Rolling multi regression in R data table - r

Question

Say I have an R data.table DT which has a list of returns:
Date Return
2016-01-01 -0.01
2016-01-02 0.022
2016-01-03 0.1111
2016-01-04 -0.006
...
I want to do a rolling multi regression of the previous N observations of Return predicting the next Return over some window K. E.g. Over the last K = 120 days do a regression of the last N = 14 observations to predict the next observation. Once I have this regression I want to use the predict function to get a prediction for each row based on the regression. In pseudocode it would be something like:
DT[, Prediction := predict(lm(Return[prev K - N -1] ~ Return[N observations prev for each observation]), Return[N observations previous for this observation])]
To be clear i want to do a multi regression so if N was 3 it would be:
lm(Return ~ Return[-1] + Return[-2] + Return[-3]) ## where the negatives are the prev rows
How do I write this (as efficiently as possible).
Thanks

Answer 1

If I understand correctly you want a quarterly auto-regression.
There's a related thread on time-series with data.table here.
You can setup a rolling date in data.table like this (see the link above for more context):
#Example for quarterly data
quarterly[, rollDate:=leftBound]
storeData[, rollDate:=date]
setkey(quarterly,"rollDate")
setkey(storeData,"rollDate")
Since you only provided a few rows of example data, I extended the series through 2019 and made up random return values.
First get your data setup:
require(forecast)
require(xts)
DT <- read.table(con<- file ( "clipboard"))
dput(DT) # the dput was too long to display here
DT[,1] <- as.POSIXct(strptime(DT[,1], "%m/%d/%Y"))
DT[,2] <- as.double(DT[,2])
dat <- xts(DT$V2,DT$V1, order.by = DT$V1)
x.ts <- to.quarterly(dat) # 120 days
dat.Open dat.High dat.Low dat.Close
2016 Q1 1292 1292 1 698
2016 Q2 138 1290 3 239
2016 Q3 451 1285 5 780
2016 Q4 355 1243 27 1193
2017 Q1 878 1279 4 687
2017 Q2 794 1283 12 411
2017 Q3 858 1256 9 1222
2017 Q4 219 1282 15 117
2018 Q1 554 1286 32 432
2018 Q2 630 1272 30 46
2018 Q3 310 1288 18 979
2019 Q1 143 1291 10 184
2019 Q2 250 1289 8 441
2019 Q3 110 1220 23 571
Then you can do a rolling ARIMA model with or without re-estimation like this:
fit <- auto.arima(x.ts)
order <- arimaorder(fit)
fcmat <- matrix(0, nrow=nrow(x), ncol=1)
n <- nrow(x)
for(i in 1:n)
{
x <- window(x.ts, end=2017.99 + (i-1)/4)
refit <- Arima(x, order=order[1:3], seasonal=order[4:6])
fcmat[i,] <- forecast(refit, h=h)$mean
}
Here's a good related resource with several examples of different ways you might construct this: http://robjhyndman.com/hyndsight/rolling-forecasts/

Answer 2

You have to have the lags in the columns anyway, so I if i understand you correctly you can do something like this, say for a lag of 3:
setkey(DT,date)
lag_max<-3
for(i in 1:lag_max){
set(DT,NULL,paste0("lag",i),shift(DT[["return"]],1L,type="lag"))
}
DT[, prediction := lm(return~lag1+lag2+lag3)[["fitted.values"]]]