est_lin2: Estimation for linear AR(1) models with intercept by...
In ChrisKust/rexpar: Simplicial Depth for Explosive Autoregressive Processes

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

This function implements an algortihm to estimate a linear AR(1) model with intercept and explosion by simplicial depth or one of the proposed simplified notions in Kustosz, Mueller and Wendler (2016).

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est_lin2(y, maxit = 25, candy = FALSE, candy_eps = FALSE, perc = 1, acc = 0.1, 
plots = FALSE, normtype = 1, pv = 2, wgt = c(1, 0.5), unique = TRUE, 
notion = dS3_lin2, optim_rude = FALSE)

`y`	An observed series form an linear AR(1) process with intercept.
`maxit`	A value for the maximal number of iterations of the optimisation algorithm.
`candy`	A switch deciding, if just edges of simplices defined by the residuals shall be evaluated `candy = FALSE` or if points interior of the simplices should be considered `candy = TRUE`. This swich just applies, if candy_eps is set to FALSE.
`candy_eps`	A switch deciding, if just edges of simplices defined by the residuals shall be evaluated `candy_eps= FALSE` or if points interior of the simplices defined by a epsilon distance shall be evaluated. This swich overrides the candy option.
`perc`	A value in (0,1), defining how large the search regions around an acual candidate should be. A small value defines a very small region, while the value 1 means, that all potential candidates are considered.
`acc`	A value in (0,1) defining the search regions in the iteration steps. A value of 1 gives large regions, while a value close to 0 defines small regions, measured by the distance to the actual candidate.
`plots`	A switch (TRUE/FALSE) which enables plots of the iterations steps.
`normtype`	A parameter which defines the norm used to define distances to the actual paramter in the optimisation algorithm (see `Ele_Norm` for details).
`pv`	A parameter defining the power in the norm to calculate distances (see `Ele_Norm`).
`wgt`	A vector of weights used for the norm used to calculate distances (see `Ele_Norm`).
`unique`	A switch (TRUE/FALSE) defining, if a unique maximum shall be the result if multiple points with maximal depth exist. In this case the median point is selected.
`notion`	Here the function which is used for depth calculation is defined. The following notions are allowed: "dS1_lin2", "dS2_lin2", "dS3_lin2", "dS_lin2".
`optim_rude`	This switch allows a rude optimisation by a Nelder-Mead algorithm. WARNING: This may be very inaccurate due to astepwise constant optimisation function.

Details can be found in Kustosz (2016).

The function returns a list with

`estimate`	Parameter maximising the selected depth notion.
`value`	Depth at the resulting maximum.
`numit`	Number of iterations.

Kustosz, Christoph

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,dS2_lin2,dS3_lin2,dS_lin2,Tri_Mid,lin2_theta_f,Ele_Norm