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_e_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, which
     includes CUSUM and MOSUM tests based on recursive or OLS
     residuals, parameter estimates or ML scores (OLS first order
     conditions).

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

     efp(formula, data, type = <<see below>>, h = 0.15,
         dynamic = FALSE, rescale = TRUE)

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

 formula: a symbolic description 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 '"RE"' or '"ME"')

_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 'type' is either '"RE"' 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. The recursive
     estimates test is also called fluctuation test, therefore setting
     'type' to '"fluctuation"' was used to specify it in earlier
     versions of strucchange. It still can be used now, but will be
     forced to '"RE"'.

     If 'type' is '"Score-CUSUM"' or '"Score-MOSUM"' a
     _k+1_-dimensional process will be returned, one for each score of
     the regression coefficients and one for the scores of the
     variance. The process gives the decorrelated cumulative sums of
     the ML scores (in a gaussian model) or first order conditions
     respectively (in an OLS framework).

     If there is a single structural change point t^*, the recursive
     CUSUM path starts to depart from its mean 0 at t^*. The Brownian
     bridge type paths will have their respective peaks around t^*. The
     Brownian bridge increments type paths should have a strong change
     at t^*.

     The function 'plot' has a method to plot the empirical fluctuation
     process; with 'sctest' the corresponding test on structural change
     can be performed.

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

     'efp' returns a list of class '"efp"' with components inlcuding 

 process: the fitted empirical fluctuation process of class '"ts"' or
          '"mts"' respectively,

    type: a string with the 'type' of the process fitted,

    nreg: the number of regressors,

    nobs: the number of observations,

     par: the bandwidth 'h' used.

_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.

     Hansen B. (1992), Testing for Parameter Instability in Linear
     Models, _Journal of Policy Modeling_, *14*, 517-533.

     Hjort N.L., Koning A. (2002), Tests for Constancy of Model
     Parameters Over Time, _Nonparametric Statistics_, *14*, 113-132.

     Krmer 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., Krmer W. (1992), The CUSUM test with OLS residuals,
     _Econometrica_, *60*, 271-285.

     Zeileis A., Leisch F., Hornik K., Kleiber C. (2002),
     'strucchange': An R Package for Testing for Structural Change in
     Linear Regression Models, _Journal of Statistical Software_,
     *7*(2), 1-38.

     Zeileis A., Hornik K. (2003), Generalized M-Fluctuation Tests for
     Parameter Instability, Report 80, SFB "Adaptive Information
     Systems and Modelling in Economics and Management Science", Vienna
     University of Economics, <URL:
     http://www.wu-wien.ac.at/am/reports.htm#80>.

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

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

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

     if(! "package:stats" %in% search()) library(ts)

     ## Nile data with one breakpoint: the annual flows drop in 1898
     ## because the first Ashwan dam was built
     data(Nile)
     plot(Nile)

     ## test the null hypothesis that the annual flow remains constant
     ## over the years
     ## compute OLS-based CUSUM process and plot
     ## with standard and alternative boundaries
     ocus.nile <- efp(Nile ~ 1, type = "OLS-CUSUM")
     plot(ocus.nile)
     plot(ocus.nile, alpha = 0.01, alt.boundary = TRUE)
     ## calculate corresponding test statistic
     sctest(ocus.nile)

     ## UK Seatbelt data: a SARIMA(1,0,0)(1,0,0)_12 model
     ## (fitted by OLS) is used and reveals (at least) two
     ## breakpoints - one in 1973 associated with the oil crisis and
     ## one in 1983 due to the introduction of compulsory
     ## wearing of seatbelts in the UK.
     data(UKDriverDeaths)
     seatbelt <- log10(UKDriverDeaths)
     seatbelt <- cbind(seatbelt, lag(seatbelt, k = -1), lag(seatbelt, k = -12))
     colnames(seatbelt) <- c("y", "ylag1", "ylag12")
     seatbelt <- window(seatbelt, start = c(1970, 1), end = c(1984,12))
     plot(seatbelt[,"y"], ylab = expression(log[10](casualties)))

     ## use RE process
     re.seat <- efp(y ~ ylag1 + ylag12, data = seatbelt, type = "RE")
     plot(re.seat)
     plot(re.seat, functional = NULL)
     sctest(re.seat)

