test_asymnorm {ambit}

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 \Delta_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, \ldots, n-1; the test statistic will be computed for the time point k*\Delta_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{\sqrt{n\Delta_{n}}}{\sqrt{\sigma_{a}^2(k \Delta_n)}} \left(\hat{a}(k\Delta_n)-a(k \Delta_n)\right),

for k \in \{0, 1, \ldots, 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)