For the case where one has to compute the outliers quickly, one could use the idea of Rob Hyndman and Mahito Sugiyama ( https://github.com/BorgwardtLab/sampling-outlier-detection , library(spoutlier), function qsp ) to compute the outliers as follows:

library(spoutlier)
rapidtsoutliers <- function(x,plot=FALSE,seed=123)
{
    random.seed(seed)
    x <- as.numeric(x)
    tt <- 1:length(x)
    qspscore <- qsp(x)
    limit <- quantile(qspscore,prob=c(0.95))
    score <- pmax((qspscore - limit),0)
    if(plot)
    {
        plot(x,type="l")
        x2 <- ts(rep(NA,length(x)))
        x2[score>0] <- x[score>0]
        tsp(x2) <- tsp(x)
        points(x2,pch=19,col="red")
        return(invisible(score))
    }
    else
        return(score)
}

For the case where one has to compute the outliers quickly, one could use the idea of Rob Hyndman and Mahito Sugiyama ( https://github.com/BorgwardtLab/sampling-outlier-detection , library(spoutlier), function qsp ) to compute the outliers as follows:

library(spoutlier)
rapidtsoutliers <- function(x,plot=FALSE,seed=123)
{
    set.seed(seed)
    x <- as.numeric(x)
    tt <- 1:length(x)
    qspscore <- qsp(x)
    limit <- quantile(qspscore,prob=c(0.95))
    score <- pmax((qspscore - limit),0)
    if(plot)
    {
        plot(x,type="l")
        x2 <- ts(rep(NA,length(x)))
        x2[score>0] <- x[score>0]
        tsp(x2) <- tsp(x)
        points(x2,pch=19,col="red")
        return(invisible(score))
    }
    else
        return(score)
}