SuperGauss-package {SuperGauss}

Superfast inference for stationary Gaussian time series.

Description

Likelihood evaluations for stationary Gaussian time series are typically obtained via the Durbin-Levinson algorithm, which scales as O(n^2) in the number of time series observations. This package provides a "superfast" O(n log^2 n) algorithm written in C++, crossing over with Durbin-Levinson around n = 300. Efficient implementations of the score and Hessian functions are also provided, leading to superfast versions of inference algorithms such as Newton-Raphson and Hamiltonian Monte Carlo. The C++ code provides a Toeplitz matrix class packaged as a header-only library, to simplify low-level usage in other packages and outside of R.

Details

While likelihood calculations with stationary Gaussian time series generally scale as O(N^2) in the number of observations, this package implements an algorithm which scales as ⁠O(N log^2 N)⁠. "Superfast" algorithms for loglikelihood gradients and Hessians are also provided. The underlying C++ code is distributed through a header-only library found in the installed package's include directory.

Author(s)

Maintainer: Martin Lysy [e-mail]

Authors:

• Yun Ling

Examples

# Superfast inference for the timescale parameter
# of the exponential autocorrelation function
exp_acf <- function(lambda) exp(-(1:N-1)/lambda)

# simulate data
lambda0 <- 1
N <- 1000
X <- rnormtz(n = 1, acf = exp_acf(lambda0))

# loglikelihood function
# allocate memory for a NormalToeplitz distribution object
NTz <- NormalToeplitz$new(N)
loglik <- function(lambda) {
  NTz$logdens(z = X, acf = exp_acf(lambda))
  ## dSnorm(X = X, acf = Toep, log = TRUE)
}

# maximum likelihood estimation
optimize(f = loglik, interval = c(.2, 5), maximum = TRUE)