TimeSeriesTests           package:fSeries           R Documentation

_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 testing various
     aspects of univariate  time series, including independence, and
     neglected  nonlinearities. 

     The family of time series tests includes the following  hypothesis
     tests:

       'bdsTest'  Brock-Dechert-Scheinkman test for iid series,
       'tnnTest'  Teraesvirta NN test for neglected nonlinearity,
       'wnnTest'  White NN test for neglected nonlinearity.

_U_s_a_g_e:

     bdsTest(x, m = 3, eps = NULL, title = NULL, description = NULL) 
     tnnTest(x, lag = 1, title = NULL, description = NULL) 
     wnnTest(x, lag = 1, qstar = 2, q = 10, range = 4, title = NULL, description = NULL) 

_A_r_g_u_m_e_n_t_s:

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

     eps: [bdsTest] - 
           a numeric vector of epsilon values for close points. The BDS
          test is computed for each element of 'eps'. It should  be set
          in terms of the standard deviation of 'x'. If 'eps' is
          'NULL', then the four default values 'seq(0.5*sd(x), 2*sd(x),
          length = 4)' are used. 

     lag: [tnnTest][wnnTest] -
           an integer which specifies the model order in terms of lags. 

       m: [bdsTest] - 
           an integer indicating that the BDS test statistic is
          computed for embedding dimensions '2', ..., 'm'. 

       q: [wnnTest] -
           an integer representing the number of phantom hidden units
          used to compute the test statistic. 

   qstar: [wnnTest] -
           the test is conducted using 'qstar' principal components of
          the phantom hidden units. The first principal component is 
          omitted since in most cases it appears to be collinear with
          the  input vector of lagged variables. This strategy
          preserves power  while still conserving degrees of freedom. 

   range: [wnnTest] -
           the input to hidden unit weights are initialized uniformly
          over '[-range/2, range/2]'. 

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

       x: a numeric vector or an object of class '"timeseries"'. 

_D_e_t_a_i_l_s:

     *Brock-Dechert-Sheinkman Test:* 

      The 'bdsTest' test examines the _spatial dependence_ of the 
     observed series. To do this, the series is embedded in 'm'-space 
     and the dependence of 'x' is examined by counting _near_  points.
     Points for which the distance is less than 'eps' are  called near.
     The BDS test statistic is asymptotically standard Normal. Note,
     that missing values are not allowed. There is a special print
     method for objects of class '"bdsTest"' which by default uses 4
     digits to format real numbers.  
      '[tseries:bds.test]' 

     *Teraesvirta Neural Network Test:* 

        The null is the hypotheses of linearity in 'mean'. This test 
     uses a Taylor series expansion of the activation function to 
     arrive at a suitable test statistic. If 'type' equals '"F"',  then
     the F-statistic instead of the Chi-Squared statistic is used in
     analogy to the classical linear regression.  Missing values are
     not allowed.  
       '[tseries:teraesvirta.test]' 

     *White Neural Network Test:* 

      The null is the hypotheses of linearity in ``mean''. This type of
     test is consistent against arbitrary nonlinearity in mean. If
     'type' equals '"F"', then the F-statistic instead of the
     Chi-Squared statistic is used in analogy to the classical linear
     regression.  
      '[tseries:white.test]'

_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. 

_N_o_t_e:

     There is nothing really new in this package. The benefit you will 
     get from this help page, that we bring together a collection of 
     time series tests from several R-packages which may be of interest
      for economists and financial engineers.

     On the other hand the user can still use the underlying function
     calls from the imported R-packages.

     The output of the various hypothesis tests is an object of class
     'htest'. The associated 'print' method gives an unique  report
     about the test results.

_A_u_t_h_o_r(_s):

     Adrian Trapletti for the tests from R's tseries package,
      Blake LeBaron for the 'bds' C program,
       Diethelm Wuertz for the Rmetrics R-port.

_R_e_f_e_r_e_n_c_e_s:

     Brock, W.A., Dechert W.D., Sheinkman J.A. (1987);  _A Test of
     Independence Based on the Correlation  Dimension_,  SSRI no. 8702,
     Department of Economics, University of  Wisconsin, Madison.

     Conover, W.J. (1980); _Practical Nonparametric Statistics_,  New
     York, Wiley. 

     Cromwell J.B., Labys W.C., Terraza M. (1994); _Univariate Tests
     for Time Series Models_, Sage, Thousand Oaks, CA, pages 32-36.

     Lee T.H., White H., Granger C.W.J. (1993);  _Testing for neglected
     nonlinearity in time series models_, Journal of Econometrics 56,
     269-290.

     Teraesvirta T., Lin C.F., Granger C.W.J. (1993); _Power of the
     Neural Network Linearity Test_, Journal of Time Series Analysis
     14, 209-220.

_E_x_a_m_p_l_e_s:

     ## SOURCE("fSeries1.35B-TimeSeriesTests")

     ## bdsTest -
        xmpSeries("\nNext: Brock-Dechert-Sheinkman Test for iid Series >")
        # iid Time Series:
        par(mfrow = c(3, 1))
        x = rnorm(100)
        plot(x, type = "l", main = "iid Time Series")
        bdsTest(x, m = 3)
        # Non Identically Distributed Time Series:
        x = c(rnorm(50), runif(50))
        plot(x, type = "l", main = "Non-iid Time Series")
        bdsTest(x, m = 3)  
        # Non Independent Innovations from Quadratic Map:
        x = rep(0.2, 100)
        for (i in 2:100) x[i] = 4*(1-x[i-1])*x[i-1]
        plot(x, type = "l", main = "Quadratic Map")
        bdsTest(x, m = 3)
        
     ## tnnTest -
        xmpSeries("\nNext: Teraesvirta NN test for Neglected Nonlinearity >")
        # Time Series Non-linear in "mean" regression 
        par(mfrow = c(2, 1))
        n = 1000
        x = runif(1000, -1, 1)  
        tnnTest(x)
        # Generate time series which is nonlinear in "mean"
        x[1] = 0.0
        for (i in (2:n)) {
          x[i] = 0.4*x[i-1] + tanh(x[i-1]) + rnorm (1, sd = 0.5) }
        plot(x, main = "Teraesvirta Test", type = "l")
        tnnTest(x)
        
     ## wnnTest -
        xmpSeries("\nNext: White NN test for Neglected Nonlinearity >")
        # Time Series Non-Linear in "mean" Regression
        par(mfrow = c(2, 1))
        n = 1000
        x = runif(1000, -1, 1)
        wnnTest(x)
        # Generate time series which is nonlinear in "mean"
        x[1] = 0.0
        for (i in (2:n)) {
          x[i] = 0.4*x[i-1] + tanh(x[i-1]) + rnorm (1, sd = 0.5) }
        plot(x, main = "White Test", type = "l")
        wnnTest(x)                     

