costat (version 2.4.1)

localvar: Compute the time-localized (unconditional) variance for a time series

Description

Compute the time localized variance from an evolutionary wavelet spectrum of a time series

Usage

localvar(spec)

Value

A vector representing the local variance estimate at successive times.

Arguments

spec

An evolutionary wavelet spectrum, such as that computed by ewspec in WaveThresh.

Author

Guy Nason

Details

One can compute the local variance of a time series by first computing its evolutionary wavelet spectrum, e.g., by using ewspec, and then applying localvar on the S component of that returned by ewspec.

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

ewspec

Examples

#
# Let's look at a iid standard normal sequence, variance should be 1, always
# for all times.
#
zsim <- rnorm(64)
#
# Note, in the following I use var as the method of deviance estimation,
# as described in the help there it can be more accurate when transformations
# are not used.
#
z.ews <- ewspec(zsim, smooth.dev=var)$S
#
# Compute the local variance
#
z.lv <- localvar(z.ews)
#
# Plot the local variance against time
#
if (FALSE) ts.plot(z.lv)
#
# Should be around 1. Note, the vertical scale of the plot might be
# deceptive, as R plots expand the function to the maximum available
# space. If you look again it should be quite close to 1 (e.g. on the
# example I am looking at now the variance is within +/- 0.15 of 1.
#
# However, it might not be close to 1 because the sample size is quite small,
# only 64, so repeat the above analysis with a larger sample size, e.g. 1024.
#