locits-package {locits}

New test of second-order stationarity and confidence intervals for localized autocovariance.

Description

Provides functionality to perform a new test of second-order stationarity for time series. The method works by computing a wavelet periodogram and then examining its Haar wavelet coefficients for significant ones. The other main feature of the software is to compute the localized autocovariance and pointwise confidence intervals.

Details

For the test of stationarity there are two main functions. The original is the hwtos2 function and this returns a tos object. The hwtos2 function works on data sets whose length is a power of two. Version 1.5 introduced a new function, hwtos which carries out the test on arbitrary length data. The summary.tos function performs a Bonferroni and FDR statistical analysis to detect which Haar wavelet coefficients are significant. The function plot.tos provides a plot of the original time series with any non-stationarities clearly indicated on the plot (actually locations and scales of the Haar wavelet coefficients).

For the localized autocovariance the main function is Rvarlacf. This computes the localized autocovariance values and approximate pointwise condifence intervals. The function plot.lacfCI can then plot the localized autocovariance and its confidence intervals in a number of forms.

Author(s)

Guy Nason

Maintainer: Guy Nason

References

Nason, G.P. (2013) A test for second-order stationarity and approximate confidence intervals for localized autocovariances for locally stationary time series. J. R. Statist. Soc. B, 75, 879-904. doi:10.1111/rssb.12015

See Also

Rvarlacf, hwtos2

Examples

#
# Here's a simple simulated example.
#
# A series which is a concatenation of two iid Gaussian series with
# different variances.
#
x <- c(rnorm(256, sd=1), rnorm(256, sd=2))
#
# Let's do a test of stationarity
#
st.test <- hwtos2(x)
#8    7    6    5    4    3  
#
# Ok, that's the computation gone, let's look at the results.
#
st.test

#Class 'tos' : Stationarity Object :
#~~~~  : List with 9 components with names
#	nreject rejpval spvals sTS AllTS AllPVal alpha x xSD 
#
#
#summary(.):
#----------
#There are  186  hypothesis tests altogether
#There were  4  FDR rejects
#The rejection p-value was  0.0001376564 
#Using Bonferroni rejection p-value is  0.0002688172 
#And there would be  4  rejections.
#Listing FDR rejects... (thanks Y&Y!)
#P: 5 HWTlev:  0  indices on next line...[1] 1
#P: 6 HWTlev:  0  indices on next line...[1] 1
#P: 7 HWTlev:  0  indices on next line...[1] 1
#P: 8 HWTlev:  0  indices on next line...[1] 1
#
# In the lines above if there are any rejects then the series is
# deemed to be nonstationary, and note that there were 4 in both
# the lines above (sometimes FDR rejects a few more).
#
# You can also plot the object and it shows you where it thinks the
# nonstationarities are
#
## Not run: plot(st.test)
#
# See the help page for the hwtos2 function, where there is an example
# with a stationary series.
#
# For the localized autocovariance...
#
# Let's use the function tvar1sim which generates a time-varying AR model
# with AR(1) paramter varying over the extent of the series from 0.9
# to -0.9 (that is, near the start of the series it behaves like an
# AR(1) with parameter 0.9, and near the end like an AR(1) with parameter
# -0.9, and in between the parameter is somewhere between 0.9 and -0.9
# figured linearly between the two.
#
x <- tvar1sim()
#
# Plot it, so you know what the series looks like, should always do this.
#
## Not run: ts.plot(x)
#
# Now, let's compute the localized autocovariance and also confidence intervals
# For the variance, let's look at the first 20 lags
#
# Do it at t=50 and t=450, ie what is the localized autocovariance at these
# two times.
#
x.lacf.50 <- Rvarlacf(x=x, nz=50, var.lag.max=20)
x.lacf.450 <- Rvarlacf(x=x, nz=450, var.lag.max=20)
#
# Now plot the answers, you may want to do this on two different plots
# so that you can compare the answers
#
#
## Not run: plot(x.lacf.50, plotcor=FALSE, type="acf")
## Not run: plot(x.lacf.450, plotcor=FALSE, type="acf")
#
# Note that the plotcor argument is set so covariances and not correlations
# are plotted. Also, the type is set to "acf" to make the plot *look* like
# the regular acf plot. But DON'T be fooled, it is not the regular acf
# that is plotted, but a time localized plot. The two plots should look
# very different, both like AR(1) but with different parameters (from the
# same time series).
#
# You could also plot the regular acf and see how it gets it wrong!
#