rolloptim is a package that provides analytical computation of rolling optimization for time-series data.
Install the development version from GitHub:
# install.packages("devtools")
devtools::install_github("jasonjfoster/rolloptim") # roll (>= 1.1.7)Load the package and supply a dataset:
library(rolloptim)
n_vars <- 3
n_obs <- 15
x <- matrix(rnorm(n_obs * n_vars), nrow = n_obs, ncol = n_vars)
y <- rnorm(n_obs)
mu <- roll::roll_mean(x, 5)
xx <- roll::roll_crossprod(x, x, 5)
xy <- roll::roll_crossprod(x, y, 5)
sigma <- roll::roll_cov(x, width = 5)Then, to compute rolling optimization, use the functions:
# rolling optimization to minimize variance
roll_min_var(sigma)
# rolling optimization to maximize mean
roll_max_mean(mu)
# rolling optimization to minimize residual sum of squares
roll_min_rss(xx, xy)
# rolling optimization to maximize utility
roll_max_utility(mu, sigma, lambda = 1)Note that handling of constraints is implemented by default (see the total, lower, and upper arguments).
Markowitz, H.M. (1952). "Portfolio Selection." The Journal of Finance, 7(1), 77–91.
Tam, A. (2021). "Lagrangians and Portfolio Optimization." https://www.adrian.idv.hk/2021-06-22-kkt/.
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