to_vario: Autocovariance to Semivariogram

In CovEsts: Nonparametric Estimators for Covariance Functions

Autocovariance to Semivariogram

Description

This function computes an estimated semivariogram using an estimated autocovariance function.

Usage

to_vario(estCov)

## Default S3 method:
to_vario(estCov)

## S3 method for class 'CovEsts'
to_vario(estCov)

Arguments

estCov

A vector whose values are an estimate autocovariance function or a CovEsts S3 object.

Details

The semivariogram, \gamma(h) and autocovariance function, C(h), under the assumption of weak stationarity are related as follows:

\gamma(h) = C(0) - C(h) .

When an empirical autocovariance function is considered instead, this relation does not necessarily hold, however, it can be used to obtain a function that is close to a semivariogram, see Bilchouris and Olenko (2025).

Value

A numeric vector whose values are an estimate of the semivariogram or an VarioEsts S3 object (list) with the following values

vario

A numeric vector whose values are an estimate of the semivariogram.

lags

A numeric vector containing the lag indices used to compute the estimates on, inherited from the argument estCov.

est_used

The estimator function used, in this case, 'to_vario'.

If a numeric vector is given for the argument estCov, then a numeric vector output is given, and if a CovEsts S3 object is given, a VarioEsts object is given as output.

Methods (by class)

• to_vario(default): Method for numeric vectors.

• to_vario(CovEsts): Method for CovEsts objects.

References

Bilchouris, A. & Olenko, A (2025). On Nonparametric Estimation of Covariogram. Austrian Statistical Society 54(1), 112-137. 10.17713/ajs.v54i1.1975

Examples

X <- c(1, 2, 3)
estCov <- standard_est(X, meanX=mean(X), maxLag = 2, pd=FALSE)
to_vario(estCov)

CovEsts documentation built on April 19, 2026, 5:06 p.m.