compute_V_pT: Compute V_{pT} Statistic for Covariance Time-Variation...

In TVMVP: Time-Varying Minimum Variance Portfolio

Compute V_{pT} Statistic for Covariance Time-Variation Hypothesis Testing

Description

This function calculates the V_{pT} statistic, which is part of the hypothesis testing procedure to determine whether the covariance matrix of asset returns is time-varying. It incorporates kernel-weighted factor interactions and residual correlations.

Usage

compute_V_pT(local_factors, residuals, h, iT, ip, kernel_func)

Arguments

local_factors	A list where each element is a numeric matrix representing the local factor scores for a specific time period. Each matrix should have T rows (time periods) and m columns (factors).
residuals	A numeric matrix of residuals with T rows (time periods) and p columns (assets).
h	A numeric value indicating the bandwidth parameter for the kernel function.
iT	An integer specifying the number of time periods.
ip	An integer specifying the number of assets.
kernel_func	A function representing the kernel used for weighting. Typically, an Epanechnikov kernel or another boundary kernel function.

Details

The function performs the following steps:

1. Iterates over each pair of time periods (s, r) where s < r.

2. Computes the two-fold convolution kernel value \bar{K}_{sr} using the two_fold_convolution_kernel function.

3. Calculates the squared dot product of local factors weighted by the factor covariance matrix.

4. Computes the squared dot product of residuals between time periods s and r.

5. Aggregates these values across all relevant time period pairs and scales by \frac{2}{T^2 × p × h} to obtain V_{pT}.

Value

A numeric scalar V_{pT} representing the computed statistic based on kernel-weighted factor interactions and residual correlations.

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