ewspec.diff: Estimation of Evolutionary Wavelet Spectrum of Non-Zero Mean...

In TrendLSW: Wavelet Methods for Analysing Locally Stationary Time Series

Estimation of Evolutionary Wavelet Spectrum of Non-Zero Mean Time Series via Differencing

Description

Internal function to estimate the evolutionary wavelet spectrum (EWS) of a time series that may include a trend component. The estimate is computed by taking the non-decimated wavelet transform of the first differenced time series data, squaring it; smoothing using a running mean and then correcting for bias using the appropriate correction matrix. Inherits the smoothing functionality from the ewspec3 function in the R package locits. This function is not intended for general use by regular users of the package.

Usage

ewspec.diff(
  x,
  lag = 1,
  filter.number = 4,
  family = "DaubExPhase",
  binwidth = floor(2 * sqrt(length(x))),
  diff.number = 1,
  max.scale = floor(log2(length(x)) * 0.7),
  S.smooth = TRUE,
  smooth.type = "epan",
  boundary.handle = FALSE,
  AutoReflect = FALSE,
  supply.inv.mat = FALSE,
  inv.mat = NULL
)

Arguments

x	The time series you wish to analyse.
lag	An integer indicating which lag to use for differencing.
filter.number	The index number for the wavelet used to analyse the time series. For the "DaubExPhase" family, the filter number can be between 1 to 10. For the "DaubLeAsymm" family, the filter number can be between 4 to 10.
family	The family of the wavelet used. It is recommended to use either the Daubechies Extremal Phase family, or the Daubechies Least Asymmetric family, corresponding to the "DaubExPhase" or the "DaubLeAsymm" options.
binwidth	The bin width of the running mean smoother used to smooth the raw wavelet periodogram.
diff.number	The number of differences used to remove the trend of the series. A first difference is recommended as default.
max.scale	The coarsest level to which the time series is analysed to. Should be a positive integer less than J, where T=2^J is the length of the time series. The default setting is 0.7J, to control for bias.
S.smooth	Argument that dictates if smoothing is performed on the raw wavelet periodogram.
smooth.type	String indicating which type of smoothing to use on wavelet periodogram. Can be "mean", "median", or "epan". Default is "epan".
boundary.handle	Logical variable, if TRUE, then boundary handling will be applied when computing the periodogram. Recommended to set as FALSE, will be set as TRUE automatically if non-dyadic data is used.
AutoReflect	As in wavethresh. Decides whether or not the time series is reflected when computing the wavelet transform. Strongly recommended to leave as FALSE.
supply.inv.mat	Not intended for general use. If TRUE, user must supply the appropriate correction matrix.
inv.mat	Not intended for general use. If supply.mat is TRUE, user must supply the appropriate correction matrix used to correct the raw wavelet periodogram. Equal to (2A-2A_1)^{-1} for first differences.

Details

Computes an estimate of the evolutionary wavelet spectrum of a time series that displays nonstationary mean and autocovariance. The estimation procedure is as follows:

1. The time series is differenced to remove the trend.

2. The squared modulus of the non-decimated wavelet transform is computed, known as the raw wavelet periodogram. This is returned by the function.

3. The raw wavelet periodogram is smoothed using a running mean smoother.

4. The smoothed periodogram is bias corrected using the inverse of the bias matrix.

The final estimate, stored in the S component, can be plotted using the plot function, please see the example below.

Value

A list object, containing the following fields:

S	The evolutionary wavelet spectral estimate of the input data. This object is of class wd and so can be plotted and printed in the usual way using wavethresh functionality.
WavPer	The raw wavelet periodogram of the input data. The EWS estimate (above) is the smoothed corrected version of the wavelet periodogram.
SmoothWavPer	The smoothed, un-corrected raw wavelet periodogram of the input data.
max.scale, boundary.handle, S.smooth, smooth.type, binwidth, lag, diff.number	Input parameters

References

McGonigle, E. T., Killick, R., and Nunes, M. (2022). Modelling time-varying first and second-order structure of time series via wavelets and differencing. Electronic Journal of Statistics, 6(2), 4398-4448. wavethresh::plot.wd(spec.est$S)

See Also

TLSW, ewspec3

TrendLSW documentation built on May 29, 2024, 6:06 a.m.