spectrum0                package:coda                R Documentation

_E_s_t_i_m_a_t_e _s_p_e_c_t_r_a_l _d_e_n_s_i_t_y _a_t _z_e_r_o

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

     The spectral density at frequency zero is estimated by fitting a
     glm to the low-frequency end of the periodogram. 
     'spectrum0(x)/length(x)' estimates the variance of 'mean(x)'.

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

     spectrum0(x, max.freq = 0.5, order = 1, max.length = 200) 

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

       x: A time series.

max.freq: The glm is fitted on the frequency range (0, max.freq]

   order: Order of the polynomial to fit to the periodogram.

max.length: The data 'x' is aggregated if necessary by taking batch
          means so that the length of the series is less than
          'max.length'.  If this is set to 'NULL' no aggregation
          occurs.

_D_e_t_a_i_l_s:

     The raw periodogram is calculated for the series 'x' and a
     generalized linear model with family 'Gamma' and log link is
     fitted to the periodogram.

     The linear predictor is a polynomial in terms of the frequency. 
     The degree of the polynomial is determined by the parameter
     'order'.

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

     A list with the following values 

    spec: The predicted value of the spectral density at frequency
          zero.

_T_h_e_o_r_y:

     Heidelberger and Welch (1991) observed that the usual
     non-parametric estimator of the spectral density, obtained by
     smoothing the periodogram, is not appropriate for frequency zero. 
     They proposed an alternative parametric method which consisted of
     fitting a linear model to the log periodogram of the batched time
     series. Some technical problems  with model fitting in their
     original proposal can be overcome by using a generalized linear
     model.

     Batching of the data, originally proposed in order to save space,
     has the side effect of flattening the spectral density and making
     a polynomial fit more reasonable.  Fitting a polynomial of degree
     zero is equivalent to using the `batched means' method.

_N_o_t_e:

     The definition of the spectral density used here differs from that
     used by 'spec.pgram'. We consider the frequency range to be
     between 0 and 0.5, not between 0 and 'frequency(x)/2'.

     The model fitting may fail on chains with very high
     autocorrelation.

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

     Heidelberger, P and Welch, P.D. A spectral method for confidence
     interval generation and run length control in simulations.
     Communications of the ACM, Vol 24, pp233-245, 1981.

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

     'spectrum', 'spectrum0.ar', 'glm'.

