avar_to_cpp function

Compute Tau-Overlap Allan Variance

Computation of Tau-Overlap Allan Variance

avar_to_cpp(x)

Arguments

• x: A vector with dimensions N x 1.

Returns

av A matrix that contains:

• Col 1The size of the cluster
• Col 2The Allan variance
• Col 3The 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, a sampling of $m = \left\lfloor {\frac{{N - 1}}{n}} \right\rfloor - 1$ samples exist. The tau-overlap estimator is given by:

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_to_cpp(combined.ts)

References

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

Author(s)

JJB