flicker: Flicker noise process ('time_series_model')

In gmwmx2: Estimate Functional and Stochastic Parameters of Linear Models with Correlated Residuals and Missing Data

Flicker noise process (time_series_model)

Description

Constructs a time_series_model for flicker noise with variance sigma2. The process has spectral density S(f) \propto \frac{1}{|f|}. Hence, \kappa = -1 (Bos et al., 2008). The process is non-stationary and its covariance matrix is assumed to be given by

\mathbf C = \sigma^2 \mathbf U^\top \mathbf U,

where \mathbf U \in \mathbb{R}^{N \times N} is an upper-triangular Toeplitz matrix with entries

U_{i,j} = \begin{cases} h_{j-i}, & j \ge i, \\ 0, & j < i, \end{cases} \qquad i,j = 1, \ldots, N.

The coefficients \{h_i\}_{i \ge 0} define a causal linear filter and are given recursively by

h_0 = 1, \qquad h_i = \left(i - \frac{\kappa}{2} - 1\right)\frac{h_{i-1}}{i}, \quad i > 0.

Usage

flicker(sigma2 = NULL)

Arguments

sigma2

Innovation variance (> 0).

Value

A time_series_model object.

References

Bos MS, Fernandes RMS, Williams SDP, Bastos L (2008). "Fast error analysis of continuous GPS observations." Journal of Geodesy, 82, 157-166.

Examples

mod <- flicker(sigma2 = 1)
mod

gmwmx2 documentation built on June 10, 2026, 5:06 p.m.