Spectral Density Functions     package:waveslim     R Documentation

_S_p_e_c_t_r_a_l _D_e_n_s_i_t_y _F_u_n_c_t_i_o_n_s _f_o_r _L_o_n_g-_M_e_m_o_r_y _P_r_o_c_e_s_s_e_s

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

     Draws the spectral density functions (SDFs) for standard
     long-memory processes including fractional difference (FD),
     seasonal persistent (SP), and seasonal fractional difference (SFD)
     processes.

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

     fdp.sdf(freq, d, sigma2 = 1)
     spp.sdf(freq, d, fG, sigma2 = 1)
     spp2.sdf(freq, d1, f1, d2, f2, sigma2 = 1)
     sfd.sdf(freq, s, d, sigma2 = 1)

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

    freq: vector of frequencies, normally from 0 to 0.5

 d,d1,d2: fractional difference parameter

fG,f1,f2: Gegenbauer frequency

       s: seasonal parameter

  sigma2: innovations variance

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

     The power spectrum from an FD, SP or SFD process.

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

     B. Whitcher

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

     'fdp.mle', 'spp.mle'.

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

     dB <- function(x) 10 * log10(x)

     fdp.main <- expression(paste("FD", group("(",d==0.4,")")))
     sfd.main <- expression(paste("SFD", group("(",list(s==12, d==0.4),")")))
     spp.main <- expression(paste("SPP",
         group("(",list(delta==0.4, f[G]==1/12),")")))

     freq <- 0:512/1024

     par(mfrow=c(2,2), mar=c(5-1,4,4-1,2), col.main="darkred")
     plot(freq, dB(fdp.sdf(freq, .4)), type="l", xlab="frequency",
          ylab="spectrum (dB)", main=fdp.main)
     plot(freq, dB(spp.sdf(freq, .4, 1/12)), type="l", xlab="frequency",
          ylab="spectrum (dB)", font.main=1, main=spp.main)
     plot(freq, dB(sfd.sdf(freq, 12, .4)), type="l", xlab="frequency",
          ylab="spectrum (dB)", main=sfd.main)

