CODEWITHSUNDEEP
rlinear-regression
Andrew Bannerman
Andrew Bannerman

Reputation: 1305

Fix starting point of rolling linear regression

take two series 

xiv <- read.table("D:/R Projects/Final Scripts/VIX_term_structure/xiv.txt", header=FALSE, stringsAsFactors=FALSE) 

2010-12-02  6.559722e-02
2010-12-03  5.868252e-02
2010-12-06  1.911059e-02
2010-12-07  9.420547e-03
2010-12-08  1.734460e-02
2010-12-09  2.258762e-02
2010-12-10  8.547732e-03
2010-12-13 -1.418142e-02
2010-12-14 -6.724549e-03
2010-12-15 -2.176708e-02
2010-12-16  1.340342e-02
2010-12-17  2.195712e-02
2010-12-20  2.646760e-02
2010-12-21  1.640722e-02
2010-12-22  2.594454e-03
2010-12-23 -3.210416e-02
2010-12-27 -2.665218e-02

spy <- read.table("D:/R Projects/Final Scripts/VIX_term_structure/spy.txt", header=FALSE, stringsAsFactors =FALSE) 

2010-12-02  1.280823e-02
2010-12-03  2.692895e-03
2010-12-06 -1.058301e-03
2010-12-07  5.706029e-04
2010-12-08  3.663117e-03
2010-12-09  3.894063e-03
2010-12-10  5.817504e-03
2010-12-13  6.424447e-04
2010-12-14  8.838366e-04
2010-12-15 -4.588375e-03
2010-12-16  5.817468e-03
2010-12-17  1.064127e-03
2010-12-20  2.413213e-03
2010-12-21  6.340508e-03
2010-12-22  3.109997e-03
2010-12-23 -1.431073e-03
2010-12-27  3.984963e-04

Using the date above, lets prepare it for our example: 

# Prepare data for reproducible example 
spy <- read.table("D:/R Projects/Final Scripts/VIX_term_structure/spy.txt", header=FALSE, stringsAsFactors =FALSE) 
xiv <- read.table("D:/R Projects/Final Scripts/VIX_term_structure/xiv.txt", header=FALSE, stringsAsFactors=FALSE) 
colnames(spy)[1] <- "Date"
colnames(spy)[2] <- "SPY"
colnames(xiv)[1] <- "Date"
colnames(xiv)[2] <- "XIV"
library(lubridate)
spy$Date <- ymd(spy$Date)  # convert to date format
xiv$Date <- ymd(xiv$Date)  
df <- merge(spy,xiv, by='Date') # Merge two series to one data frame
# Package roll for rolling linear regression
library(roll)
runs <- roll::roll_lm(x=as.matrix(df$SPY), y=as.matrix(df$XIV),width = 2, intercept = TRUE)
head(runs)
beta.spy.independant <- as.data.frame(runs$coefficients[, "x1"])
colnames(beta.spy.independant)[1] = "beta"
plot(beta.spy.independant$beta,type="l")

All is fine and well, its short sample so we only run a regression width of 2 days. So what I wish to do is fix the start point of the regression and then allow it to run over the full sample. This is in contrast to picking a sliding window ie a width of 2 would run 1:2.. then 2:3, 3:4 etc... where a fixed window runs 1:2, 1:3, 1:4 etc...

How can I achieve this?

Upvotes: 2

Views: 294

Answers (1)

G. Grothendieck
G. Grothendieck

Reputation: 269431

Read the data in using read.zoo to create two zoo series, cbind them together to create both and run rollapplyr on that using a width vector of 1:nrow(both) which says to run the first regression with a width of 1, the second with a width of 2, etc. linreg is defined to regress the first column on the second column with an intercept returning the coefficients. Coefs is an n by 2 zoo series of the coefficients. 

library(zoo)

# ser1 <- read.zoo("myfile")

ser1 <- read.zoo(text = Lines1)
ser2 <- read.zoo(text = Lines2)

both <- cbind(ser1, ser2)
n <- nrow(both)
linreg <- function(m) if (is.null(dim(m))) NA else coef(lm(as.data.frame(m)))
Coefs <- rollapplyr(both, 1:n, linreg, by.column = FALSE)

plot(Coefs[, 2])

rollapplyr also works on plain matrices and on data frames. Note that if z is a zoo object then coredata(z) and time(z) are its data (as a plain vector or matrix) and index, respectively. fortify.zoo(z) is its data frame representation.

Note: Input used is:

Lines1 <- "
2010-12-02  6.559722e-02
2010-12-03  5.868252e-02
2010-12-06  1.911059e-02
2010-12-07  9.420547e-03
2010-12-08  1.734460e-02
2010-12-09  2.258762e-02
2010-12-10  8.547732e-03
2010-12-13 -1.418142e-02
2010-12-14 -6.724549e-03
2010-12-15 -2.176708e-02
2010-12-16  1.340342e-02
2010-12-17  2.195712e-02
2010-12-20  2.646760e-02
2010-12-21  1.640722e-02
2010-12-22  2.594454e-03
2010-12-23 -3.210416e-02
2010-12-27 -2.665218e-02"

Lines2 <- "
2010-12-02  1.280823e-02
2010-12-03  2.692895e-03
2010-12-06 -1.058301e-03
2010-12-07  5.706029e-04
2010-12-08  3.663117e-03
2010-12-09  3.894063e-03
2010-12-10  5.817504e-03
2010-12-13  6.424447e-04
2010-12-14  8.838366e-04
2010-12-15 -4.588375e-03
2010-12-16  5.817468e-03
2010-12-17  1.064127e-03
2010-12-20  2.413213e-03
2010-12-21  6.340508e-03
2010-12-22  3.109997e-03
2010-12-23 -1.431073e-03
2010-12-27  3.984963e-04"

Upvotes: 2

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