msd2acf: Convert mean square displacement to autocorrelations.

Description Usage Arguments Details Value Examples

View source: R/msd2acf.R

Description

Converts the mean squared displacement (MSD) of positions to the autocorrelation (ACF) of the corresponding increments.

Usage

1
msd2acf(msd)

Arguments

msd

Length-N vector of MSDs at regular timepoints dt, 2*dt, ..., N*dt.

Details

For a stationary increments process X_t, converts a sequence η_1, …, η_N of regularly spaced MSDs,

η_i = E[(X_(i*Δ t) - X_0)^2],

into γ_1, …, γ_N, a sequence of regularly spaced ACFs,

γ_i = cov{X_((i+1)*Δ t) - X_(i * Δ t), X_(Δ t) - X_0}.

This only produces correct results when msd corresponds to equally-spaced observations.

Value

Length N vector of ACFs.

Examples

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# autocorrelation of fBM increments
msd2acf(msd = fbm.msd(tseq = 0:10, H = .3))

SuperGauss documentation built on May 1, 2019, 7:58 p.m.