UnitrootUrcaInterface       package:fUnitRoots       R Documentation

_U_n_i_t _R_o_o_t _T_i_m_e _S_e_r_i_e_s _T_e_s_t_s

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

     A collection and description of functions  for unit root testing.
     This is a Rmetrics conform interface to the unitroot tests 
     implemented by B. Pfaff available through the contributed package
     "urca". 

     Added functions based on the 'urca' package include:

       'urdfTest'    Augmented Dickey-Fuller test for unit roots,
       'urersTest'   Elliott-Rothenberg-Stock test for unit roots,
       'urkpssTest'  KPSS unit root test for stationarity,
       'urppTest'    Phillips-Perron test for unit roots,
       'urspTest'    Schmidt-Phillips test for unit roots,
       'urzaTest'    Zivot-Andrews test for unit roots.

     Note, that the contributed R package 'urca' is required!

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

     urdfTest(x, lags = 1, type = c("nc", "c", "ct"), doplot = TRUE)
     urersTest(x, type = c("DF-GLS", "P-test"), model = c("constant", "trend"),
         lag.max = 4, doplot = TRUE)
     urkpssTest(x, type = c("mu", "tau"), lags = c("short", "long", "nil"),
         use.lag = NULL, doplot = TRUE)
     urppTest(x, type = c("Z-alpha", "Z-tau"), model = c("constant", "trend"),
         lags = c("short", "long"), use.lag = NULL, doplot = TRUE)
     urspTest(x, type = c("tau", "rho"), pol.deg = c(1, 2, 3, 4),
         signif = c(0.01, 0.05, 0.1), doplot = TRUE)
     urzaTest(x, model = c("intercept", "trend", "both"), lag, doplot = TRUE)

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

  doplot: [ur*Test] - 
           a logical flag, by default 'TRUE'. Should a diagnostical
          plot be displayed? 

 lag.max: [urersTest] - 
           the maximum numbers of lags used for testing of a decent lag
           truncation for the '"P-test"', BIC used, or the maximum 
          number of lagged differences to be included in the test 
          regression for '"DF-GLS"'. 

     lag: [urzaTest] - 
           the highest number of lagged endogenous differenced
          variables  to be included in the test regression. 

    lags: [urkpssTest][urppTest] - 
           the maximum number of lags used for error term correction. 

   model: [urersTest] - 
           a character string dennoting the deterministic model used
          for  detrending, either '"constant"', the default, or 
          '"trend"'. 
           [urppTest] - 
           a character string which determines the deterministic part
          in  the test regression, either '"constant"', the default, or
           '"trend"'. 
           [urzaTest] - 
           a character string specifying if the potential break occured
           in either the '"intercept"', the linear '"trend"' or  in
          '"both"'. 

 pol.deg: [urspTest] - 
           the polynomial degree in the test regression. 

  signif: [urspTest] - 
           the significance level for the critical value of the test 
          statistic. 

    type: [urkpssTest] - 
           a character string which denotes the type of deterministic
          part, either '"mu"', the default, or '"tau"'. 
           [urppTest] - 
           a character string which specifies the test type, either 
          '"Z-alpha"', the default, or '"Z-tau"'. 
           [urspTest] - 
           a character string which specifies the test type, either 
          '"tau"', the default, or '"rho"'. 

 use.lag: [urkpssTest] - 
           a character string specifying the number of lags. Allowed
          arguments are 'lags=c("short", "long", "nil")', for more 
          information see the details section.
           [urppTest] - 
                 Use of a different lag number, specified by the user. 

       x: a numeric vector or time series object. 

