alrtest             package:urca             R Documentation(latin1)

_L_i_k_e_l_i_h_o_o_d _r_a_t_i_o _t_e_s_t _f_o_r _r_e_s_t_r_i_c_t_i_o_n_s _o_n _a_l_p_h_a

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

     This function estimates a restricted VAR, where the restrictions
     are base upon *alpha*, _i.e._ the loading vectors. The test
     statistic is distributed as chi^2 with r(p-m) degrees of freedom,
     with m equal to the columns of the restricting matrix *A*.

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

     alrtest(z, A, r)

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

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

       A: The (p times m) matrix containing the restrictions on
          *alpha*.

       r: The count of cointegration relationships; 
           inferred from 'summary(ca.jo-object)'.

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

     The orthogonal matrix to *A* can be accessed as 'object@B'. The
     restricted *alpha* matrix is normalised with respect to the first
     variable.

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

     An object of class 'cajo.test'.

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

     Bernhard Pfaff

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

     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', 'blrtest', 'ablrtest', 'cajo.test-class', 'ca.jo-class'
     and 'urca-class'.

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

     data(denmark)
     sjd <- denmark[, c("LRM", "LRY", "IBO", "IDE")]
     sjd.vecm <- ca.jo(sjd, ecdet = "const", type="eigen", K=2, spec="longrun",
     season=4)
     DA <- matrix(c(1,0,0,0), c(4,1))
     summary(alrtest(sjd.vecm, A=DA, r=1))

