hadam_to_cpp: Compute Tau-Overlap Hadamard Variance
In SMAC-Group/gmwm: Generalized Method of Wavelet Moments

Description Usage Arguments Details Value Author(s) References Examples

Computation of Hadamard Variance

1	hadam_to_cpp(x)

`x`	A `vector` with dimensions M x 1.

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}}} .

A matrix that contains:

Col 1The size of the cluster
Col 2The Hadamard variance
Col 3The 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_to_cpp(combined.ts)