NormalityTests            package:fBasics            R Documentation

_N_o_r_m_a_l_i_t_y _T_e_s_t_s

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

     A collection and description of functions of one sample tests for
     testing normality of financial return series. 

     The functions for testing normality are:

       'ksnormTest'      Kolmogorov-Smirnov normality test,
       'shapiroTest'     Shapiro-Wilk's test for normality,
       'jarqueberaTest'  Jarque-Bera test for normality,
       'dagoTest'        D'Agostino normality test.

     Functions for high precision Jarque Bera LM and ALM tests:

       'jbTest'  Performs finite sample adjusted JB LM and ALM test.

     Additional functions for testing normality from the 'nortest'
     package:

       'adTest'      Anderson-Darling normality test,
       'cvmTest'     Cramer-von Mises normality test,
       'lillieTest'  Lilliefors (Kolmogorov-Smirnov) normality test,
       'pchiTest'    Pearson chi-square normality test,
       'sfTest'      Shapiro-Francia normality test.

     For SPlus/Finmetrics Compatibility:

       'normalTest'  test suite for some normality tests.

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

      
     ksnormTest(x, title = NULL, description = NULL)

     jbTest(x, title = NULL, description = NULL)
     shapiroTest(x, title = NULL, description = NULL)
     normalTest(x, method = c("sw", "jb"), na.rm = FALSE) 

     jarqueberaTest(x, title = NULL, description = NULL)
     dagoTest(x, title = NULL, description = NULL)

     adTest(x, title = NULL, description = NULL)            
     cvmTest(x, title = NULL, description = NULL)      
     lillieTest(x, title = NULL, description = NULL) 
     pchiTest(x, title = NULL, description = NULL)    
     sfTest(x, title = NULL, description = NULL) 

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

description: optional description string, or a vector of character
          strings. 

  method: [normalTest] - 
           indicates four different methods for the normality test, 
          '"ks"' for the Kolmogorov-Smirnov one-sample test,  '"sw"'
          for the Shapiro-Wilk test, '"jb"' for the Jarque-Bera Test,
          and '"da"' for the D'Agostino Test.  The default value is
          '"ks"'. 

   na.rm: [normalTest] - 
           a logical value. Should missing values removed before
          computing the tests? The default value is 'FALSE'.  

   title: an optional title string, if not specified the inputs data 
          name is deparsed. 

       x: a numeric vector of data values or a S4 object of class 
          'timeSeries'. 

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

     The hypothesis tests may be of interest for many financial and
     economic applications, especially for the investigation  of
     univariate time series returns.  

     *Normal Tests:* 

      Several tests for testing if the records from a data set are
     normally distributed are available. The input to all these
     functions may be just a vector 'x' or a univariate time series
     object 'x'  of class 'timeSeries'. 

     First there exists a wrapper function which allows to call one
     from  two normal tests either the Shapiro-Wilks test or the
     Jarque-Bera  test. This wrapper was introduced for compatibility
     with S-Plus'  FinMetrics package. 

     Also available are the Kolmogorov-Smirnov one sample test and the 
     D'Agostino normality test. 

     The remaining five normal tests are the Anderson-Darling test, 
     the Cramer-von Mises test, the Lilliefors (Kolmogorov-Smirnov) 
     test, the Pearson chi-square test, and the Shapiro-Francia test. 
     They are calling functions from R's contributed package 'nortest'.
        The difference to the original test functions implemented in R
     and  from contributed R packages is that the Rmetrics functions
     accept time series objects as input and give a more detailed
     output report.

     The Anderson-Darling test is used to test if a sample of data came
      from a population with a specific distribution, here the normal 
     distribution. The 'adTest' goodness-of-fit test can be considered
     as a modification of the Kolmogorov-Smirnov test which  gives more
     weight to the tails than does the 'ksnormTest'.

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

     In contrast to R's output report from S3 objects of class
     '"htest"' a different output report is produced. The tests here
     return an S4  object of class '"fHTEST"'. The object contains the
     following slots:

   @call: the function call.   

   @data: the data as specified by the input argument(s). 

   @test: a list whose elements contail the results from the
          statistical test. The information provided is similar to a
          list object of class{"htest"}. 

  @title: a character string with the name of the test. This can be 
          overwritten specifying a user defined input argument. 

@description: a character string with an optional user defined
          description.  By default just the current date when the test
          was applied will be returned. 

statistic: the value(s) of the test statistic. 

 p.value: the p-value(s) of the test. 

parameters: a numeric value or vector of parameters. 

estimate: a numeric value or vector of sample estimates. 

conf.int: a numeric two row vector or matrix of 95 

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

data.name: a character string giving the name(s) of the data. 


