acf                  package:stats                  R Documentation

_A_u_t_o- _a_n_d _C_r_o_s_s- _C_o_v_a_r_i_a_n_c_e _a_n_d -_C_o_r_r_e_l_a_t_i_o_n _F_u_n_c_t_i_o_n _E_s_t_i_m_a_t_i_o_n

_D_e_s_c_r_i_p_t_i_o_n:

     The function 'acf' computes (and by default plots) estimates of
     the autocovariance or autocorrelation function.  Function 'pacf'
     is the function used for the partial autocorrelations.  Function
     'ccf' computes the cross-correlation or cross-covariance of two
     univariate series.

_U_s_a_g_e:

     acf(x, lag.max = NULL,
         type = c("correlation", "covariance", "partial"),
         plot = TRUE, na.action = na.fail, demean = TRUE, ...)

     pacf(x, lag.max, plot, na.action, ...)

     ## Default S3 method:
     pacf(x, lag.max = NULL, plot = TRUE, na.action = na.fail,
         ...)

     ccf(x, y, lag.max = NULL, type = c("correlation", "covariance"),
         plot = TRUE, na.action = na.fail, ...)

     ## S3 method for class 'acf':
     x[i, j]

_A_r_g_u_m_e_n_t_s:

    x, y: a univariate or multivariate (not 'ccf') numeric time series
          object or a numeric vector or matrix, or an '"acf"' object.

 lag.max: maximum lag at which to calculate the acf. Default is
          10*log10(N/m) where N is the number of observations and m the
          number of series.  Will be automatically limited to one less
          than the number of observations in the series.

    type: character string giving the type of acf to be computed.
          Allowed values are '"correlation"' (the default),
          '"covariance"' or '"partial"'.

    plot: logical. If 'TRUE' (the default) the acf is plotted.

na.action: function to be called to handle missing values. 'na.pass'
          can be used.

  demean: logical.  Should the covariances be about the sample means?

     ...: further arguments to be passed to 'plot.acf'.

       i: a set of lags (time differences) to retain.

       j: a set of series (names or numbers) to retain.

_D_e_t_a_i_l_s:

     For 'type' = '"correlation"' and '"covariance"', the estimates are
     based on the sample covariance. (The lag 0 autocorrelation is
     fixed at 1 by convention.)

     By default, no missing values are allowed.  If the 'na.action'
     function passes through missing values (as 'na.pass' does), the
     covariances are computed from the complete cases.  This means that
     the estimate computed may well not be a valid autocorrelation
     sequence, and may contain missing values.  Missing values are not
     allowed when computing the PACF of a multivariate time series.

     The partial correlation coefficient is estimated by fitting
     autoregressive models of successively higher orders up to
     'lag.max'.

     The generic function 'plot' has a method for objects of class
     '"acf"'.

     The lag is returned and plotted in units of time, and not numbers
     of observations.

     There are 'print' and subsetting methods for objects of class
     '"acf"'.

_V_a_l_u_e:

     An object of class '"acf"', which is a list with the following
     elements:

     lag: A three dimensional array containing the lags at which the
          acf is estimated.

     acf: An array with the same dimensions as 'lag' containing the
          estimated acf.

    type: The type of correlation (same as the 'type' argument).

  n.used: The number of observations in the time series.

  series: The name of the series 'x'.

  snames: The series names for a multivariate time series.


     The lag 'k' value returned by 'ccf(x,y)' estimates the correlation
     between 'x[t+k]' and 'y[t]'.

     The result is returned invisibly if 'plot' is 'TRUE'.

_A_u_t_h_o_r(_s):

     Original: Paul Gilbert, Martyn Plummer. Extensive modifications
     and univariate case of 'pacf' by B. D. Ripley.

_R_e_f_e_r_e_n_c_e_s:

     Venables, W. N. and Ripley, B. D. (2002) _Modern Applied
     Statistics with S_.  Fourth Edition. Springer-Verlag.

     (This contains the exact definitions used.)

_S_e_e _A_l_s_o:

     'plot.acf', 'ARMAacf' for the exact autocorrelations of a given
     ARMA process.

_E_x_a_m_p_l_e_s:

     require(graphics)

     ## Examples from Venables & Ripley
     acf(lh)
     acf(lh, type = "covariance")
     pacf(lh)

     acf(ldeaths)
     acf(ldeaths, ci.type = "ma")
     acf(ts.union(mdeaths, fdeaths))
     ccf(mdeaths, fdeaths, ylab = "cross-correlation")
     # (just the cross-correlations)

     presidents # contains missing values
     acf(presidents, na.action = na.pass)
     pacf(presidents, na.action = na.pass)