UnitrootDistribution         package:fSeries         R Documentation

_U_n_i_t _R_o_o_t _D_i_s_t_r_i_b_u_t_i_o_n_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 the unit root test
     statistics.  

     The functions are:

       'punitroot'  the cumulative probability,
       'qunitroot'  the quantiles of the unit root test statistics,
       'adfTable'   the table of cumulative probabilities,
       'pdftest'    the cumulative probability for the ADF test,
       'qdftest'    the quantiles for the ADF test.

_U_s_a_g_e:

     punitroot(q, n.sample = 0, trend = c("c", "nc", "ct", "ctt"), 
         statistic = c("t", "n"), na.rm = FALSE)
     qunitroot(p, n.sample = 0, trend = c("c", "nc", "ct", "ctt"), 
         statistic = c("t", "n"), na.rm = FALSE)
         
     pdftest(q, n.sample, trend = c("nc", "c", "ct"), statistic = c("t", "n")) 
     qdftest(p, n.sample, trend = c("nc", "c", "ct"), statistic = c("t", "n"))
     dfTable(trend = c("nc", "c", "ct"), statistic = c("t", "n"))

_A_r_g_u_m_e_n_t_s:

n.sample: the number of observations in the sample from which the 
          quantiles are to be computed.
           [*unitroot] - 
           Specify 'n.sample=0' for asymptotic quantiles. The  default
          is 0.  

   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 'padf' returns the cumulative probability of  the
     finite sample distribution of the unit root test statistics. 

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

     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 programs 'padf' and 'qadf' use the tables from  A. Banerjee et
     al. (1993).

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

_A_u_t_h_o_r(_s):

     J.G. McKinnon for the underlying Fortran routine and the tables, 
      Diethelm Wuertz for the Rmetrics R-port.

_R_e_f_e_r_e_n_c_e_s:

     Banerjee A., Dolado J.J., Galbraith J.W., Hendry D.F. (1993);
     _Cointegration, Error Correction, and the Econometric  Analysis of
     Non-Stationary Data_, Oxford University Press, Oxford. 

     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:

      
     ## SOURCE("fSeries.32A-UnitrootDistribution")

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

     ## qunitroot -
        # Finite sample quantile of n-statistic
        qunitroot(0.95, n.sample = 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.sample = 100, trend = "nc", statistic = "n")

