MacKinnonPValues        package:urca        R Documentation(latin1)

_M_a_c_K_i_n_n_o_n'_s _U_n_i_t _R_o_o_t _p _V_a_l_u_e_s

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

     A collection and description of functions  to compute the
     distribution and and quantile  function for MacKinnon's unit root
     test statistics.  

     The functions are:

       'punitroot'      the returns cumulative probability,
       'qunitroot'      the returns quantiles of the unit root test statistics,
       'unitrootTable'  tables p values from MacKinnon's response surface.

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

     punitroot(q, N = Inf, trend = c("c", "nc", "ct", "ctt"), 
         statistic = c("t", "n"), na.rm = FALSE)
     qunitroot(p, N = Inf, trend = c("c", "nc", "ct", "ctt"), 
         statistic = c("t", "n"), na.rm = FALSE)
         
     unitrootTable(trend = c("c", "nc", "ct", "ctt"), statistic = c("t", "n")) 

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

       N: the number of observations in the sample from which the 
          quantiles are to be computed.


   na.rm: a logical value. If set to 'TRUE', missing values will  be
          removed otherwise not, the default is 'FALSE'.  

       p: a numeric vector of probabilities. Missing values are 
          allowed.  

       q: vector of quantiles or test statistics. Missing values  are
          allowed.  

statistic: a character string describing the type of test statistic. 
          Valid choices are '"t"' for t-statistic, and '"n"'  for
          normalized statistic, sometimes referred to as the 
          rho-statistic. The default is '"t"'.  

   trend: a character string describing the regression from which the 
          quantiles are to be computed. Valid choices are: '"nc"'  for
          a regression with no intercept (constant) nor time trend, 
          and '"c"' for a regression with an intercept (constant)  but
          no time trend, '"ct"' for a regression with an intercept 
          (constant) and a time trend. The default is '"c"'.  

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

     The function 'punitroot' returns the cumulative probability  of
     the asymptotic or finite sample distribution of the unit root 
     test statistics. 

     The function 'qunitroot' returns the quantiles of the  asymptotic
     or finite sample distribution of the unit root test  statistics,
     given the probabilities.

_N_o_t_e:

     The function 'punitroot' and 'qunitroot' use Fortran  routines and
     the response surface approach from J.G. MacKinnon (1988).  Many
     thanks to J.G. MacKinnon putting his code and tables under the 
     GPL license, which made this implementation possible.

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

     J.G. MacKinnon for the underlying Fortran routine and the tables, 
      Diethelm Wuertz for the formerly Rmetrics R-port and Bernhard
     Pfaff for the porting to 'urca'.

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

     Dickey, D.A., Fuller, W.A. (1979); _Distribution of the estimators
     for autoregressive time  series with a unit root_,  Journal of the
     American Statistical Association 74, 427-431. 

     MacKinnon, J.G. (1996); _Numerical distribution functions for unit
     root and  cointegration tests_, Journal of Applied Econometrics
     11, 601-618.

     Phillips, P.C.B., Perron, P. (1988); _Testing for a unit root in
     time series regression_,  Biometrika 75, 335-346.

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

      
     ## qunitroot -
        # Asymptotic quantile of t-statistic
        qunitroot(0.95, trend = "nc", statistic = "t")

     ## qunitroot -
        # Finite sample quantile of n-statistic
        qunitroot(0.95, N = 100, trend = "nc", statistic = "n") 
        
     ## punitroot -
        # Asymptotic cumulative probability of t-statistic
        punitroot(1.2836, trend = "nc", statistic = "t")

     ## punitroot -
        # Finite sample cumulative probability of n-statistic
        punitroot(1.2836, N = 100, trend = "nc", statistic = "n")
        
     ## Mac Kinnon's unitrootTable -
        unitrootTable(trend = "nc")

