Description Usage Arguments Details Value Note Author(s) References See Also Examples
This function calculates a simplified version of simplicial depth for explosive AR(1) processes, when non partially overlapping residuals with the middle residual fixed are evaluated. Thereby the parameter θ and the process y are fixed. The assumed model given by the model parameter.
1 2 |
theta |
θ is the parameter vector to evaluate dS1 in. |
res |
Instead of a model and a parameter θ, residuals can be plugged in directly. Then just the sign changes are calculated and the statistic is evaluated. |
y |
y = (y_0,...,y_N) is an oberserved process to evaluate dS2 in. |
model |
Here the model for the calculation of the underlying residuals is specified. currently the following
models are available Y_n = θ_1 Y_{n-1} + E_n "linAR1" = linear AR(1) model with intercept Y_n = θ_1 Y_{n-1} θ_0 + E_n "linAR2" = linear AR(2) model without intercept Y_n = θ_1 Y_{n-1} + θ_2 Y_{n-2} + E_n "nlinAR1" = linear AR(1) model without intercept but with power parameter Y_n = Y_{n-1} + θ_1 Y_{n-1}^{θ_3} + E_n "linARc" = linear AR(1) model with intercept and fixed and knwon power cpow Y_n = θ_1 Y_{n-1}^{cpow} + θ_0 + E_n |
cpow |
Fixed and known power parameter for the Y_n = θ_1*Y_{n-1}^{cpow} + θ_0 model |
The theoretical details can be found in Kustosz, Mueller and Wendler (2016). The computational details are in Kustosz (2016).
The result is a real number which gives the depth of θ based on the obervation vector y.
This expression is a simplification of dS, which is the full simplicial depth for explosive AR(1) processes
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.
resARMod_lin2
, dS_lin2
,dS1_lin2
, dS2_lin2
, dS3_lin2
1 2 3 4 | y <- RandomARMod_lin2(200, 0.2, 1.01, 15, "0")
theta <- c(0.2, 1.01)
dS2_lin2(theta = theta, y = y)
dS2_lin2(theta = theta+0.1, y = y)
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