tapered_single: Computes the Tapered Autocovariance for a Specified Lag.

In CovEsts: Nonparametric Estimators for Covariance Functions

Computes the Tapered Autocovariance for a Specified Lag.

Description

This helper function computes the tapered autocovariance for a specified lag h,

\widehat{C}_{N}^{a} (h) = (H_{2, n})^{-1} \sum_{j=1}^{N-h} (X(j) - \bar{X} ) ( X(j+ h) - \bar{X} ) a((j - 1/2) / n; \rho) a((j + h - 1/2) / n; \rho) ,

where a(\cdot) is a window function, \rho is a scale parameter. This taper functions is used in tapered_est.

Usage

tapered_single(X, meanX, h, h2n, taperVals_t, taperVals_h)

Arguments

X	A vector representing observed values of the time series.
meanX	The average value of the X.
h	The lag at which the tapered autocovariance function is computed at.
h2n	The value of H_{2, n}(0), computed within tapered_est.
taperVals_t	The taper values for each index of the process, computed within tapered_est.
taperVals_h	The taper values shifted by the lag, computed within tapered_est.

Value

The tapered autocovariance function at the specified lag.

Examples

X <- c(1, 2, 3)
tapered_single(X, mean(X), 2, 2.5, c(0.75, 1, 0.75), c(0.75, 1, 0.75))

CovEsts documentation built on Sept. 10, 2025, 10:39 a.m.