HaarMA              package:wavethresh              R Documentation

_G_e_n_e_r_a_t_e _H_a_a_r _M_A _p_r_o_c_e_s_s_e_s.

_D_e_s_c_r_i_p_t_i_o_n:

     This function generates an arbitrary number of observations from a
     Haar MA process of any order with a particular variance.

_U_s_a_g_e:

     HaarMA(n, sd=1, order=5)

_A_r_g_u_m_e_n_t_s:

       n: The number of observations in the realization that you want
          to create. Note that n does NOT have to be a power of two.

      sd: The standard deviation of the innovations.

   order: The order of the Haar MA process.

_D_e_t_a_i_l_s:

     A Haar MA process is a special kind of time series moving-average
     (MA) process. A Haar MA process of order k is a MA process of
     order 2^k. The coefficients of the Haar MA process are given by
     the filter coefficients of the discrete Haar wavelet at different
     scales. 

     For example: the Haar MA process of order 1 is an MA process of
     order 2. The coefficients are 1/sqrt(2) and -1/sqrt(2). The Haar
     MA process of order 2 is an MA process of order 4. The
     coefficients are 1/2, 1/2, -1/2, -1/2 and so on. It is possible to
     define other processes for other wavelets as well. 

     Any Haar MA process is a good example of a (stationary) LSW
     process because it is sparsely representable by the
     locally-stationary wavelet machinery defined in Nason, von Sachs
     and Kroisandt.

_V_a_l_u_e:

     A vector containing a realization of a Haar MA process of the
     specified order, standard deviation and number of observations.

_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:

     'HaarConcat', 'ewspec',

_E_x_a_m_p_l_e_s:

     #
     # Generate a Haar MA process of order 1 (high frequency series)
     #
     #MyHaarMA <- HaarMA(n=151, sd=2, order=1)
     #
     # Plot it
     #
     #ts.plot(MyHaarMA)
     #
     # Generate another Haar MA process of order 3 (lower frequency), but of
     # smaller variance
     #
     #MyHaarMA2 <- HaarMA(n=151, sd=1, order=3)
     #
     # Plot it
     #
     #ts.plot(MyHaarMA2)
     #
     # Let's plot them next to each other so that you can really see the
     # differences.
     # 
     # Plot a vertical dotted line which indicates where the processes are
     # joined
     #
     #ts.plot(c(MyHaarMA, MyHaarMA2))
     #abline(v=152, lty=2)

