Different color in the same price plot

The problem is that the clusters get merged in the lines. You could use the rle lengths to increase the number by one when the clusters change in the time series. For this use Map to repeat consecutive numbers l times. Then you are able to split on these growing numbers but use cluster to define the color of the lines. For the latter use lapply to loop over the splitted e.

cl <- kmeans(nsdq.prices, 3)$cluster
l <- rle(as.numeric(cl))$lengths
s <- Map(rep, seq(l), l)
e <- split(cbind(nsdq.prices, cl), unlist(s))

plot(nsdq.prices, type="l", col=7, ylim=c(6000, 13000))
invisible(lapply(e, function(x) lines(x$Adjusted, col=x$cl + 1)))
legend("topleft", leg=c(sprintf("cl %s", 1:3), "missing"), col=c((1:3)+1, 7), lty=1)

Where there's no date defined there appear gaps. We could use the zoo interpolations by overplotting the original plot using a "missing" color.

I hope this piece of code helps you:

library(tseries)

####

nomiequity <- "^IXIC" 
datastart  <- "2019-09-18"

nsdq.prices <- get.hist.quote(instrument  = nomiequity,    
                              compression = "d",         
                              start       = datastart, 
                              end         = "2020-12-31", 
                              retclass    = "zoo",
                              quote       = "AdjClose")

b<-kmeans(nsdq.prices,3)
c<-b$cluster
d<- merge(nsdq.prices, c)
e<-split(nsdq.prices, c)


e3= e[['3']]
empty <- zoo(order.by=seq.Date(head(index(e3),1),tail(index(e3),1),by="days"))
e3=merge(e3,empty)


e2= e[['2']]
empty <- zoo(order.by=seq.Date(head(index(e2),1),tail(index(e2),1),by="days"))
e2=merge(e2,empty)


plot(nsdq.prices, type="l", col="green", ylim=c(6000, 13000))
lines(e2, type = "l", col="red")
lines(e3, type = "l", col="blue")

I just used this: R: Filling missing dates in a time series?

With this methodology I found the rows where cluster value changes, then selected those dates and added NA values for adjusted. geom_line breaks when NA values occur, hence giving the desired result.

library(ggplot2)
library(dplyr)
library(data.table)

#add date as a column
datum <- index(d)
d <- as.data.table(d)
d$Datum <- datum

#add row number as a column
d$Row <- 1:nrow(d)

#find rows of d where cluster value changes
rows <- which(d$c != dplyr::lag(d$c))
rows <- d[Row %in% rows]

#add NA values for Adjusted at the Dates where values change(which breaks the geom_line)
rows <- rows[, Adjusted := NA]

#merge rows (NA values of Adjusted) with d
d <- rbind(rows, d)

#create a plot
ggplot(d, aes(x = Datum, y = Adjusted, col = as.factor(c))) + geom_line() + scale_color_manual(values = c("green", "red", "blue"))