Compute the time localized variance from an evolutionary wavelet spectrum of a time series
An evolutionary wavelet spectrum, such as that computed
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
A vector representing the local variance estimate at successive times.
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.
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# # 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 # ## Not run: 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. #