marma                  package:evd                  R Documentation

_S_i_m_u_l_a_t_e _M_A_R_M_A(_p,_q) _P_r_o_c_e_s_s_e_s

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

     Simulation of MARMA(p,q) processes.

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

     marma(n, p = 0, q = 0, psi, theta, init = rep(0, p), n.start = p,
         rand.gen = rfrechet, ...)
     mar(n, p = 1, psi, init = rep(0, p), n.start = p, rand.gen =
         rfrechet, ...)
     mma(n, q = 1, theta, rand.gen = rfrechet, ...)

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

       n: The number of observations.

       p: The AR order of the MARMA process.

       q: The MA order of the MARMA process.

     psi: A vector of non-negative parameters, of length 'p'. Can be
          omitted if 'p' is zero.

   theta: A vector of non-negative parameters, of length 'q'. Can be
          omitted if 'q' is zero.

    init: A vector of non-negative starting values, of length 'p'.

 n.start: A non-negative value denoting the length of the burn-in
          period. If 'n.start' is less than 'p', then 'p' minus
          'n.start' starting values will be included in the output
          series.

rand.gen: A simulation function to generate the innovations.

     ...: Additional arguments for 'rand.gen'.  Most usefully, the
          scale and shape parameters of the innovations generated by
          'rfrechet' can be specified by 'scale' and 'shape'
          respectively.

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

     A max autoregressive moving average process {X_k}, denoted by
     MARMA(p,q), satisfies

 X_k = max[phi_1 X_{k-1}, ..., phi_p X_{k-p}, epsilon_k, theta_1 epsilon_{k-1}, ..., theta_q epsilon_{k-q}]

     where 'phi' = (phi_1, ..., phi_p) and 'theta' = (theta_1, ...,
     theta_q) are non-negative vectors of parameters, and where
     {epsilon_k} is a series of _iid_ random variables with a common
     distribution defined by 'rand.gen'.

     The functions 'mar' and 'mma' generate MAR(p) and MMA(q) processes
     respectively. A MAR(p) process {X_k} is equivalent to a MARMA(p,
     0) process, so that

       X_k = max[phi_1 X_{k-1}, ..., phi_p X_{k-p}, epsilon_k].

     A MMA(q) process {X_k} is equivalent to a MARMA(0, q) process, so
     that

 X_k = max[epsilon_k, theta_1 epsilon_{k-1}, ..., theta_q epsilon_{k-q}].

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

     A numeric vector of length 'n'.

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

     'evmc'

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

     marma(100, p = 1, q = 1, psi = 0.75, theta = 0.65)
     mar(100, psi = 0.85, n.start = 20)
     mma(100, q = 2, theta = c(0.75, 0.8))

