Two weeks ago I presented ahead, an R package for univariate and multivariate time series forecasting. And last week, I’ve shown how ahead::dynrmf could be used for automatic univariate forecasting.

This week, I compare the speeds of execution of ahead::ridge2f (quasi-randomized autoregressive network) and ahead::varf (Vector AutoRegressive model), with their default parameters (notably 1 lag, and 5-steps-ahead forecasting). For more examples of multivariate time series forecasting with ahead, you can type ?ahead::ridge2f, ?ahead::varf(x), or ?ahead::plot.mtsforecast in R console, once the package is installed and loaded.

Here’s how to install ahead:

  • 1st method: from R-universe

    In R console:

      options(repos = c(
          techtonique = '',
          CRAN = ''))
  • 2nd method: from Github

    In R console:




Loading packages for the demo:



With 10 time series and 10000 observations:

x <- ts(matrix(rnorm(100000), ncol = 10))
(res <- microbenchmark::microbenchmark(ahead::ridge2f(x), ahead::varf(x), times = 10L))
Unit: milliseconds
             expr       min        lq      mean    median        uq      max neval
ahead::ridge2f(x)  28.74215  32.22568  48.10457  35.70773  39.54476 104.5946    10
ahead::varf(x)    126.64908 138.91396 171.74475 157.16234 207.46105 237.5916    10


With 100 time series and 1000 observations:

x <- ts(matrix(rnorm(100000), ncol = 100))
(res <- microbenchmark::microbenchmark(ahead::ridge2f(x), ahead::varf(x), times = 10L))
Unit: milliseconds
             expr       min         lq      mean     median         uq       max neval
ahead::ridge2f(x)   46.8317   48.44567   81.1854   53.52305   61.06889  220.5755    10
ahead::varf(x)    2276.9425 2293.05932 2360.1591 2316.90078 2362.63500 2696.0487    10


With 1000 time series and 100 observations:

x <- ts(matrix(rnorm(100000), ncol = 1000))
(res <- microbenchmark::microbenchmark(ahead::ridge2f(x), ahead::varf(x), times = 10L))
Unit: seconds
             expr        min        lq       mean     median         uq        max neval
ahead::ridge2f(x)   1.891717   2.18807   2.315703   2.253376   2.286887   3.048088    10
ahead::varf(x)    226.133743 234.94063 240.931083 239.235557 247.780707 259.656456    10


ahead::ridge2f is fast and scalable, mostly because I implemented some of its parts in C++, via Rcpp. In addition, the algorithm is mainly made of matrices products and inversions – with the inversions being the most expensive parts, according to profvis::profvis.

If you are interested in making the algorithm even faster in a GitHub fork, notice that: the most training time is spent at lines 267–275 of this file, which corresponds to section 2.3 of the paper.

R version 4.0.4 (2021-02-15)
Platform: x86_64-apple-darwin17.0 (64-bit)
Running under: macOS Big Sur 10.16

Matrix products: default
LAPACK: /Library/Frameworks/R.framework/Versions/4.0/Resources/lib/libRlapack.dylib

[1] fr_FR.UTF-8/fr_FR.UTF-8/fr_FR.UTF-8/C/fr_FR.UTF-8/fr_FR.UTF-8

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base     

other attached packages:
[1] bigtime_0.2.1

loaded via a namespace (and not attached):
 [1] Rcpp_1.0.7           urca_1.3-0           compiler_4.0.4       pillar_1.4.6         iterators_1.0.13    
 [6] vars_1.5-3           tools_4.0.4          digest_0.6.25        corrplot_0.84        ahead_0.2.0         
[11] lifecycle_0.2.0      tibble_3.0.3         gtable_0.3.0         nlme_3.1-152         lattice_0.20-41     
[16] pkgconfig_2.0.3      rlang_0.4.10         foreach_1.5.1        rstudioapi_0.11      microbenchmark_1.4-7
[21] dplyr_1.0.2          generics_0.0.2       vctrs_0.3.4          tidyselect_1.1.0     lmtest_0.9-38       
[26] grid_4.0.4           glue_1.4.2           R6_2.5.0             randtoolbox_1.30.1   fpp_0.5             
[31] farver_2.0.3         purrr_0.3.4          ggplot2_3.3.3        magrittr_1.5         scales_1.1.1        
[36] codetools_0.2-18     ellipsis_0.3.1       MASS_7.3-53          strucchange_1.5-2    colorspace_1.4-1    
[41] sandwich_3.0-0       rngWELL_0.10-6       munsell_0.5.0        crayon_1.3.4         zoo_1.8-8