avar: Calculate the Allan Variance
In gmwm: Generalized Method of Wavelet Moments

Description Usage Arguments Details Value Author(s) References Examples

Computes the Allan Variance

1	avar(x, type = "mo")

`x`	A `vec` containing the time series under observation.
`type`	A `string` containing either `"mo"` for Maximal Overlap or `"to"` for Tau Overlap

The decomposition and the amount of time it takes to perform it depends on whether you are using the Tau Overlap or the Maximal Overlap.

Maximal Overlap Allan Variance 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 is given by: \frac{1}{{2≤ft( {N - 2k + 1} \right)}}∑\limits_{t = 2k}^N {{{≤ft[ {{{\bar Y}_t}≤ft( k \right) - {{\bar Y}_{t - k}}≤ft( k \right)} \right]}^2}}

where {{\bar y}_t}≤ft( τ \right) = \frac{1}{τ }∑\limits_{i = 0}^{τ - 1} {{{\bar y}_{t - i}}} .

Tau-Overlap Allan Variance 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, a sampling of m = ≤ft\lfloor {\frac{{N - 1}}{n}} \right\rfloor - 1 samples exist. The tau-overlap estimator is given by:

where {{\bar y}_t}≤ft( τ \right) = \frac{1}{τ }∑\limits_{i = 0}^{τ - 1} {{{\bar y}_{t - i}}} .

Allan variance fixed

av A list that contains:

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

JJB

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

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)