SETAR                 package:tsDyn                 R Documentation

_S_e_l_f _T_h_r_e_s_h_o_l_d _A_u_t_o_r_e_g_r_e_s_s_i_v_e _m_o_d_e_l

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

     Self Exciting Threshold AutoRegressive model.

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

     setar(x, m, d=1, steps=d, series, mL=m, mH=m, thDelay=0, th,
     trace=FALSE)

     setar(x, m, d=1, steps=d, series, mL=m, mH=m, mTh, th,
     trace=FALSE)

     setar(x, m, d=1, steps=d, series, mL=m, mH=m, thVar, th,
     trace=FALSE)

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

       x: time series 

m, d, steps: embedding dimension, time delay, forecasting steps 

  series: time series name (optional) 

      mL: autoregressive order for 'low' regime (dafult: m). Must be
          <=m

      mH: autoregressive order for 'high' regime (default: m). Must be
          <=m

 thDelay: 'time delay' for the threshold variable (as multiple of
          embedding time delay d)

     mTh: coefficients for the lagged time series, to obtain the
          threshold variable

   thVar: external threshold variable

      th: threshold value (if missing, a search over a resonable grid
          is tried)

   trace: should additional infos be printed? (logical)

     ...: further arguments to be passed to 'nlar'

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

     Self Exciting Threshold AutoRegressive model.


 x[t+steps] = ( phi1[0] + phi1[1] x[t] + phi1[2] x[t-d] + ... + phi1[mL] x[t - (mL-1)d] ) I( z[t] <= th) + ( phi2[0] + phi2[1] x[t] + phi2[2] x[t-d] + ... + phi2[mH] x[t - (mH-1)d] ) I( z[t] > th) + eps[t+steps]


     with z the treshold variable. The threshold variable can
     alternatively be specified by (in that order):

     _t_h_D_e_l_a_y 'z[t] = x[t - thDelay*d ]' 

     _m_T_h 'z[t] = x[t] mTh[1] + x[t-d] mTh[2] + ... + x[t-(m-1)d]
          mTh[m]' 

     _t_h_V_a_r 'z[t] = thVar[t]' 

     For fixed 'th' and threshold variable, the model is linear, so
     'phi1' and 'phi2' estimation can be done directly by CLS
     (Conditional Least Squares). Standard errors for phi1 and phi2
     coefficients provided by the 'summary' method for this model are
     taken from the linear regression theory, and are to be considered
     asymptoticals.

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

     An object of class 'nlar', subclass 'setar'

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

     Antonio, Fabio Di Narzo

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

     Non-linear time series models in empirical finance, Philip Hans
     Franses and Dick van Dijk, Cambridge: Cambridge University Press
     (2000).

     Non-Linear Time Series: A Dynamical Systems Approach, Tong, H.,
     Oxford: Oxford University Press (1990).

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

     'plot.setar' for details on plots produced for this model from the
     'plot' generic.

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

     #fit a SETAR model, with threshold as suggested in Tong(1990)
     mod.setar <- setar(log10(lynx), m=2, thDelay=1, th=3.25)
     mod.setar
     summary(mod.setar)

