avar_mo_cpp | R Documentation |
Computation of Maximal-Overlap Allan Variance
avar_mo_cpp(x)
x |
A |
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}}}
.
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)
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)
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