compute_B_pT: Compute B_{pT} Statistic for Covariance Time-Variation...
In TVMVP: Time-Varying Minimum Variance Portfolio

compute_B_pT

R Documentation

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

Description

This function calculates the B_{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 local and global factor interactions along with residuals.

Usage

compute_B_pT(local_factors, global_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).
`global_factors`	A numeric matrix of global factor scores with `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:

Computes the sum of squared residuals for each time period s.
Constructs the kernel matrix K[s,t] by applying the boundary_kernel function to each pair of time periods (s,t).
Calculates the local dot-product matrix L[s,t] as the dot product between the local factors at time s and t.
Computes the global dot-product matrix G[s,t] as the dot product between the global factors at time s and t.
Computes the element-wise squared difference between K * L and G, multiplies it by the residuals, and sums over all s,t.
Scales the aggregated value by \frac{\sqrt{h}}{T^2 \sqrt{p}} to obtain B_{pT}.