dS_lin2_test: Test based on dS for explosive AR(1) processes with intercept

In ChrisKust/rexpar: Simplicial Depth for Explosive Autoregressive Processes

Description

The function evaluates the asymptotic test based on dS proposed in Kustosz, Leucht and Mueller (2016). It returns the test statistic and the decision. The default model is given by

Y_n = θ_0 + θ_1 Y_{n-1}^{cpow} + E_n

with med(E_n)=0.

Usage

dS_lin2_test(thetaN, alpha, y, ncores = 1, cpow = 1, dS)

Arguments

thetaN	Parameter defining the Null hypothesis H0: θ = θ^0. Thereby θ is defined by the model.
alpha	Value in (0,1) defining the level of the test.
y	Observed series y=(y_0,...,y_N) for which the parameter test has to be executed.
ncores	Defines the number of cores to use for parallel computation of the simplicial depth statistic. If no value is definied the standard value of 1 is passed and no parallel methods are applied.
cpow	Fixed and known power parameter for the Y_n = θ_2\cdot Y_{n-1}^{cpow} + θ_0 model.
dS	Here an evaluated depth statistic dS can be defined, instead of evaluation of data y, to calculate the test statistic for dS directly.

Details

The theoretical details can be found in Kustosz, Leucht and Mueller (2016). The computational details are in Kustosz (2016).

Value

TS	Returns the value of the rescaled and centred test statistic.
phi	Retuns the test decision, phi = 1 means reject H0, and phi = 0 means do not reject H0.

Note

Note, that the evaluation depends on the simulated results of the limit process, which are included in the rexpar package.

Author(s)

Christoph Kustosz and Sebastian Szugat

References

Kustosz, C. (2016). Depth based estimators and tests for autoregressive processes with application. Ph. D. thesis. TU Dortmund.

Kustosz C., Leucht A. and Mueller Ch. H. (2016). Tests based on simplicial depth for AR(1) models with explosion. Journal of Time Series Analysis. In press.

See Also

dS_lin2,

Examples

y <- RandomARMod_lin2(100, 0.2, 1.01, 15, "0")
dS_lin2_test(thetaN = c(0.2, 1.01), alpha =  0.05, y = y)
dS_lin2_test(thetaN = c(0.1, 1.11), alpha = 0.05, y = y)

ChrisKust/rexpar documentation built on May 6, 2019, 11:48 a.m.