# 'runstats' R package: Fast Computation of Running Statistics for Time Series

Package runstats provides methods for fast computation of running sample statistics for time series. The methods utilize Convolution Theorem to compute convolutions via Fast Fourier Transform (FFT). Implemented running statistics include:

1. mean,
2. standard deviation,
3. variance,
4. covariance,
5. correlation,
6. euclidean distance.

# Website

Package website is located here.

# Installation

install.packages("runstats")


# Usage

library(runstats)

## Example: running correlation
x0 <- sin(seq(0, 2 * pi * 5, length.out = 1000))
x  <- x0 + rnorm(1000, sd = 0.1)
pattern <- x0[1:100]
out1 <- RunningCor(x, pattern)
out2 <- RunningCor(x, pattern, circular = TRUE)

## Example: running mean
x <- cumsum(rnorm(1000))
out1 <- RunningMean(x, W = 100)
out2 <- RunningMean(x, W = 100, circular = TRUE)


# Running statistics

To better explain the details of running statistics, package’s function runstats.demo(func.name) allows to visualize how the output of each running statistics method is generated. To run the demo, use func.name being one of the methods' names:

1. "RunningMean",
2. "RunningSd",
3. "RunningVar",
4. "RunningCov",
5. "RunningCor",
6. "RunningL2Norm".
## Example: demo for running correlation method
runstats.demo("RunningCor") ## Example: demo for running mean method
runstats.demo("RunningMean") # Performance

We use rbenchmark to measure elapsed time of RunningCov execution, for different lengths of time-series x and fixed length of the shorter pattern y.

library(rbenchmark)
library(ggplot2)

set.seed (20190315)
x.N.seq <- 10^(3:7)
x.list  <- lapply(x.N.seq, function(N) runif(N))
y <- runif(100)

## Benchmark execution time of RunningCov
out.df <- data.frame()
for (x.tmp in x.list){
out.df.tmp <- benchmark(
"runstats" = runstats::RunningCov(x.tmp, y),
replications = 10,
columns = c("test", "replications", "elapsed",
"relative", "user.self", "sys.self"))
out.df.tmp$x_length <- length(x.tmp) out.df.tmp$pattern_length <- length(y)
out.df <- rbind(out.df, out.df.tmp)
}

knitr::kable(out.df)

test replications elapsed relative user.self sys.self x_length pattern_length
runstats 10 0.004 1 0.003 0.000 1000 100
runstats 10 0.023 1 0.019 0.004 10000 100
runstats 10 0.183 1 0.148 0.035 100000 100
runstats 10 1.700 1 1.592 0.107 1000000 100
runstats 10 19.852 1 17.185 2.576 10000000 100

## Compare RunningCov {runstats} with a conventional method

To compare runstats performance with “conventional” loop-based way of computing running covariance in R, we use rbenchmark package to measure elapsed time of runstats::RunningCov and running covariance implemented with sapply loop, for different lengths of time-series x and fixed length of the shorter time-series y.

## Conventional approach
RunningCov.sapply <- function(x, y){
l_x <- length(x)
l_y <- length(y)
sapply(1:(l_x - l_y + 1), function(i){
cov(x[i:(i+l_y-1)], y)
})
}

out.df2 <- data.frame()
for (x.tmp in x.list[c(1:4)]){
out.df.tmp <- benchmark(
"conventional" = RunningCov.sapply(x.tmp, y),
"runstats" = runstats::RunningCov(x.tmp, y),
replications = 10,
columns = c("test", "replications", "elapsed",
"relative", "user.self", "sys.self"))
out.df.tmp$x_length <- length(x.tmp) out.df2 <- rbind(out.df2, out.df.tmp) }  Benchmark results plt1 <- ggplot(out.df2, aes(x = x_length, y = elapsed, color = test)) + geom_line() + geom_point(size = 3) + scale_x_log10() + theme_minimal(base_size = 14) + labs(x = "Vector length of x", y = "Elapsed [s]", color = "Method", title = "Running covariance (x,y) rbenchmark", subtitle = "Vector length of y = 100") + theme(legend.position = "bottom") plt2 <- plt1 + scale_y_log10() + labs(y = "Log of elapsed [s]", title = "") cowplot::plot_grid(plt1, plt2, nrow = 1, labels = c('A', 'B')) ## Compare RunningCov {runstats} with sliding_cov {dvmisc} c++ implementation dvmisc package (GitHub, CRAN) is a package for Convenience Functions, Moving Window Statistics, and Graphics, and includes functions for calculating moving-window statistics efficiently via c++, written by Dane Van Domelen. Here, we compare RunningCov {runstats} performance with c++ implementation from sliding_cov {dvmisc}. Dane contributed the code in its large part. # devtools::install_github("vandomed/dvmisc") library(dvmisc) set.seed(20100315) x.N.seq <- 10^(3:6) x.list <- lapply(x.N.seq, function(N) runif(N)) get.out.df <- function(y){ out.df <- data.frame() for (x.tmp in x.list){ if (length(x.tmp) < length(y)){ out.df.tmp <- data.frame( test = NA, replications = NA, elapsed = NA, relative = NA, user.self = NA, sys.self = NA) } else { out.df.tmp <- benchmark( "runstats" = runstats::RunningCov(x.tmp, y), "dvmisc" = dvmisc::sliding_cov(y, x.tmp), replications = 10, columns = c("test", "replications", "elapsed", "relative", "user.self", "sys.self")) } out.df.tmp$x_length <- length(x.tmp)
out.df <- rbind(out.df, out.df.tmp)
}
return(out.df)
}

out.df_y10    <- get.out.df(runif(10^1))
out.df_y100   <- get.out.df(runif(10^2))
out.df_y1000  <- get.out.df(runif(10^3))
out.df_y10000 <- get.out.df(runif(10^4))


