NOAV function

Non-stationary Non-overlapping Allan Variance

Calculation of the theoretical Non-overlapping Allan variance for constant-mean non-stationary time series data.

NOAV(n, covmat)

Arguments

• n: An integer indicating the length of each vector of consecutive observations considered for the average.
• covmat: A matrix indicating the T-by-T covariance matrix of the time series with length T.

Returns

A field <numeric> that is the theoretical Non-overlapping Allan variance for constant-mean non-stationary time series data.

Details

This calculation of Non-overlapping Allan variance is based on the definition on "A Study of the Allan Variance for Constant-Mean Non-Stationary Processes" by Xu et al., 2017, IEEE Signal Processing Letters, 24(8): 1257–1260. Here n is an integer larger than 1 and smaller than $floor(log2(dim(T)[1]))-1$.

Examples

set.seed(999)
Xt = arima.sim(n = 100, list(ar = 0.3))
avar(Xt, type = "to")

a = matrix(rep(0, 1000^2), nrow = 1000)
for (i in 1:1000){
  a[,i] = seq(from = 1 - i, length.out = 1000)
}
a.diag = diag(a)
a[upper.tri(a,diag=TRUE)] = 0
a = a + t(a) + diag(a.diag)
covmat = 0.3^a
sapply(1:8, function(y){NOAV(2^y, covmat)})

Author(s)

Haotian Xu