dS3_lin2_test: Test based on dS3 for explosive AR(1) processes with...
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 dS3 proposed in Kustosz, Mueller and Wendler (2016). It returns the test statistic and the decision. The main model is given by

Y_n = θ_0 + θ_1 Y_{n-1} + E_n .

1	dS3_lin2_test(thetaN, alpha, y, exact = FALSE, cpow = 1, dS3)

`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.
`cpow`	fixed and known power parameter for the Y_n = θ_1Y_{n-1}^{cpow} + θ_0* model
`dS3`	Here an evaluated dS3 statistic can be inserted instead of a vector y. Then just the test statistic is calculated and the test is evaluated directly.

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_lin2(1000, 0.2, 1.01, 15, "0")
dS3_lin2_test(thetaN = c(0.2, 1.01), alpha = 0.05, y = y)
dS3_lin2_test(thetaN = c(0.1, 1.01), alpha = 0.05, y = y)