ewspec              package:wavethresh              R Documentation

_C_o_m_p_u_t_e _e_v_o_l_u_t_i_o_n_a_r_y _w_a_v_e_l_e_t _s_p_e_c_t_r_u_m _e_s_t_i_m_a_t_e.

_D_e_s_c_r_i_p_t_i_o_n:

     This function computes the evolutionary wavelet spectrum (EWS)
     estimate from a time series (or non-decimated wavelet transform of
     a time series). The estimate is computed by taking the
     non-decimated wavelet transform of the time series data, taking
     its modulus; smoothing using TI-wavelet shrinkage and then
     correction for the redundancy caused by use of the non-decimated
     wavelet transform. Options below beginning with smooth. are passed
     directly to the TI-wavelet shrinkage routines.

_U_s_a_g_e:

     ewspec(x, filter.number = 10, family = "DaubLeAsymm",
             UseLocalSpec = TRUE, DoSWT = TRUE, WPsmooth = TRUE, verbose = FALSE,
             smooth.filter.number = 10, smooth.family = "DaubLeAsymm", smooth.levels
              = 3:(nlevels(WPwst) - 1), smooth.dev = madmad, smooth.policy =
             "LSuniversal", smooth.value = 0, smooth.by.level = FALSE, smooth.type =
             "soft", smooth.verbose = FALSE, smooth.cvtol = 0.01, smooth.cvnorm = l2
             norm, smooth.transform = I, smooth.inverse = I)

_A_r_g_u_m_e_n_t_s:

       x: The time series that you want to analyze. (See DETAILS below
          on how to supply preprocessed versions of the time series
          which bypass early parts of the ewspec function). 

filter.number : This selects the index of the wavelet used in the
          analysis of the time series (i.e. the wavelet basis functions
          used to model the time series). For Daubechies compactly
          supported wavelets the filter number is the number of
          vanishing moments. 

 family : This selects the wavelet family to use in the analysis of the
          time series (i.e. which wavelet family to use to model the
          time series). Only use the Daubechies compactly supported
          wavelets 'DaubExPhase' and 'DaubLeAsymm'. 

UseLocalSpec : If you input a time series for 'x' then this argument
          should always be 'T'. (However, you can precompute the
          modulus of the non-decimated wavelet transform yourself and
          supply it as 'x' in which case the 'LocalSpec' call within
          this function is not necessary and you can set UseLocalSpec
          equal to 'F'). 

  DoSWT : If you input a time series for 'x' then this argument should
          always be 'T'. (However, you can precompute the non-decimated
          wavelet transform yourself and supply it as 'x' in which case
          the 'wd' call within the function will not be necessary and
          you can set DoSWT equal to 'F'). 

WPsmooth: Normally a wavelet periodogram is smoothed before it is
          corrected. Use 'WPsmooth=F' is you do not want any wavelet
          periodogram smoothing (correction is still done). 

 verbose: If this option is 'T' then informative messages are printed
          as the function progresses. 

smooth.filter.number : This selects the index number of the wavelet
          that smooths each scale of the wavelet periodogram. See
          'filter.select' for further details on which wavelets you can
          use. Generally speaking it is a good idea to use a smoother
          wavelet for smoothing than the one you used for analysis
          (above) but since one still wants local smoothing it is best
          not to use a wavelet that is much smoother. 

smooth.family: This selects the wavelet family that smooths each scale
          of the wavelet periodogram. See 'filter.select' for further
          details on which wavelets you can use. There is no need to
          use the same family as you used to analyse the time series. 

smooth.levels : The levels to smooth when performing the TI-wavelet
          shrinkage smoothing. 

smooth.dev : The method for estimating the variance of the empirical
          wavelet coefficients for smoothing purposes. 

smooth.policy : The recipe for smoothing: determines how the threshold
          is chosen. See 'threshold' for TI-smoothing and choice of
          potential policies. For EWS estimation 'LSuniversal' is
          recommended for thi Chi-squared nature of the periodogram
          coefficients. However, if the coefficients are transformed
          (using 'smooth.transform' and 'smooth.inverse') then other,
          more standard, policies may be appropriate. 

smooth.value : When a manual policy is being used this argument is used
          to supply a threshold value. See 'threshold' for more
          information. 

smooth.by.level : If 'TRUE' then the wavelet shrinkage is performed by
          computing and applying a separate threshold to each level in
          the non-decimated wavelet transform of each scale. Note that
          each scale in the EWS is smoothed separately and
          independently: and each smooth consists of taking the
          (second-stage) non-decimated wavelet transform and applying a
          threshold to each level of a wavelet transformed scale. 