     The meaning of the elements of the '@test' slot is the following:

     'ksnormTest'  
      returns the values for the 'D' statistic and p-values for the
     three  alternatives 'two-sided, 'less' and 'greater'. 

     'shapiroTest'  
      returns the values for the 'W' statistic and the p-value.  

     'jarqueberaTest'
      'jbTest' 
      returns the values for the 'Chi-squared' statistic with 2 degrees
     of freedom, and the asymptotic p-value. 'jbTest' is the finite
     sample version of the Jarque Bera Lagrange multiplier, LM, and
     adjusted Lagrange multiplier test, ALM.

     'dagoTest'  
      returns the values for the 'Chi-squared', the 'Z3' (Skewness) and
     'Z4' (Kurtosis) statistic together with the corresponding p
     values.

     'adTest'  
      returns the value for the 'A' statistic and the p-value. 

     'cvmTest'  
      returns the value for the 'W' statistic and the p-value.  

     'lillieTest'  
      returns the value for the 'D' statistic and the p-value.  

     'pchiTest'  
      returns the value for the 'P' statistic and the p-values for the
     adjusted and not adjusted test cases.  In addition the number of 
     classes is printed, taking the default value due to Moore (1986)
     computed from the expression 'n.classes = ceiling(2 * (n^(2/5)))',
     where 'n' is the number of observations.

     'sfTest'  
      returns the value for the 'W' statistic and the p-value.

_N_o_t_e:

     Some of the test implementations are selected from R's 'ctest' 
     and 'nortest' packages.

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

     R-core team for the tests from R's ctest package,
      Adrian Trapletti for the runs test from R's tseries package,
      Juergen Gross for the normal tests from R's nortest package,
      James Filliben for the Fortran program producing the runs report,
      Diethelm Wuertz and Helmut Katzgraber for the finite sample JB
     tests, 
      Diethelm Wuertz for the Rmetrics R-port.

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

     Anderson T.W., Darling D.A. (1954);  _A Test of Goodness of Fit_,
     JASA 49:765-69.

     Conover, W. J. (1971); _Practical nonparametric statistics_, New
     York: John Wiley & Sons.

     D'Agostino R.B., Pearson E.S. (1973);  _Tests for Departure from
     Normality_, Biometrika 60, 613-22.

     D'Agostino R.B., Rosman B. (1974);  _The Power of Geary's Test of
     Normality_, Biometrika 61, 181-84.

     Durbin J. (1961);  _Some Methods of Constructing Exact Tests_,
     Biometrika 48, 41-55. 

     Durbin,J. (1973); _Distribution Theory Based on the Sample
     Distribution Function_, SIAM, Philadelphia.

     Geary R.C. (1947);  _Testing for Normality_;  Biometrika 36,
     68-97.

     Lehmann E.L. (1986);  _Testing Statistical Hypotheses_,  John
     Wiley and Sons, New York.

     Linnet K. (1988);  _Testing Normality of Transformed Data_,
     Applied Statistics 32, 180-186. 

     Moore, D.S. (1986); _Tests of the chi-squared type_,  In:
     D'Agostino, R.B. and Stephens, M.A., eds.,  Goodness-of-Fit
     Techniques, Marcel Dekker, New York. 

     Shapiro S.S., Francia R.S. (1972);  _An Approximate Analysis of
     Variance Test for Normality_, JASA 67, 215-216.

     Shapiro S.S., Wilk M.B., Chen V. (1968);  _A Comparative Study of
     Various Tests for Normality_, JASA 63, 1343-72.

     Thode H.C. (2002); _Testing for Normality_,  Marcel Dekker, New
     York. 

     Weiss M.S. (1978);  _Modification of the Kolmogorov-Smirnov 
     Statistic for Use with Correlated Data_,  JASA 73, 872-75.

     Wuertz D., Katzgraber H.G. (2005); _Precise finite-sample
     quantiles of the Jarque-Bera adjusted Lagrange multiplier test_,
     ETHZ Preprint.

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

     ## Series:
        x = rnorm(100)
        
     ## ksnormTests - 
        # Kolmogorov - Smirnov One-Sampel Test
        ksnormTest(x)

     ## shapiroTest - Shapiro-Wilk Test
        shapiroTest(x)

     ## jarqueberaTest - 
        # Jarque - Bera Test
        # jarqueberaTest(x)
        # jbTest(x)

