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)
    }