alphaols            package:urca            R Documentation(latin1)

_O_L_S _r_e_g_r_e_s_s_i_o_n _o_f _V_E_C_M _w_e_i_g_h_t_i_n_g _m_a_t_r_i_x

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

     This functions estimates the *alpha* matrix of a VECM. The
     following OLS regression of the R-form of the VECM is hereby
     utilised:

 *R*_{0t} = *alpha**beta*prime *R*_{kt} + *varepsilon*_t qquad t=1, ..., T

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

     alphaols(z, reg.number = NULL)

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

       z: An object of class 'ca.jo'.

reg.number: The number of the equation in the R-form that should be
          estimated or if set to 'NULL' (the default), all equations
          within the R-form are estimated.

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

     The cointegrating relations, _i.e._ *R*_{kt}prime *beta* are
     calculated by using 'z@RK' and 'z@V'.

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

     Returns an object of class 'lm'.

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

     Bernhard Pfaff

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

     Johansen, S. (1988), Statistical Analysis of Cointegration
     Vectors, _Journal of Economic Dynamics and Control_, *12*,
     231-254.

     Johansen, S. and Juselius, K. (1990), Maximum Likelihood
     Estimation and Inference on Cointegration - with Applications to
     the Demand for Money, _Oxford Bulletin of Economics and
     Statistics_, *52, 2*, 169-210.

     Johansen, S. (1991), Estimation and Hypothesis Testing of
     Cointegration Vectors in Gaussian Vector Autoregressive Models,
     _Econometrica_, *Vol. 59, No. 6*, 1551-1580.

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

     'ca.jo', 'lm', 'ca.jo-class' and 'urca-class'.

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

     data(denmark)
     sjd <- denmark[, c("LRM", "LRY", "IBO", "IDE")]
     sjd.vecm1 <- ca.jo(sjd, ecdet = "const", type="eigen", K=2, spec="longrun",
     season=4)
     summary(alphaols(sjd.vecm1))
     summary(alphaols(sjd.vecm1, reg.number=1))

