test_asymnorm: Computing the infeasible test statistic from the trawl...

In ambit: Simulation and Estimation of Ambit Processes

Computing the infeasible test statistic from the trawl function estimation CLT

Description

This function computes the infeasible test statistic appearing in the CLT for the trawl function estimation.

Usage

test_asymnorm(ahat, n, Delta, k, c4, varlevyseed = 1, trawlfct, trawlfct_par)

Arguments

ahat	The term \hat a(k Δ_n) in the CLT
n	The number n of observations in the sample
Delta	The width Delta of the observation grid
k	The time point in 0, 1, …, n-1; the test statistic will be computed for the time point k*Δ_n.
c4	The fourth cumulant of the Levy seed of the trawl process
varlevyseed	The variance of the Levy seed of the trawl process, the default is 1
trawlfct	The trawl function for which the asymptotic variance will be computed (Exp, supIG or LM)
trawlfct_par	The parameter vector of the trawl function (Exp: lambda, supIG: delta, gamma, LM: alpha, H)

Details

As derived in Sauri and Veraart (2022), the infeasible test statistic is given by

\frac{√{nΔ_{n}}}{√{σ_{a}^2(k Δ_n)}} ≤ft(\hat{a}(kΔ_n)-a(k Δ_n)\right),

for k \in \{0, 1, …, n-1\}.

Value

The function returns the infeasible test statistic specified above.

Examples

test_asymnorm(ahat=0.9, n=5000, Delta=0.1, k=1, c4=1, varlevyseed=1,
              trawlfct="Exp", trawlfct_par=0.1)

ambit documentation built on Aug. 19, 2022, 5:19 p.m.