How to extract te residual standard error from rolling regressions - r

Question

I'm trying to get the residual standard deviation (residual standard error in R summaries) for rolling regressions. I'm trying to do rolling regressions on 20 days of stock returns over a total of 4000 days. I can do rolling regressions, and I can get the residual standard deviation from a regular lm regression, but not for the rolling regression.
My data is similar to the following, where the data frame has the returns of multiple stocks and the vector is an index return:
data<-as.data.frame(matrix(rexp(20000, rate=.1), ncol=20))
vector<-rexp(1000,rate=0.1)
I can produce a sigma for an lm regression: sigma(lm(data$V1~vector))
I can produce a rolling regression with library(roll) and roll_lm(vector,data$V1,width=20)and with library(rollRegres)and roll_regres(data$V1~vector,width=20)
Is there a way to get the residual standard error / residual standard deviation / sigma from such rolling regressions?
I would like to end up with a data frame containing only the residual standard deviations.
Thanks!

Answer 1

If you read the code for summary.lm, the residual standard error is the square root of residual sum of squares (rss) / degree of freedom of residuals (rdf). Since roll_lm doesn't retain this, you need to use the coefficients to get the prediction and calculate this again:
data<-as.data.frame(matrix(rexp(20000, rate=.1), ncol=20))
vector<-rexp(1000,rate=0.1)
library(roll)
WI = 20
rlm = roll_lm(vector,data$V1,width=WI)
rdf = WI - ncol(rlm$coefficients)
Below we go through every window, get the prediction and calculate rss and from there get the sigma:
sigma = sapply(1:(nrow(data)-WI+1),function(i){
# basically intercept + predictor * coef
pred = cbind(rep(1,WI),vector[i:(i+WI-1)]) %*% rlm$coefficients[WI+i-1,]
rss = sum((data$V1[i:(i+WI-1)] - pred)^2)
sqrt(rss/rdf)
})
We can wrap this up in a function, that takes as input an x,y:
roll_w_sigm = function(x,y,WI=20){
rlm = roll_lm(x=vector,y=y,width=WI)
rdf = WI - ncol(rlm$coefficients)
rlm$sigma = sapply(1:(length(y)-WI+1),function(i){
pred = cbind(rep(1,WI),vector[i:(i+WI-1)]) %*% rlm$coefficients[WI+i-1,]
rss = sum((y[i:(i+WI-1)] - pred)^2)
sqrt(rss/rdf)
})
rlm
}
For 1 column:
res = roll_w_sigm(vector,data$V1)
head(res$sigma)
[1] 9.102188 9.297425 9.324338 9.509460 7.849201 7.993087
For all columns:
lapply(data,function(i)roll_w_sigm(vector,i))