rrar                  package:VGAM                  R Documentation

_N_e_s_t_e_d _r_e_d_u_c_e_d-_r_a_n_k _a_u_t_o_r_e_g_r_e_s_s_i_v_e _m_o_d_e_l_s _f_o_r _m_u_l_t_i_p_l_e
_t_i_m_e _s_e_r_i_e_s

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

     Estimates the parameters of a  nested reduced-rank autoregressive
     model for multiple time series.

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

     rrar(Ranks = 1, coefstart = NULL)

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

   Ranks: Vector of integers: the ranks of the model. Each value must
          be at least one and no more than 'M', where 'M' is the number
          of response variables in the time series.  The length of
          'Ranks' is the _lag_, which is often denoted by the symbol
          _L_ in the literature. 

coefstart: Optional numerical vector of initial values for the
          coefficients.  By default, the family function chooses these
          automatically. 

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

     Full details are given in Ahn and Reinsel (1988). Convergence may
     be very slow, so setting 'maxits=50', say, may help. If
     convergence is not obtained, you might like to try inputting
     different  initial values. 

     Setting 'trace=TRUE' in 'vglm' is useful for monitoring the
     progress at each iteration.

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

     An object of class '"vglmff"' (see 'vglmff-class'). The object is
     used by modelling functions such as 'vglm' and 'vgam'.

_N_o_t_e:

     This family function should be used within 'vglm' and not with
     'rrvglm' because it does not fit into the RR-VGLM framework
     exactly. Instead, the reduced-rank model is formulated as a VGLM!

     A methods function 'Coef.rrar', say, has yet to be written. It
     would return the quantities  'Ak1', 'C', 'D', 'omegahat', 'Phi',
     etc. as slots, and then 'print.Coef.rrar' would also need to be
     written.

_A_u_t_h_o_r(_s):

     T. W. Yee

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

     Ahn, S. and Reinsel, G. C. (1988) Nested reduced-rank
     autoregressive models for multiple time series. _Journal of the
     American Statistical Association_, *83*, 849-856.

     Documentation accompanying the 'VGAM' package at <URL:
     http://www.stat.auckland.ac.nz/~yee> contains further information
     and examples.

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

     'vglm', 'usagrain'.

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

     ## Not run: 
     data(usagrain)
     year = seq(1961+1/12, 1972+10/12, by=1/12)
     par(mar=c(4,4,2,2)+0.1, mfrow=c(2,2))
     for(i in 1:4) {
         plot(year, usagrain[,i], main=names(usagrain)[i], type="l", xlab="", ylab="")
         points(year, usagrain[,i], pch="*")
     }
     apply(usagrain, 2, mean)     # mu vector
     cgrain = scale(usagrain, scale=FALSE) # Center the time series only
     fit = vglm(cgrain ~ 1, rrar(Ranks=c(4,1)), trace=TRUE)
     summary(fit)

     print(fit@misc$Ak1, dig=2)
     print(fit@misc$Cmatrices, dig=3)
     print(fit@misc$Dmatrices, dig=3)
     print(fit@misc$omegahat, dig=3)
     print(fit@misc$Phimatrices, dig=2)

     par(mar=c(4,4,2,2)+0.1, mfrow=c(4,1))
     for(i in 1:4) {
         plot(year, fit@misc$Z[,i], main=paste("Z", i, sep=""),
              type="l", xlab="", ylab="")
         points(year, fit@misc$Z[,i], pch="*")
     }
     ## End(Not run)

