dS_lin1_test: Test based on dS for explosive AR(1) processes without...
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 dS proposed in Kustosz and Mueller (2014). It returns the test statistic and the decision. The main model is given by

Y_n = θ_1 Y_{n-1} + E_n

with med(E_n)=0.

1	dS_lin1_test(thetaN, alpha, y, mod = FALSE)

`thetaN`	Parameter defining the Null hypothesis H0: θ = θ^0.
`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.
`mod`	Switch to enable full tangential depth derivative (multiplication with y_{n-1}) in the test statistic, if `mod= TRUE`.

The theoretical details can be found in Kustosz and Mueller (2014). 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.

Kustosz, Christoph

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

Kustosz C. and Mueller Ch. H. (2014). Analysis of crack growth with robust distribution- free estimators and tests for nonstationary autoregressive processes. Statistical Papers 55, 125-140.

dS_lin1,

y <- RandomARMod_lin2(100, 0, 1.01, 15, "0")
theta <- 1.01
dS_lin1_test(thetaN = theta, alpha = 0.05, y = y)
dS_lin1_test(thetaN = theta + 0.1, alpha = 0.05, y = y)