AntiAR {costat}

Undo autoreflection action for an EWS object (wd stationary)

Description

The BootTOS function has the ability to deal with boundary conditions by augmenting the right-hand end of a time series by a reflected version of that series. So, the series doubles in length and the new vector has periodic boundary conditions. One can then compute a local spectrum on this data which returns an EWS in a wd object, usually with a type attribute of "station". This function can take this wd object and properly can return the first half of it, which corresponds to the boundary-correct spectrum of the original series.

Usage

AntiAR(S)

Arguments

S

A wd class object of type "station". This corresponds to a EWS estimate on a reflected time series.

Details

This function arises because using spectral estimation functions, like ewspec from the wavethresh package doesn't always work that well at the boundaries. This is because the wavelet functions in wavethresh usually assume periodic boundary conditions and this is not appropriate for a discrete time series where time 1 and time T are usually very different (and cannot be assumed to be the same).

Hence, a previous function could generate a new time series by taking the original, e.g. x, reflecting it with rev(x) and then sticking the reflected onto the right-hand end of the original. Spectral estimation, (e.g. using ewspec) can then be applied to this new reflected/augmented series and the boundaries are now roughly correct as the start and end of the series correspond to time 1.

The spectral estimate so obtained though is double the size of the the one that is needed, and contains the spectrum of the reflected series. Hence, this function obtains the first half of the estimate and returns it.

Not usually intended for the casual user

Value

A wd class object containing the boundary-corrected estimate of the spectrum for the original series.

Author(s)

G. P. Nason.

References

Cardinali, A. and Nason, Guy P. (2013) Costationarity of Locally Stationary Time Series Using costat. Journal of Statistical Software, 55, Issue 1.

Cardinali, A. and Nason, G.P. (2010) Costationarity of locally stationary time series. J. Time Series Econometrics, 2, Issue 2, Article 1.

See Also

BootTOS

Examples

#
# Generate example, temporary series
#
x <- rnorm(128)	
#
# Reflect it about its end point
#
x2 <- c(x, rev(x))
#
# Compute EWS estimate
#
x2ews <- ewspec(x2)
#
# Now get bit corresponding to x into object
#
xews <- AntiAR(x2ews$S)