Dear all,
you can find below my solution for sliding a window. Please find below the code for the two alternatives and the benchmarks.
 
 
install.packages('caTools')
require(caTools)
do_sliding_for_a_window_duty_cycle <- function(DataToAnalyse,  windowSize) {


  data<-DataToAnalyse
  out <- numeric()
  elements<- numeric()
  if (length(data[,1]) >= windowSize){
      for (i in 1:(length(data[,1]) - windowSize +1  )) {
        out[i] <- mean(data[i:(i + windowSize - 1), ])
        elements[i]<-length(i:(i + windowSize - 1))
      }
  }

  return (list(result=out , numberOfElements=elements, windowSize=windowSize ))
}


do_sliding_for_a_window_duty_cycle_alternative <- function(DataToAnalyse, 
windowSize) {
    result= runmean(rowMeans(DataToAnalyse),windowSize,endrule="trim",alg="C")

    return( list(result= result, windowSize=windowSize))
}



DataToAnalyse<-matrix(data=round(seq(1:100000000)),nrow=10000,byrow=TRUE)



# How much time they need to runmean


system.time(a<-do_sliding_for_a_window_duty_cycle_alternative(DataToAnalyse,500))

system.time(b<-do_sliding_for_a_window_duty_cycle(DataToAnalyse,500))



# Are the results the same

# Print the difference of the resulted length. 
print(length(a$result)-length(b$result))

# Difference of the returned values
boxplot(a$result-b$result)


 
 
 
 
My results on a normal dual core laptop cpu
 
system.time(a<-do_sliding_for_a_window_duty_cycle_alternative(DataToAnalyse,500))
   user  system elapsed
  0.352   0.004   0.368

 system.time(b<-do_sliding_for_a_window_duty_cycle(DataToAnalyse,500))
    user   system  elapsed
2834.009  207.989 3080.434


> print(length(a$result)-length(b$result))
[1] 0

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