test_asymnorm_est_dev: Computing the feasible statistic of the trawl function CLT

In ambit: Simulation and Estimation of Ambit Processes

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

Details

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

T(k Δ_n)_n:=\frac{√{nΔ_{n}}}{ √{\widehat{σ_{a}^2( Δ_n)}}} ≤ft(\hat{a}( Δ_n)-a( Δ_n)\right)

.

Value

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

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