Forecast Linear Augmented Projection

The Forecast Linear Augmented Projection (flap) method reduces forecast variance by adjusting the forecasts of multivariate time series to be consistent with the forecasts of linear combinations (components) of the series by projecting all forecasts onto the space where the linear constraints are satisfied. The forecast variance can be reduced monotonically by including more components. For a given number of components, the flap method achieves maximum forecast variance reduction among linear projections.

flap

The goal of flap is to provide the Forecast Linear Augmented Projection method that can reduce forecast variance by adjusting the forecasts of multivariate time series to be consistent with the forecasts of linear combinations (components) of the series by projecting all forecasts onto the space where the linear constraints are satisfied.

Installation

You can install the stable version from CRAN.

install.packages("flap")

You can install the development version from Github

# install.packages("remotes")
remotes::install_github("FinYang/flap")

Example

This is a basic workflow to flap:

## The following pacakges are required to run this example
# install.packages("tidyr")
# install.packages("ggplot2")
# install.packages("forecast")
# install.packages("fpp2")

library(flap)
library(tidyr)
library(ggplot2)

# Obtain the forecast and the residual of the original series
mdl <- apply(fpp2::visnights, 2, forecast::ets)
#> Registered S3 method overwritten by 'quantmod':
#>   method            from
#>   as.zoo.data.frame zoo
fc <- vapply(mdl, function(mdl) forecast::forecast(mdl, h=12)$mean, 
             FUN.VALUE = numeric(12))
res <- vapply(mdl, residuals, 
              FUN.VALUE = numeric(nrow(fpp2::visnights)))

# Obtain components and their forecasts and residuals
pca <- stats::prcomp(fpp2::visnights, center = FALSE, scale. = FALSE)
mdl_comp <- apply(pca$x, 2, forecast::ets)
fc_comp <- vapply(mdl_comp, function(mdl) forecast::forecast(mdl, h=12)$mean, 
                  FUN.VALUE = numeric(12))
res_comp <- vapply(mdl_comp, residuals, 
                   FUN.VALUE = numeric(nrow(pca$x)))
Phi <- t(pca$rotation)

# flap!
proj_fc <- flap(fc, fc_comp, Phi, res, res_comp)
proj_fc
#> Forecast Linear Augmented Projection
#> A named list of numeric matrices of projected forecasts
#> ------------
#>  Num. of Series:            m = 20
#>  Num. of Components:        p = 1-20
#>  Num. of Forecast Horizons: 12
#> ------------
#> List of 20
#>  $ 1 : num [1:12, 1:20] 7.8 7.91 ...
#>  $ 2 : num [1:12, 1:20] 7.64 7.76 ...
#>  $ 3 : num [1:12, 1:20] 7.64 7.78 ...
#>  $ 4 : num [1:12, 1:20] 7.39 7.48 ...
#>  $ 5 : num [1:12, 1:20] 7.39 7.49 ...
#>   [list output truncated]

# Plot
if(interactive()) {
  proj_fc %>% 
    as.data.frame() %>% 
    pivot_longer(!c(h, p)) %>% 
    ggplot(aes(x = h, y = value, colour = p, group = p)) +
    geom_line() +
    facet_wrap("name", scales = "free_y")
}