mra                 package:wavelets                 R Documentation

_M_u_l_t_i_r_e_s_o_l_u_t_i_o_n _A_n_a_l_y_s_i_s

_D_e_s_c_r_i_p_t_i_o_n:

     Computes the multiresolution analysis for a univariate or
     multivariate time series.

_U_s_a_g_e:

     mra(X, filter="la8", n.levels, boundary="periodic", fast=TRUE, method="dwt")

_A_r_g_u_m_e_n_t_s:

       X: A univariate or multivariate time series. Numeric vectors,
          matrices and data frames are also accepted.

  filter: Either a 'wt.filter' object, a character string indicating
          which wavelet filter to use in the decomposition, or a
          numeric vector of wavelet coefficients (not scaling
          coefficients). See 'help(wt.filter)' for acceptable filter
          names.

n.levels: An integer specifying the level of the decomposition. By
          default this is the value J such that the length of X is at
          least as great as the length of the level J wavelet filter,
          but less than the length of the level J+1 wavelet filter.
          Thus, j <= log((N-1)/(L-1)+1), where N is the length of X.

boundary: A character string indicating which boundary method to use.
          'boundary = "periodic"' and 'boundary = "reflection"' are the
          only supported methods at this time.

    fast: A logical flag which, if true, indicates that the pyramid
          algorithm is computed with an internal C function. 
          Otherwise, only R code is used in all computations.

  method: A character string, taking values "dwt" or "modwt", that
          indicates which type of transform to use when computing the
          MRA.

_V_a_l_u_e:

     Returns an object of class 'mra', which is an S4 object with slots       

       D: A list with element i comprised of a matrix containing the
          ith level wavelet detail.

       S: A list with element i comprised of a matrix containing the
          ith level wavelet smooths.

  filter: A 'wt.filter' object containing information for the filter
          used in the decomposition. See 'help(wt.filter)' for details.

   level: An integer value representing the level of wavelet
          decomposition.

boundary: A character string indicating the boundary method used in the
          wavelet decomposition. Valid values are "periodic" or
          "reflection".

  series: The original time series, 'X', in matrix format.

 class.X: A character string indicating the class of the input series. 
          Possible values are '"ts"', '"mts"', '"numeric"', '"matrix"',
          or '"data.frame"'.

  attr.X: A list containing the attributes information of the original
          time series, 'X'.  This is useful if 'X' is an object of
          class 'ts' or 'mts' and it is desired to retain relevant time
          information. If the original time series, 'X', is a matrix or
          has no attributes, then 'attr.X' is an empty list.

  method: A character string indicating which type of wavelet
          decomposition was performed (either "dwt" or "modwt").

_A_u_t_h_o_r(_s):

     Eric Aldrich. ealdrich@gmail.com.

_R_e_f_e_r_e_n_c_e_s:

     Percival, D. B. and A. T. Walden (2000) _Wavelet Methods for Time
     Series Analysis_, Cambridge University Press.

_S_e_e _A_l_s_o:

     'dwt', 'modwt', 'wt.filter'.

_E_x_a_m_p_l_e_s:

     # obtain the two series listed in Percival and Walden (2000), page 42
     X1 <- c(.2,-.4,-.6,-.5,-.8,-.4,-.9,0,-.2,.1,-.1,.1,.7,.9,0,.3)
     X2 <- c(.2,-.4,-.6,-.5,-.8,-.4,-.9,0,-.2,.1,-.1,.1,-.7,.9,0,.3)

     # combine them and compute MRA
     newX <- cbind(X1,X2)
     mra.out <- mra(newX, n.levels=3, boundary="reflection")

