eNchange (version 1.0)

Z_trans: Transformation of an irregularly spaces time series.

Description

Transformation of a irregularly spaces time series. For the tvACD model, we calculate \(U_t = g_0(x_t, \psi_t) = \frac{x_t}{{\psi}_t}\), where \({\psi}_t = C_0 + \sum_{j=1}^p C_j x_{t-j} + \sum_{k=1}^q C_{p+k} \psi_{t-k}+\epsilon x_t\). where the last term \(\epsilon x_t\) is added to ensure the boundness of \(U_t\).

Usage

Z_trans(
  H,
  start.values = c(0.9, 0.6),
  dampen.factor = "auto",
  epsilon = 1e-05,
  LOG = TRUE,
  process = "acd",
  acd_p = 0,
  acd_q = 1
)
# S4 method for ANY
Z_trans(
  H,
  start.values = c(0.9, 0.6),
  dampen.factor = "auto",
  epsilon = 1e-05,
  LOG = TRUE,
  process = "acd",
  acd_p = 0,
  acd_q = 1
)

Arguments

H

The input irregular time series.

start.values

Warm starts for the optimizers of the likelihood functions.

dampen.factor

The dampen factor in the denominator of the residual process. Default is "auto".

epsilon

A parameter added to ensure the boundness of the residual process. Default is 1e-6.

LOG

Take the log of the residual process. Default is TRUE.

process

Choose between acd or hawkes. Default is acd.

acd_p

The p order of the ACD model. Default is 0.

acd_q

The q order of the ACD model. Default is 1.

Value

Returns the transformed residual series.

References

Korkas Karolos. "Ensemble Binary Segmentation for irregularly spaced data with change-points" Preprint <arXiv:2003.03649>.

Examples

# NOT RUN {
pw.acd.obj <- new("simACD")
[e-mail] <- c(0.25,0.75)
pw.acd.obj@lambda_0 <- c(1,2,1)
pw.acd.obj@alpha <- rep(0.2,3)
pw.acd.obj@beta <- rep(0.7,3)
pw.acd.obj@N <- 1000
pw.acd.obj <- pc_acdsim(pw.acd.obj)
ts.plot(Z_trans(pw.acd.obj@x))
# }