peacf                  package:pear                  R Documentation

_P_e_r_i_o_d_i_c _A_u_t_o_c_o_r_r_e_l_a_t_i_o_n _F_u_n_c_t_i_o_n

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

     The periodic autocorrelation for a time series with period p may
     be defined as for period (m=1,...,p) and lag, l=1,2,... by r(m, l)
     = c(m, l)/sqrt(c(m, 0)*c(m-l, 0)) where c(m, l) is the periodic
     autocovariance defined by c(m, l) = sum(z[t] * z[t-l]) where the
     sum is over all data in period m. When p=1, peacf produces output
     which is equivalent to that produced by Splus function acf.

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

     peacf(z, lag.max, plot=TRUE)

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

       z: a univariate time series object. Note that the period of z is
          given by attr(z, "tsp")[3]. Additional information about the
          time series can be provided in a title string by setting
          attr(z, "title") to the desired string. This title will then
          be displayed on the plot. Abbreviations for the periods may
          be provided in attr(z, "abb"). For example, to use the
          standard monthly abbreviations: attr(z, "abb")<-month.abb.
          These abbreviations  will be used to aid one in interpreting
          the output. 

 lag.max: maximum lag, if missing default is 0.25*length(z)/p, where p
          = attr(z, "tsp")[3] 

    plot: if plot=TRUE, a plot of the periodic autocorrelations is
          produced. 

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

     The use of the periodic autocorrelation and its plot are discussed
     in McLeod (1994) and a portmanteau model adequacy test is
     developed therein. The periodicity test is discussed in McLeod
     (1993). For more details, see the references below.

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

     a list is returned with the following components:  means          
                periodic means standard.deviations        periodic
     standard deviations acf                        matrix of periodic
     autocorrelations benchmark.sd               1/sqrt(nyrs),
     nyrs=ceiling(length(z)/p) sub.lengths                number of
     observations in each period period                     p = attr(z,
     "tsp")[3] title                      title = attr(z, "title")
     periodicity.test           list: test for periodic correlation at
     lag 1 The components of this list are: Q1 = scalar value, the test
     statistic Q1.sl = signifiance level (upper tail) portmanteau.test 
              list: portmanteau test at various lags The components of
     this list are: QM = matrix of portmanteau statistics for each
     period and lag QM.df = corresponding df of QM

_S_i_d_e _E_f_f_e_c_t_s:

     a plot may be produced if plot=TRUE

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

     Hipel, K.W. and McLeod, A.I. (1994) "Time Series Modelling of 
     Water Resources and Environmental Systems"  Elsevier, Amsterdam
     ISBN 0-444-89270-2.  (1013 pages). McLeod, A.I. (1993),
     "Parsimony, Model Adequacy and Periodic Correlation in Time Series
     Forecasting", International Statistical Review,  Vol. 61, No. 3,
     pp.387-393. McLeod, A.I. (1994), "Diagnostic Checking of Periodic
     Autoregression" Journal of Time Series Analysis, Vol. 15, No. 2,
     pp.221-233.

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

     peacf.plot, pepacf, peplot, peboxplot, pear, acf, acf.plot

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

     data(fraser)
     peacf(log(fraser))

