How can I fit data with flat lines over a specific range in R?

I have been trying to fit some data with a change in the average y-values over a certain range of x values. I have been stuck on trying to get this to work for a little while now.

For example, given some controlled randomized data and a desired fit:

library(tidyverse)

Data <- data.frame(Time = c(1:100, 101:500, 501:1000), 
                   Value = c(runif(100, 0, 500), 
                             runif(400, 500, 1000), 
                             runif(500, 0, 100)),
                   Desired_fit = c(rep_len(250,100), 
                                   rep_len(750,400),
                                   rep_len(50,500)))

plot(Data$Time, Data$Value)
lines(Data$Time, Data$Desired_fit, col = "red")

I have tried to smooth, get a running average, and spline my data, but this produced a curve fit instead of the Desired_fit above. In essence, I am trying to fit a horizontal line across each inflection point in the data set.

The closest thing I have tried is by using the rollmean()from the zoo package:

library(zoo)

moving_average <- rollmean(Data$Value, 50, fill = NA)

plot(Data$Time, Data$Value)
lines(Data$time, moving_average, col = "red")

Any help or advice would be greatly appreciated!

Thank you!

Calculate the segment breakpoints using dpseg. Each row of dp$segments defines one segment with start and end
columns being indexes of start and end points of that segment and x1 and x2 columns being the corresponding times. Finally plot the means of the data in each segment.

library(dpseg)

plot(Value ~ Time, Data)

dp <- with(Data, dpseg(x = Time, y = Value, jumps = TRUE))
segs <- dp$segments

xx <- with(segs, c(rbind(x1, x2)))
yy <- mapply(\(st,en) mean(Data$Value[st:en]), segs$start, segs$end) |> rep(each=2)
lines(xx, yy, col = "red", lwd = 3)

Alternately replace everything from the xx<-... line onwards above with the following if the vertical line segments are not wanted.

nr <- nrow(segs)
for(i in 1:nr) with(segs[i, ],
  segments(x0 = x1, 
           y0 = mean(Data$Value[start:end]),
           x1 = x2, col = "red", lwd = 3))

Old

This did not work so well.

Calculate the breakpoints using breakpoints from strucchange and then plot.the data and the fitted values.

library(strucchange)
bp <- with(Data, breakpoints(Value ~ 1))
plot(Value ~ Time, Data)
lines(fitted(bp) ~ Time, Data, col = "red", lwd = 2)

Note

Since random numbers were used to generate the data in the question we used set.seed first to make it reproducible.

set.seed(123)
Data <- data.frame(Time = c(1:100, 101:500, 501:1000), 
                   Value = c(runif(100, 0, 500), 
                             runif(400, 500, 1000), 
                             runif(500, 0, 100)),
                   Desired_fit = c(rep_len(250,100), 
                                   rep_len(750,400),
                                   rep_len(50,500)))