LSTAR                 package:tsDyn                 R Documentation

_L_o_g_i_s_t_i_c _S_m_o_o_t_h _T_r_a_n_s_i_t_i_o_n _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:

     Logistic Smooth Transition AutoRegressive model.

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

     lstar(x, m, d=1, steps=d, series, mL, mH, thDelay, 
                             th, phi1, phi2, gamma, trace=TRUE, control=list())

     lstar(series, m, d, steps, mL, mH, mTh,
         phi1, phi2, th, gamma, trace=TRUE, control=list())

     lstar(series, m, d, steps, mL=m, mH=m, thVar,
         phi1, phi2, th, gamma, trace=TRUE, control=list())

_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

phi1, phi2, th, gamma: starting values for coefficients in the LSTAR
          model. If missing, SETAR estimations are used

   trace: should additional infos be printed? (logical)

 control: further arguments to be passed as 'control' list to 'optim'

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


 x[t+steps] = ( phi1[0] + phi1[1] x[t] + phi1[2] x[t-d] + ... + phi1[mL] x[t - (mL-1)d] ) G( z[t], th, gamma ) + ( phi2[0] + phi2[1] x[t] + phi2[2] x[t-d] + ... + phi2[mH] x[t - (mH-1)d] ) (1 - G( z[t], th, gamma ) ) + eps[t+steps]

     with z the treshold variable, and G the logistic function,
     computed as 'plogis(q, location = th, scale = 1/gamma)', so see
     'plogis' documentation for details on the logistic function
     formulation and parameters meanings.  The threshold variable can
     alternatively be specified by:

     _m_T_h z[t] = x[t] mTh[1] + x[t-d] mTh[2] + ... + x[t-(m-1)d] mTh[m] 

     _t_h_D_e_l_a_y z[t] = x[t - thDelay*d ] 

     _t_h_V_a_r z[t] = thVar[t] 

     Note that if starting values for phi1 and phi2 are provided, isn't
     necessary to specify mL and mH. Further, the user has to specify
     only one parameter between mTh, thDelay and thVar for indicating
     the threshold variable.

     Estimation is done by minimizing residuals sum of squares with
     respect to phi1, phi2, th and gamma, using the 'optim' function,
     with its default optimization method. You can pass further
     arguments directly to the 'control' list argument of this
     function. For example, the option 'maxit' maybe useful when there
     are convergence issues (see examples).

     Note that 'lstar' is only a convenience wrapper to nlar (for not
     having to specify 'm', which can be deduced from the other
     parameters).

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

     An object of class 'nlar', subclass 'lstar', i.e. a list with
     fitted model informations.

_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.lstar' for details on plots produced for this model from the
     'plot' generic.

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

     #fit a LSTAR model. Note 'maxit': slow convergence
     mod.lstar <- lstar(log10(lynx), m=2, mTh=c(0,1), control=list(maxit=3000))
     mod.lstar

