acf2msd: Convert autocorrelation of stationary increments to mean...

Description Usage Arguments Details Value Examples

View source: R/acf2msd.R

Description

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

Usage

1

Arguments

acf

length-N ACF vector of a stationary increment sequence.

Details

If X(t) is a stationary increments process, then Δ X_0, Δ X_1, … with

Δ X_n = X((n+1)Δ t) - X(n Δ t)

is a stationary time series. This function converts the ACF of this series into the MSD of the corresponding positions, namely returns the sequence η_1, …, η_N, where η_i = var(X(iΔ t)).

Value

Length-N MSD vector of the corresponding positions.

Examples

1
acf2msd(acf = exp(-(0:10)))

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