pear                  package:pear                  R Documentation

_f_i_t _a _p_e_r_i_o_d_i_c _a_u_t_o_r_e_g_r_e_s_s_i_o_n _m_o_d_e_l

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

     Periodic time series models of any order, say m[j], for the j-th
     period, j=1,...,p can be fit to a periodic time series of period
     p. A generalization of the Yule-Walker method is used so that when
     p=1 the results from this function will be equivalent to the Splus
     function ar.yw(). If desired the aic or bic criterion can be used
     to select the model orders. Otherwise the user can select based on
     the partial autocorrelation function as suggested in Box and
     Jenkins (1976) and McLeod (1994).

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

     pear(z, m, ic="none")

_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. 

       m: If ic="none" then m is a required argument. In this case m
          specifies the order of the periodic autoregression to be
          fitted. Typically m is specified as a vector of length p
          where p is the period and m[k], k=1,...,p indicates the order
          for the k-th period. For convenience, if all periods are the
          same order then m can just be that scalar value. When
          ic="aic" or ic="bic" then the argument m is ignored. 

      ic: The default ic="none" means the model orders are supplied.
          Otherwise if ic="aic" or ic="bic" the automatic criteria aic
          or bic are used. 

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

     Let z[t] be a period time series with period p and let m[j] denote
     the order of the autoregressive model for the j-th period,
     j=1,...,p. The parameters of this model can be estimated using the
     Yule-Walker type equations given in McLeod eq (3.1) and (3.2). The
     covariance matrix of the autoregressive parameters is obtained by
     replacing the theoretical autocovariances in eq (3.3, note
     addendum correction) with their sample values.

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

     a list with the following named components: model.orders          
        vector of length p, indicating the fitted ar order for each
     period k, k=1,...,p phi                       matrix of dimension
     p by m where m =  max(model.orders). The (i,j) entry is phi[i,j]
     which is the autoregression  coefficient for period i and lag j.
     se.phi                    matrix of standard deviations for the
     estimated phi's. For those phi's set to 0, the corresponding
     se.phi's are  also set to 0. resvar                    vector of
     length p residuals                 time series object of length(z)
     portmanteau.test           list: portmanteau test at various lags
     The named components of this list are: QM = matrix of portmanteau
     statistics for each period and lag QM.df = corresponding df of QM
     QM.sl = corresponding sl of QM residual.acf              residual
     autocorrelation matrix residual.acf.sd           estimated
     standard errors of the residual autocorrelations cov              
             list with p components: cov[[i]] is the estimated
     covariance matrix for the parameters of period i

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

     none

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

     Box, G.E.P. and Jenkins, G.M. (1976), "Time Series Analysis:
     Forecasting and Control", Holden-Day: San Franciso. 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. (1994), "Diagnostic
     Checking of Periodic Autoregression" Journal of Time Series
     Analysis, Vol. 15, No. 2, pp.221-233. McLeod, A.I. (1995), Errata
     (see file errata.tex included with these files)

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

     peacf, pepacf, ar.yw

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

     data(fraser)
     pear(log(fraser), ic="bic")