Benchmark results

get.plt <- function(data, subtitle){
ggplot(data, aes(x = x_length, y = elapsed, color = test)) +
geom_line() + geom_point(size = 3) + scale_x_log10() +
theme_minimal(base_size = 14) +  scale_y_log10() +
labs(x = "Vector length of x",
y = "Log of elapsed [s]",
color = "Method",
subtitle = subtitle) +
theme(legend.position = "bottom")
}

plt1 <- get.plt(out.df_y10, "Vector length of y = 10") +
labs(title = "Running covariance (x,y) rbenchmark")
plt2 <- get.plt(out.df_y100,   "Vector length of y = 100")
plt3 <- get.plt(out.df_y1000,  "Vector length of y = 1,000")
plt4 <- get.plt(out.df_y10000, "Vector length of y = 1,0000")

cowplot::plot_grid(plt1, plt2, plt3, plt4, nrow = 2, labels = c('A', 'B', 'C', 'D')) ## Session info

sessioninfo::session_info()


## ─ Session info ───────────────────────────────────────────────────────────────
##  setting  value
##  version  R version 3.5.2 (2018-12-20)
##  os       macOS Mojave 10.14.2
##  system   x86_64, darwin15.6.0
##  ui       X11
##  language (EN)
##  collate  en_US.UTF-8
##  ctype    en_US.UTF-8
##  tz       America/New_York
##  date     2019-11-14
##
## ─ Packages ───────────────────────────────────────────────────────────────────
##  package     * version date       lib source
##  assertthat    0.2.1   2019-03-21  CRAN (R 3.5.2)
##  cli           1.1.0   2019-03-19  CRAN (R 3.5.2)
##  colorspace    1.4-1   2019-03-18  CRAN (R 3.5.2)
##  crayon        1.3.4   2017-09-16  CRAN (R 3.5.0)
##  digest        0.6.22  2019-10-21  CRAN (R 3.5.2)
##  dplyr         0.8.3   2019-07-04  CRAN (R 3.5.2)
##  evaluate      0.14    2019-05-28  CRAN (R 3.5.2)
##  fftwtools     0.9-8   2017-03-25  CRAN (R 3.5.0)
##  ggplot2     * 3.2.1   2019-08-10  CRAN (R 3.5.2)
##  glue          1.3.1   2019-03-12  CRAN (R 3.5.2)
##  gtable        0.3.0   2019-03-25  CRAN (R 3.5.2)
##  htmltools     0.3.6   2017-04-28  CRAN (R 3.5.0)
##  knitr         1.26    2019-11-12  CRAN (R 3.5.2)
##  lazyeval      0.2.2   2019-03-15  CRAN (R 3.5.2)
##  magrittr      1.5     2014-11-22  CRAN (R 3.5.0)
##  munsell       0.5.0   2018-06-12  CRAN (R 3.5.0)
##  pillar        1.4.2   2019-06-29  CRAN (R 3.5.2)
##  pkgconfig     2.0.3   2019-09-22  CRAN (R 3.5.2)
##  purrr         0.3.3   2019-10-18  CRAN (R 3.5.2)
##  R6            2.4.1   2019-11-12  CRAN (R 3.5.2)
##  rbenchmark  * 1.0.0   2012-08-30  CRAN (R 3.5.0)
##  Rcpp          1.0.3   2019-11-08  CRAN (R 3.5.2)
##  rlang         0.4.1   2019-10-24  CRAN (R 3.5.2)
##  rmarkdown     1.15    2019-08-21  CRAN (R 3.5.2)
##  rstudioapi    0.10    2019-03-19  CRAN (R 3.5.2)
##  runstats    * 1.1.0   2019-11-14  CRAN (R 3.5.2)
##  scales        1.0.0   2018-08-09  CRAN (R 3.5.0)
##  sessioninfo   1.1.1   2018-11-05  CRAN (R 3.5.0)
##  stringi       1.4.3   2019-03-12  CRAN (R 3.5.2)
##  stringr       1.4.0   2019-02-10  CRAN (R 3.5.2)
##  tibble        2.1.3   2019-06-06  CRAN (R 3.5.2)
##  tidyselect    0.2.5   2018-10-11  CRAN (R 3.5.0)
##  withr         2.1.2   2018-03-15  CRAN (R 3.5.0)
##  xfun          0.11    2019-11-12  CRAN (R 3.5.2)
##  yaml          2.2.0   2018-07-25  CRAN (R 3.5.0)
##
##  /Library/Frameworks/R.framework/Versions/3.5/Resources/library