MOAV {avar} R Documentation

## Non-stationary Maximal-overlapping Allan Variance

### Description

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

### Usage

```MOAV(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.

### Details

This calculation of Maximal-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.

### Value

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

Haotian Xu

### 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){MOAV(2^y, covmat)})

```

[Package avar version 0.1.1 Index]