estimateParameters: Estimate parameter in the Random Walk Autoregressive model

In DeCAFS: Detecting Changes in Autocorrelated and Fluctuating Signals

Estimate parameter in the Random Walk Autoregressive model

Description

This function perform robust estimation of parameters in the Random Walk plus Autoregressive model using a method of moments estimator. To model the time-dependency DeCAFS relies on three parameters. These are sdEta, the standard deviation of the drift (random fluctuations) in the signal, modeled as a Random Walk process, sdNu, the standard deviation of the AR(1) noise process, and phi, the autocorrelation parameter of the noise process. The final estimation of the change locations is affected by the l0 penalty beta and the estimation of the process by those three initial parameters. Therefore, the choice of penalties for DeCAFS is important: where possible investigate resulting segmentations. Should the algorithm return a misspecified estimation of the signal, it might be good to constrain the estimation of the parameters to an edge case. This can be done through the argument model. Alternatively, one could employ a range of penalties or tune these on training data. To manually specify different penalties, see DeCAFS() documentation. If unsure of which model is the most suited for a given sequence, see guidedModelSelection() for guided model selection.

Usage

estimateParameters(
  y,
  model = c("RWAR", "AR", "RW"),
  K = 15,
  phiLower = 0,
  phiUpper = 0.999,
  sdEtaUpper = Inf,
  sdNuUpper = Inf,
  warningMessage = FALSE
)

Arguments

y	A vector of observations
model	Constrain estimation to an edge case of the RWAR model. Defaults to "RWAR". To fit an AR model only with a piece-wise constant signal, specify "AR". To fit a a random walk plus noise, specify "RW".
K	The number of K-lags differences of the data to run the robust estimation over. Default set at 15.
phiLower	Smallest value of the autocorrelation parameter. Default set at 0.
phiUpper	Highest value of the autocorrelation parameter. Default set at 0.99.
sdEtaUpper	Highest value of the RW standard deviation. Default set at Inf
sdNuUpper	Highest value of the AR(1) noise standard deviation. Default set at Inf
warningMessage	A message to warn the user when the automatic parameter estimation is employed.

Value

Returns a list of estimates that can be employed as an argument for parameter modelParam to run DeCAFS(). Those are:

sdEta

the SD of the drift (random fluctuations) in the signal,

sdNu

the SD of the AR(1) noise process,

phi

the autocorrelation parameter of the noise process.

Examples

set.seed(42)
y <- dataRWAR(n = 1e3, phi = .5, sdEta = 1, sdNu = 3,  jumpSize = 15, type = "updown", nbSeg = 5)$y
estimateParameters(y)

DeCAFS documentation built on Jan. 6, 2023, 5:27 p.m.