avar (version 0.1.3)

avar_mo_cpp: Compute Maximal-Overlap Allan Variance using Means

Description

Computation of Maximal-Overlap Allan Variance

Usage

avar_mo_cpp(x)

Value

av A list that contains:

• "clusters"The size of the cluster

• "allan"The Allan variance

• "errors"The error associated with the variance estimation.

Arguments

x

A vector with dimensions N x 1.

Author

JJB

Details

Given \(N\) equally spaced samples with averaging time \(\tau = n\tau _0\), where \(n\) is an integer such that \( 1 \le n \le \frac{N}{2}\). Therefore, \(n\) is able to be selected from \(\left\{ {n|n < \left\lfloor {{{\log }_2}\left( N \right)} \right\rfloor } \right\}\) Then, \(M = N - 2n\) samples exist. The Maximal-overlap estimator is given by: \(\frac{1}{{2\left( {N - 2k + 1} \right)}}\sum\limits_{t = 2k}^N {{{\left[ {{{\bar Y}_t}\left( k \right) - {{\bar Y}_{t - k}}\left( k \right)} \right]}^2}} \)

where \( {{\bar y}_t}\left( \tau \right) = \frac{1}{\tau }\sum\limits_{i = 0}^{\tau - 1} {{{\bar y}_{t - i}}} \).

References

Long-Memory Processes, the Allan Variance and Wavelets, D. B. Percival and P. Guttorp

Examples

# \donttest{
set.seed(999)
N = 100000
white.noise = rnorm(N, 0, 2)
random.walk = cumsum(0.1*rnorm(N, 0, 2))
combined.ts = white.noise+random.walk
av_mat = avar_mo_cpp(combined.ts)
# }