test_asymnorm: 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)
Value
The function returns the infeasible test statistic specified above.
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 \(k \in \{0, 1, \ldots, n-1\}\).