dS3_nlin2_test: Test based on dS1 for explosive non-linear AR(1) processes...
In ChrisKust/rexpar: Simplicial Depth for Explosive Autoregressive Processes

Description Usage Arguments Details Value Author(s) References See Also Examples

The function evaluates the asymptotic test based on d_S^3 proposed in Kustosz, Mueller and Wendler (2014). It returns the test statistic and the decision. The main model is given by

Y_n = θ_1 Y_{n-1}^{θ_2} + θ_0 + E_n

with med(E_n)=0.

1	dS3_nlin2_test(dS3, thetaN, alpha, y, exact = FALSE)

`dS3`	Here the user can pass a pre-calculated depth statistic dS3 instead of a parameter thetaN and an observation vector y to apply the test directly
`thetaN`	Parameter defining the Null hypothesis H0: θ = θ^0. Thereby θ^0 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.
`exact`	This switch allows the usage of an exact distribition of the test statistics using the sample size.

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

`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.

Christoph Kustosz and Sebastian Szugat

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

Kustosz C., Mueller Ch. H. and Wendler M. (2016). Simplified Simplicial Depth for Regression and Autoregressive Growth Processes. Journal of Statistical Planning and Inference. In press.

dS1_lin2

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y <- RandomARMod_nlin2(nobs = 100, intercept = 0, arp = 0.2, power = 1.01, start = 15, cont = "0")
dS3_nlin2_test(thetaN=c(0.2, 1.01, 0), alpha=0.05, y=y)
dS3_nlin2_test(thetaN=c(0.3, 1.1, 0.2), alpha=0.05, y=y)