующие параметры регрессии в фонды или моменты времени. Это мне нужно для последующего анализа.

Большое спасибо за вашу ценную помощь!

#Constant Alpha
constant_alpha <- matrix(NA, ncol = ncol(fund_returns),
                      nrow = 1)
colnames(constant_alpha) <- colnames(fund_returns)
row.names(constant_alpha) <- "alpha"

#Factor MKT
beta_mkt <- matrix(NA, ncol = ncol(fund_returns),
                     nrow = 1)
colnames(beta_mkt) <- colnames(fund_returns)
row.names(beta_mkt) <- "MKT.factor"

#Residuals from regression
parameter_residuals <- matrix(NA, ncol = ncol(fund_returns),
                          nrow = nrow(fund_returns))
colnames(parameter_residuals) <- colnames(fund_returns)
row.names(parameter_residuals) <- row.names(fund_returns)

#T Statistics
t_stat <- matrix(NA, ncol = ncol(fund_returns),
                        nrow = 1)
colnames(t_stat) <- colnames(fund_returns)
row.names(t_stat) <- "t.stat"

#R Squared
rsquared <- matrix(NA, ncol = ncol(fund_returns),
                 nrow = 1)
colnames(rsquared) <- colnames(fund_returns)
row.names(rsquared) <- "R Squared"


###Regression 1 Factor Model
for (j in 1:ncol(fund_returns)){
master_regression <- lm(fund_returns[,j]~MKT$log_return_spi_tr, na.action=na.exclude)
constant_alpha[,j] <- master_regression$coefficients[1]
beta_mkt[,j] <- master_regression$coefficients[2]
parameter_residuals[,j] <- resid(master_regression)
rsquared[,j] <- summary(master_regression)$r.squared
t_stat[,j] <- coeftest(master_regression,
                              vcov=NeweyWest(master_regression,
                                             lag = 3.43,
                                             prewhite = FALSE) )[, "t value"][1]
}


structure(list(Aberdeen.Global.Swiss.Equity.I.Acc.CHF = c(NA_real_, 
NA_real_, NA_real_, NA_real_, NA_real_, NA_real_), AKB.IF.AKB.Aktien.Schweiz.Top.SelectionP = c(NA_real_, 
NA_real_, NA_real_, NA_real_, NA_real_, NA_real_)), row.names = c("03/31/1999", 
"04/30/1999", "05/31/1999", "06/30/1999", "07/31/1999", "08/31/1999"
), class = "data.frame")


##2nd Data Set

structure(list(log_return_spi_tr = structure(c(0.0152816392302366, 
0.0378937104499979, -0.0478500114570899, 0.00810185769601013, 
0.000145657422827128, 0.0165672504386212, -0.00797579251287495, 
0.0290301060898823, 0.035956012214438, 0.0293666990745844, -0.0627798495617515, 
0.00711864047474897, 0.0661419241966179, -3.34929502301407e-05, 
0.0375191295938837, 0.00448358225294676, 0.0390511097581339, 
0.0317710675898706, -0.0465118023379176, 0.027155763163476, -0.00714744748013807, 
0.0157645940205189, -0.0101992619661253, -0.0447060225294802, 
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0.0139535862309081, 0.0248262330523996, 0.0141992829420161, -0.0537181232417563, 
0.00523055919656912, 0.0361945039724905, 0.0291602418812449, 
0.0324489628340583, 0.0200248476751081, -0.00548483695255975, 
0.0390590909275641, 0.0441255524510975, -0.037614994787571, 0.0295388679512012, 
0.0589998995927736, 0.00813077958503072, -0.0221443218229744, 
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0.0149797774247151, -0.029939944678576, -0.0325664977634954, 
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0.0543877372481294, 0.00615606823049397, -0.0784760943530785, 
0.0184370704749011, 0.0161816097628318, -0.0856987932191444, 
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0.081244724359415, 0.0280463262806592, 0.0102352744191538, 0.0915001691631812, 
0.0452984361954059, 0.0213082710315451, -0.0108120704703776, 
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0.0340758572877125, 0.0415602609930428, -0.0270732954426531, 
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-0.00447649405411177, 0.023395555437272, 0.0282010642429995, 
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0.0233455120050152, -0.0273777407914348, 0.037530485593793, 0.001661670959475, 
-0.0578489426612077, -0.0671254983375675, -0.0513541912196729, 
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0.0488571956434392, -0.0019629316924803, 0.017993460489711, 0.0128419976142187, 
0.0302094477057473, 0.00241447784669369, 0.0763188342216647, 
0.0340457366438898, 0.0306906837249592, 0.0247375301499897, 0.00940627970438435, 
-0.0335696635361877, 0.0206163024042301, -0.00605593712802488, 
0.034391283861515, 0.0282151088741571, 0.00487376039040655, -0.00372995773504314, 
-0.00095605779624286, 0.0412704471097314, 0.00510188350499519, 
0.0159075626361975, 0.0265578142645104, -0.0120293098732969, 
-0.0150097990230282, 0.0280038233175901, 0.0149882366892307, 
-0.000434796618657529, 0.0340518731222712, -0.0152238831376241, 
-0.069468555182322, 0.0767525394628645, 0.0238628922450435, 0.0077349349390996, 
0.0182241630561997, -0.0501762423908598, 0.0693638615623637, 
-0.0619919740481638, -0.0345123224872932, 0.0509459918610933, 
0.0108307413486894, -0.0151659678208347, -0.054605940571081, 
-0.0428675699404941, 0.00811667387153037, 0.0296418820266151, 
0.0367390665902398, -0.025895542087099, 0.0192110169171968, 0.00987271875748519, 
-0.0036563810466852, -0.0348850941679277, 0.00520632863392656, 
0.0389174699339723, 0.0108293134094204, 0.0329659159657574, 0.0284935271580142, 
0.0344982928105892, 0.0269742208242167, -0.0118300204661654, 
0.0178282679706498, -0.0130138137605087, 0.0261945540235295, 
0.0149225659576437, 0.00662992916017124, 0.00714727133565773, 
-0.00130857910353477, -0.0456183281602929, -0.00672325028241261, 
0.032349726310029, -0.0348169746356177, 0.015861102068671, 0.0537994736826288, 
-0.0145826337698072, 0.00626320025377147, -0.0160696633296418, 
-0.00893261098062226, -0.0698226339743879, 0.0672959528868269, 
0.0419181422598687, 0.0249255776965036, 0.0430047528893329, -0.0163768657126546, 
0.0368072730154179, 0.00724324069121174, -0.000292638001008427, 
0.0141773713709412, 0.00845908492939351, 0.0271121896771014, 
0.0126514556473083), .Tsp = c(1999.16666666667, 2019.91666666667, 
12), class = "ts")), row.names = c("03/31/1999", "04/30/1999", 
"05/31/1999", "06/30/1999", "07/31/1999", "08/31/1999", "09/30/1999", 
"10/31/1999", "11/30/1999", "12/31/1999", "01/31/2000", "02/29/2000", 
"03/31/2000", "04/30/2000", "05/31/2000", "06/30/2000", "07/31/2000", 
"08/31/2000", "09/30/2000", "10/31/2000", "11/30/2000", "12/31/2000", 
"01/31/2001", "02/28/2001", "03/31/2001", "04/30/2001", "05/31/2001", 
"06/30/2001", "07/31/2001", "08/31/2001", "09/30/2001", "10/31/2001", 
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"10/31/2019", "11/30/2019", "12/31/2019"), class = "data.frame")