gmwm (version 2.0.0)

avar_mo_cpp: Compute Maximal-Overlap Allan Variance using Means

Description

Computation of Maximal-Overlap Allan Variance

Usage

avar_mo_cpp(x)

Arguments

x

A vector with dimensions N x 1.

Value

av A list that contains:

• "clusters"The size of the cluster
• "allan"The Allan variance
• "errors"The error associated with the variance estimation.

Details

Given $N$ equally spaced samples with averaging time $tau = n*tau_0$, where $n$ is an integer such that $1<= n="" <="N/2$." therefore,="" $n$="" is="" able="" to="" be="" selected from="" ${n|n<="" floor(log2(n))}$="" then,="" $m="N" -="" 2n$="" samples="" exist.="" the="" maximal-overlap="" estimator="" 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(="" \right)}="" \right]}^2}}="" $<="" p="">

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

set.seed(999)
# Simulate white noise (P 1) with sigma^2 = 4
N = 100000
white.noise = rnorm(N, 0, 2)
#plot(white.noise,ylab="Simulated white noise process",xlab="Time",type="o")
#Simulate random walk (P 4)
random.walk = cumsum(0.1*rnorm(N, 0, 2))
combined.ts = white.noise+random.walk
av_mat = avar_mo_cpp(combined.ts)