hadam: Calculate the Hadamard Variance
In SMAC-Group/gmwm: Generalized Method of Wavelet Moments

Description Usage Arguments Details Value Author(s) Examples

Computes the Hadamard Variance

1	hadam(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 Hadamard Variance Given N equally spaced samples with averaging time tau = n*tau_0, where n is an integer such that 1<= n <= N/3. Therefore, n is able to be selected from {n|n< floor(log3(N))} Then, M = N - 3n samples exist. The Maximal-overlap estimator is given by: See PDF Manual

where See PDF Manual.

Tau-Overlap Hadamard 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: See PDF Manual where See PDF Manual.

Hadamard variance fixed

hadam A list that contains:

"clusters"The size of the cluster
"hadamard"The Hadamard variance
"errors"The error associated with the variance estimation.

Avinash Balakrishnan, JJB

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
hadam_mo = hadam(combined.ts)

hadam_to = hadam(combined.ts, type = "to")