          If 'FALSE' then the same threshold is applied to the
          non-decimated wavelet transform of a scale. Different
          thresholds may be computed for different scales (in the time
          series model) but the threshold will be the same for each
          level arising from the non-decimated transform of a scale. 

          Note: a 'scale' refers to a set of coefficients coming from a
          particular scale of the non-decimated wavelet transform of
          the time series data that 'models' the time series. A 'level'
          refers to the levels of wavelet coefficients obtained from
          taking the non-decimated wavelet transform of a particular
          scale.

smooth.type : The type of shrinkage: either "hard" or "soft". 

smooth.verbose : If 'T' then informative messages concerning the
          TI-transform wavelet shrinkage are printed.

smooth.cvtol : If cross-validated wavelet shrinkage
          ('smooth.policy="cv"') is used then this argument supplies
          the cross-validation tolerance. 

smooth.cvnorm: no description for object

smooth.transform : The transform function to use to transform the
          wavelet periodogram estimate. The wavelet periodogram
          coefficients are typically chi-squared in nature, a 'log'
          transform can pull the coefficients towards normality so that
          a 'smooth.policy' for Gaussian data could be used (e.g.
          'universal'). 

smooth.inverse: the inverse transform of 'smooth.transform'. 

_D_e_t_a_i_l_s:

     This function computes an estimate of the evolutionary wavelet
     spectrum of a time series according to the paper by Nason, von
     Sachs and Kroisandt. The function works as follows: 

_1 The non-decimated wavelet transform of the series is computed. 

_2 The squared modulus of the non-decimated wavelet transform is
     computed (this is the raw wavelet periodogram, which is returned). 

_3 The squared modulus is smoothed using TI-wavelet shrinkage. 

_4 The smoothed coefficients are corrected using the inverse of the
     inner product matrix of the discrete non-decimated autocorrelation
     wavelets (produced using the ipndacw function). 

     To display the EWS use the 'plot'function on the 'S' component,
     see the examples below. 

     It is possible to supply the non-decimated wavelet transform of
     the time series and set 'DoSWT=F' or to supply the squared modulus
     of the non-decimated wavelet transform using 'LocalSpec' and
     setting 'UseLocalSpec=F'. This facility saves time because the
     function is then only used for smoothing and correction.

_V_a_l_u_e:

     A list with the following components: 

       S: The evolutionary wavelet spectral estimate of the input 'x'.
          This object is of class 'wd' and so can be plotted, printed
          in the usual way. 

  WavPer: The raw wavelet periodogram of the input 'x'. The EWS
          estimate (above) is the smoothed corrected version of the
          wavelet periodgram. The wavelet periodogram is of class 'wd'
          and so can be plotted, printed in the usual way. 

      rm: This is the matrix A from the paper by Nason, von Sachs and
          Kroisandt. Its inverse is used to correct the raw wavelet
          periodogram. This matrix is computed using the 'ipndacw'
          function. 

     irm: The inverse of the matrix A from the paper by Nason, von
          Sachs and Kroisandt. It is used to correct the raw wavelet
          periodogram.

_R_E_L_E_A_S_E:

     Version 3.9 Copyright Guy Nason 1998

_R_e_f_e_r_e_n_c_e_s:

     Nason, G.P., von Sachs, R. and Kroisandt, G. (1998). Wavelet
     processes and adaptive estimation of the evolutionary wavelet
     spectrum. _Technical Report_, Department of Mathematics University
     of Bristol/ Fachbereich Mathematik, Kaiserslautern.

_S_e_e _A_l_s_o:

     'Baby Data', 'filter.select', 'ipndacw', 'LocalSpec', 'threshold'
     'wd' 'wd.object'

_E_x_a_m_p_l_e_s:

     #
     # Apply the EWS estimate function to the baby data
     #

