UnitrootTests            package:fSeries            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.
     The family of tests  includes ADF tests based on Banerjee's et al.
     tables and on J.G. McKinnons' numerical  distribution functions.
     In addition we have  included tests written by B. Pfaff. 

     The functions are:

       'adfTest'       Augmented Dickey-Fuller test for unit roots,
       'unitrootTest'  the same based on McKinnons's test statistics.

     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:

     urTest(x, method = c("unitroot", "adf", "urers", "urkpss", "urpp", 
         "ursp", "urza"), title = NULL, description = NULL, ...)

     unitrootTest(x, lags = 1, type = c("nc", "c", "ct"), title = NULL, 
         description = NULL)
     adfTest(x, lags = 1, type = c("nc", "c", "ct"), title = NULL, 
         description = NULL)

     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:

description: a character string which allows for a brief description. 

  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. 

  method: [urTest] - 
           a character string describing the desired method, one of:
          '"unitroot"', '"adf"', '"urers"', '"urkpss"',  '"urpp"',
          '"ursp"', or '"urza"'. 

   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. 

   title: a character string which allows for a project title. 

    type: [adfTest][unitrootTest] - 
           a character string describing the type of the unit root 
          regression. 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"'.  
           [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. 

     ...: [urTest] - 
           optional arguments passed to the underlying test functions. 

_D_e_t_a_i_l_s:

     *ADF Tests:*

     The 'adftest' computes test statistics and p values along the
     implementation from Trapletti's augmented Dickey-Fuller test  for
     unit roots. In contrast to Trapletti's function three kind  of
     test types can be selected. 


     *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 'ur*Test' wrapper functions fullfill the naming conventions 
     of Rmetrics, return a S4 object named 'fHTEST' as any other 
     hypothesis test from Rmetrics, and allow for 'timeSeries' objects 
     as input. These are the only differences. The Rmetrics wrappers 
     were tested with 'urca' version 0.7.9.

     If you are running Rmetrics under an operating system where the
     R-package 'urca' is not available you can load the required
     functions through the command xmpfSeries() and select  _funUrca_
     from the menu. A copy of urca and required dependent functions are
     saved in the demo file 'funUrca.R'.

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

_A_u_t_h_o_r(_s):

     Adrian Trapletti for the tests adapted from R's "tseries" package, 
      Bernhard Pfaff for the tests wrapped from 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.

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

     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:

     ## SOURCE("fSeries.32B-UnitrootTests")

     ## Not run: 
     ## adfTest - 
        xmpSeries("\nStart: Augmented Dickey-Fuller Test for Unit Roots >")
        # A time series which contains no unit-root:
        x = rnorm(1000)  
        adfTest(x)
        # A time series which contains a unit-root:
        y = cumsum(c(0, x))
        adfTest(y)
        
     ## unitrootTest - 
        xmpSeries("\nNext: ADF Test using McKinnon's Tables >")
        # A time series which contains no unit-root:
        x = rnorm(1000)  
        unitrootTest(x)
        # A time series which contains a unit-root:
        y = cumsum(c(0, x))
        unitrootTest(y)    
      
     ## Unit Root Tests build on Bernhard Pfaff's Implementation:
         
     ## ur*Test - 
        # Examples can be found in the demo file "xmpTestUnitRoots".  
     ## End(Not run)

