

spectrum {ts}                                R Documentation

_S_p_e_c_t_r_a_l _D_e_n_s_i_t_y _E_s_t_i_m_a_t_i_o_n

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

     The `spectrum' function estimates the spectral density
     of a time series. This is a wrapper function which
     calls the methods `spec.pgram' and `spec.ar'.

     The generic function `plot' has a method for `spec'
     objects: for multivariate time series it plots the
     marginal spectra of the series or pairs plots of the
     coherency and phase of the cross-spectra.

_U_s_a_g_e_:

     spectrum(x, method=c("pgram","ar"), plot = TRUE, ...)
     plot.spec(spec.obj, add=FALSE, ci=0.95,
               log=c("yes", "dB", "no"), ci.col="blue", ci.lty=3,
               plot.type = c("marginal", "coherency", "phase"), ...)

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

       x: A univariate or multivariate time series.

  method: String specifying the method used to estimate the
          spectral density. Allowed methods are "pgram" (the
          default) and "ar".

    plot: logical. If `TRUE' then the spectral density is
          plotted.

     ...: Further arguments to specific spec methods or
          `plot.spec'.

spec.obj: An object of class `spec'.

     add: logical. If `TRUE' then lines are added to the
          existing plot.

      ci: Coverage probability for confidence interval.
          Plotting of the confidence bar is omitted unless
          `ci' is strictly positive.

     log: If `"dB"', plot on log10 (decibel) scale (as S-
          PLUS), otherwise use conventional log scale or
          linear scale. Logical values are also accepted.
          The default is `"yes"' unless `options(ts.S.compat
          = TRUE)' has been set, when it is `"dB"'.

ci.col, ci.lty: Colour for plotting confidence bar, colour
          and line type for confidence intervals for
          coherency and phase.

plot.type: For multivariate time series, the type of plot
          required. Only the first character is needed.

     ...: Further graphical parameters.

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

     The spectrum here is defined with scaling `1/fre-
     quency(x)', following S-PLUS. This makes the spectral
     density a density over the range `(-frequency(x)/2,
     +frequency(x)/2]', whereas a more common scaling is 2pi
     and range  (-0.5, 0.5] (e.g. Bloomfield) or 1 and range
     (-pi, pi].

     If available, a confidence interval will be plotted by
     `plot.spec': this is asymmetric, and the width of the
     centre mark indicates the equivalent bandwidth.

_V_a_l_u_e_:

     An object of class `spec', which is a list containing
     at least the following elements:

    freq: vector of frequencies at which the spectral den-
          sity is estimated. (Possibly approximate Fourier
          frequencies.)

    spec: Vector (for univariate series) or matrix (for mul-
          tivariate series) of estimates of the spectral
          density at frequencies corresponding to `freq'.

     coh: `NULL' for univariate series. For multivariate
          time series, a matrix containing the squared
          coherency between different series. Column  i + (j
          - 1) * (j - 2)/2 of `coh' contains the squared
          coherency between columns i and j of `x', where i
          > j.

   phase: `NULL' for univariate series. For multivariate
          time series a matrix containing the cross-spectrum
          phase between different series. The format is the
          same as `coh'.

  series: The name of the time series.

  snames: For multivariate input, the names of the component
          series.

  method: The method used to calculate the spectrum.

          The result is returned invisibly if `plot' is
          true.

_N_o_t_e_:

     The default plot for `spec' objects is quite complex,
     including an error bar and default title, subtitle and
     axis labels. The defaults can all be overridden by sup-
     plying the appropriate graphical parameters.

_A_u_t_h_o_r_(_s_)_:

     Martyn Plummer, B.D. Ripley

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

     Bloomfield, P. (1976) Fourier Analysis of Time Series:
     An Introduction. Wiley.

     Brockwell, P. J. and Davis, R. A. (1991) Time Series:
     Theory and Methods. Second edition. Springer.

     Venables, W. N. and Ripley, B. D. (1997) Modern Applied
     Statistics with S-PLUS. Second edition. Springer.
     (Especially pp. 437-442.)

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

     `spec.pgram'

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

     ## Examples from Venables & Ripley
     ## spec.pgram
     par(mfrow=c(2,2))
     data(lh)
     spectrum(lh)
     spectrum(lh, spans=3)
     spectrum(lh, spans=c(3,3))
     spectrum(lh, spans=c(3,5))

     data(UKLungDeaths)
     spectrum(ldeaths)
     spectrum(ldeaths, spans=c(3,3))
     spectrum(ldeaths, spans=c(3,5))
     spectrum(ldeaths, spans=c(5,7))
     spectrum(ldeaths, spans=c(5,7), log="dB", ci=0.8)

     # for multivariate examples see the help for spec.pgram

     ## spec.ar
     spectrum(lh, method="ar")
     spectrum(ldeaths, method="ar")

