pepsi                  package:pear                  R Documentation

_m_o_v_i_n_g _a_v_e_r_a_g_e _e_x_p_a_n_s_i_o_n _o_f _a _p_e_r_i_o_d_i_c _a_u_t_o_r_e_g_r_e_s_s_i_o_n

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

     A periodic autoregression can be represented as an infinite
     periodic moving average process. This function calculates the
     coefficients in this expansion. These coefficients are needed in
     various time series computations such as in computing the
     variances of forecasts, variances of residual autocorrelations and
     theoretical autocovariances of a periodic autoregression. The
     function pepsi is used by pear to calculate the estimated standard
     deviations of the residual autocorrelations in a fitted periodic
     autoregression.

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

     pepsi(phi, lag.max)

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

     phi: matrix with (i,j)-entry phi[i, j] where phi[i,j] is the 
          autoregressive coefficient for period i at lag j. Here
          i=1,...,p  and j=1,...,m where m is highest ar order
          specified. 

 lag.max: maximum number of lags to calculate in the moving average
          expansion. 

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

     The moving average expansion for a periodic autoregressive is
     defined in equation (1.4) of McLeod (1994) and the algorithm
     implements the recursion given in equation (1.5).

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

     matrix with (i,j)-entry psi[i, j] where psi[i,j] is the 
     autoregressive coefficient for period i at lag j. Here i=1,...,p 
     and j=1,...,lag.max.

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

     none

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

     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:

     pear

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

     data(fraser)
     pear.out <- pear(log(fraser), ic="bic")
     pepsi(pear.out$phi,lag.max=20)

