avar_mo_cpp function

Compute Maximal-Overlap Allan Variance using Means

Computation of Maximal-Overlap Allan Variance

avar_mo_cpp(x)

Arguments

• x: A vector with dimensions N x 1.

Returns

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

Examples

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)

References

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

Author(s)

JJB