test_asymnorm_est_dev {ambit}

Computing the feasible statistic of the trawl function CLT

Description

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

Usage

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

Arguments

ahat

The estimated trawl function at time t: \hat{a}(t)

n

The number of observations in the data set

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)

avector

The vector (\hat a(0), \hat a(Delta_n), ..., \hat a((n-1)\Delta_n))

Details

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)

.

Value

The function returns the feasible statistic T( \Delta_n)_n if the estimated asymptotic variance is positive and 999 otherwise.