This function computes the feasible test statistic appearing in the CLT for the trawl function estimation.
test_asymnorm_est_dev(
ahat,
n,
Delta,
k,
c4,
varlevyseed = 1,
trawlfct,
trawlfct_par,
avector
)The function returns the feasible statistic \(T( \Delta_n)_n\)
if the estimated asymptotic variance is positive and 999 otherwise.
The estimated trawl function at time t: \(\hat{a}(t)\)
The number of observations in the data set
The width Delta of the observation grid
The time point in \(0, 1, \ldots, n-1\); the test statistic will be computed for the time point \(k * \Delta_n\).
The fourth cumulant of the Levy seed of the trawl process
The variance of the Levy seed of the trawl process, the default is 1
The trawl function for which the asymptotic variance will be computed (Exp, supIG or LM)
The parameter vector of the trawl function (Exp: lambda, supIG: delta, gamma, LM: alpha, H)
The vector \((\hat a(0), \hat a(Delta_n), ..., \hat a((n-1)\Delta_n))\)
As derived in Sauri and Veraart (2022), the feasible statistic is given by $$T(k \Delta_n)_n:=\frac{\sqrt{n\Delta_{n}}}{ \sqrt{\widehat{\sigma_{a}^2( \Delta_n)}}} \left(\hat{a}( \Delta_n)-a( \Delta_n)\right)$$.