two_fold_convolution_kernel: Two-Fold Convolution Kernel Function

In TVMVP: Time-Varying Minimum Variance Portfolio

Two-Fold Convolution Kernel Function

Description

This function computes the two-fold convolution of a given kernel function with itself. The convolution is evaluated over a range of inputs u and is set to zero outside the interval \([-2, 2]\).

Usage

two_fold_convolution_kernel(u, kernel_func)

Arguments

u	A numeric vector of points at which the two-fold convolution kernel is evaluated.
kernel_func	A function representing the kernel to be convolved.

Details

The two-fold convolution kernel is defined as:

K^{(2)}(u) = \int_{-1}^{1} K(v) \cdot K(u - v) \, dv

where K is the original kernel function. The function evaluates this convolution for each input u within the interval \([-2, 2]\) and sets it to zero outside this range.

Value

A numeric vector of two-fold convolution kernel values corresponding to each input u.

TVMVP documentation built on June 28, 2025, 1:08 a.m.