PleioSeq.test.H00: A sequential test of the Efficiency of a Given Portfolio...

In PengWu12245/EcoPleio: Testing Factor Models for Asset Returns: Based on Pleiotropy Model

Description

The test is for the following multivariate linear regression model:

y_j = α_j + ∑_{k=1}^q β_{jk}x_k + \varepsilon_j, j=1,...,p.

where y_j denotes the excess return on asset j; (x_1,...,x_q) is the excess return on the porfolio whose efficiency is being tested; and \varepsilon_j is the disturbance term for asset j. The disturbances are assumed to be jointly normally distributed with mean zero and nonsingular covariance matrix Σ, conditional on the excess returns for portfolios (x_1,...,x_q).

Usage

PleioSeq.test.H00(x, y)

Arguments

x	samples of predictor which is a n*q matrix.
y	samples of response which is a n*p vector.

Details

The test of the efficiency of a given portfolio is equivalent to the following hypothesis test.

• H00: all the Intercepts α are zero, i.e. α_j=0, \forall j=1,...,p.

• H1: otherwise.

Value

A list with the following elements:

• pvalue: the p-value of the sequential test for H00.

• stat: the test statistic for H00.

Examples

## Quick example for the sequential test for \code{H00}


set.seed(1)
n = 500; q = 2; p = 3
x <- matrix( rnorm(n*q), nrow = n)

# Under H0
y <- matrix(NA, nrow = n, ncol = p)
y[,1] <- x[,1] + x[,2] + rnorm(n, sd = 0.5)
y[,2] <- x[,1] + 2 * x[,2] + rnorm(n, sd = 0.5)
y[,3] <- x[,1] + 3 * x[,2] + rnorm(n, sd = 0.5)
GRS.test(x, y)$p.value
PleioSeq.test.H00(x,y)$pvalue

# Under H1
y <- matrix(NA, nrow = n, ncol = p)
y[,1] <- 0.5 + x[,1] + x[,2] + rnorm(n, sd = 0.5)
y[,2] <- 0.5 + x[,1] + 2 * x[,2] + rnorm(n, sd = 0.5)
y[,3] <- x[,1] + 3 * x[,2] + rnorm(n, sd = 0.5)
GRS.test(x, y)$p.value
PleioSeq.test.H00(x,y)$pvalue

PengWu12245/EcoPleio documentation built on Jan. 7, 2020, 12:23 a.m.