efp               package:strucchange               R Documentation

_E_m_p_i_r_i_c_a_l _F_l_u_c_t_u_a_t_i_o_n _P_r_o_c_e_s_s

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

     Computes an empirical fluctuation process according to a specified
     method from the generalized fluctuation test framework

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

     efp(formula, data, type = <<see below>>, h = 0.15, dynamic = FALSE,
       rescale = TRUE, tol = 1e-7)

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

 formula: a symbolic describtion for the model to be tested.

    data: an optional data frame containing the variables in the model.
          By default the variables are taken from the environment which
          `efp' is called from.

    type: specifies which type of fluctuation process will be computed.
          For details see below.

       h: a numeric from interval (0,1) sepcifying the bandwidth.
          determins the size of the data window relative to sample size
          (for MOSUM and ME processes only).

 dynamic: logical. If `TRUE' the lagged observations are included as a
          regressor.

 rescale: logical. If `TRUE' the estimates will be standardized by the
          regressor matrix of the corresponding subsample according to
          Kuan & Chen (1994); if `FALSE' the whole regressor matrix
          will be used. (only if `type' is either `"fluctuation"' or
          `"ME"')

     tol: tolerance when `solve' is used

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

     If `type' is one of `"Rec-CUSUM"', `"OLS-CUSUM"', `"Rec-MOSUM"' or
     `"OLS-MOSUM"' the function `efp' will return a one-dimensional
     empiricial process of sums of residuals. Either it will be based
     on recursive residuals or on OLS residuals and the process will
     contain CUmulative SUMs or MOving SUMs of residuals in a certain
     data window. For the MOSUM and ME processes all estimations are
     done for the observations in a moving data window, whose size is
     determined by `h' and which is shifted over the whole sample.

     If there is a single structural change point t^*, the standard
     CUSUM path starts to depart from its mean 0 at t^*. The OLS-based
     CUSUM path will have its peak around t^*. The MOSUM path should
     have a strong change at t^*.

     If `type' is either `"fluctuation"' or `"ME"' a k-dimensional
     process will be returned, if k is the number of regressors in the
     model, as it is based on recursive OLS estimates of the regression
     coefficients or moving OLS estimates respectively.

     Both paths should have a peak around t^* if there is a single
     structural shift.

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

     Achim Zeileis zeileis@ci.tuwien.ac.at

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

     Brown R.L., Durbin J., Evans J.M. (1975), Techniques for testing
     constancy of regression relationships over time, Journal of the
     Royal Statistal Society, B, 37, 149-163.

     Chu C.-S., Hornik K., Kuan C.-M. (1995), MOSUM tests for parameter
     constancy, Biometrika, 82, 603-617.

     Chu C.-S., Hornik K., Kuan C.-M. (1995), The moving-estimates test
     for parameter stability, Econometric Theory, 11, 669-720.

     Kraemer W., Ploberger W., Alt R. (1988), Testing for structural
     change in dynamic models, Econometrica, 56, 1355-1369.

     Kuan C.-M., Hornik K. (1995), The generalized fluctuation test: A
     unifying view, Econometric Reviews, 14, 135 - 161.

     Kuan C.-M., Chen (1994), Implementing the fluctuation and moving
     estimates tests in dynamic econometric models, Economics Letters,
     44, 235-239.

     Ploberger W., Kraemer W. (1992), The CUSUM test with OLS
     residuals, Econometrica, 60, 271-285.

_S_e_e _A_l_s_o:

     `plot.efp', `print.efp', `sctest.efp', `boundary.efp'

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

     ## Load dataset "nhtemp" with average yearly temperatures in New Haven
     data(nhtemp)
     ## plot the data
     plot(nhtemp)

     ## test the model null hypothesis that the average temperature remains constant
     ## over the years
     ## compute OLS-CUSUM fluctuation process
     temp.cus <- efp(nhtemp ~ 1, type = "OLS-CUSUM")
     ## plot the process with alternative boundaries
     plot(temp.cus, alpha = 0.01, alt.boundary = TRUE)
     ## and calculate the test statistic
     sctest(temp.cus)

     ## Load dataset "USIncExp" with income and expenditure in the US
     ## and choose a suitable subset
     data(USIncExp)
     USIncExp2 <- window(USIncExp, start=c(1970,1), end=c(1989,12))

     ## test the null hypothesis that the way the income is spent in expenditure
     ## does not change over time
     ## compute moving estimates fluctuation process
     me <- efp(expenditure~income, type="ME", data=USIncExp2, h=0.2)
     ## plot the two dimensional fluctuation process with boundaries
     plot(me, functional=NULL)
     ## and perform the corresponding test
     sctest(me)