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

     *Unit Root Tests from Berhard Pfaff's "urca" Package:* 

     _Elliott-Rothenberg-Stock Test for Unit Roots:_  
      To improve the power of the unit root test, Elliot, Rothenberg
     and  Stock proposed a local to unity detrending of the time
     series. ERS  developed a feasible point optimal test, '"P-test"',
     which  takes serial correlation of the error term into account.
     The second  test type is the '"DF-GLS"' test, which is an ADF-type
     test  applied to the detrended data without intercept. Critical
     values  for this test are taken from MacKinnon in case of
     'model="constant"' and else from Table 1 of Elliot, Rothenberg and
     Stock. 
      '[urca:ur.ers]' 

     _KPSS Test for Unit Roots:_  
      Performs the KPSS unit root test, where the Null hypothesis is 
     stationarity. The test types specify as deterministic component 
     either a constant '"mu"' or a constant with linear trend  '"tau"'.
     'lags="short"' sets the number of lags to  _root 4 of [4 times
     (n/100)_, whereas 'lags="long"'  sets the number of lags to _root
     4 of [12 times (n/100)]_.  If 'lags="nil"' is choosen, then no
     error correction is made.  Furthermore, one can specify a
     different number of maximum lags  by setting use.lag accordingly. 
      '[urca:ur.kpss]' 

     _Phillips-Perron Test for Unit Roots:_  
      Performs the Phillips and Perron unit root test. Beside the  Z
     statistics Z-alpha and Z-tau, the Z statistics for the 
     deterministic part of the test regression are computed, too.  For
     correction of the error term a Bartlett window is used. 
      '[urca:ur.pp]' 

     _Schmidt-Phillips Test for Unit Roots:_  
      Performs the Schmidt and Phillips unit root test, where under 
     the Null and Alternative Hypothesis the coefficients of the 
     deterministic variables are included. Two test types are
     available:  the '"rho-test"' and the '"tau-test"'. Both tests are 
     extracted from the LM principle. 
      '[urca:ur.sp]' 

     _Zivot-Andrews Test for Unit Roots:_  
      Performs the Zivot and Andrews unit root test, which allows a 
     break at an unknown point in either the intercept, the linear 
     trend or in both. This test is based upon the recursive estimation
      of a test regression. The test statistic is defined as the 
     minimum t-statistic of the coeffcient of the lagged endogenous 
     variable. 
      '[urca:ur.za]'

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

     All tests return an object of class '"fHTEST"' with the following
     slots:

   @call: the function call.       

   @data: a data frame with the input data. 

@data.name: a character string giving the name of the data frame. 

   @test: a list object which holds the output of the underlying test
          function. 

  @title: a character string with the name of the test. 

@description: a character string with a brief description of the test. 

$statistic: the value of the test statistic. 

$parameter: the lag order. 

$p.value: the p-value of the test. 

 $method: a character string indicating what type of test was
          performed. 

$data.name: a character string giving the name of the data. 

$alternative: a character string describing the alternative hypothesis. 

   $name: the name of the underlying function, which may be wrapped. 

 $output: additional test results to be printed. 

_N_o_t_e:

     The functions 'ur*Test()' fullfill the naming conventions  of
     Rmetrics, return an S4 object named 'fHTEST' as any other 
     hypothesis test from Rmetrics, and allow for 'timeSeries' objects 
     as input. These are the only differences to the original
     implementation of the functions. 

     Fur further details we refer to the manual pages of the  '"urca"'
     package.

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

     Bernhard Pfaff for the tests implemented in R's "urca" package,
      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. 

     Kwiatkowski D., Phillips P.C.B, Schmidt P., Shin Y. (1992);
     _Testing the Null Hypothesis of Stationarity against  the
     Alternative of a Unit Root_, Journal of Econometrics 54, 159-178.

     Perron P. (1988); _Trends and Random Walks in Macroeconomic Time
     Series_, Journal of Economic Dynamics and Control 12, 297-332.

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

     Said S.E., Dickey D.A. (1984); _Testing for Unit Roots in
     Autoregressive-Moving Average  Models of Unknown Order_,
     Biometrika 71, 599-607.

     Schwert G.W. (1989); _Tests for Unit Roots: A Monte Carlo
     Investigation_, Journal of Business and Economic Statistics 2,
     147-159.

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

     ## Not run: 
     ## Time Series 
        # A time series which contains no unit-root:
        x = rnorm(1000)  
        # A time series which contains a unit-root:
        y = cumsum(c(0, x))
        
     ## ERS Test:
        require(urca)
        urersTest(x)
        urersTest(y)
     ## End(Not run)

