

ENSO(NISTnls)                                R Documentation

_A_t_m_o_s_p_h_e_r_i_c _p_r_e_s_s_u_r_e _d_i_f_f_e_r_e_n_c_e_s

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

     The `ENSO' data frame has 168 rows and 2 columns giving
     atmospheric pressure differences over time.

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

       y: A numeric vector of monthly averaged atmospheric
          pressure differences between Easter Island and
          Darwin, Australia.

       x: A numeric vector of time values.

_F_o_r_m_a_t_:

     This data frame contains the following columns:

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

     The data are monthly averaged atmospheric pressure dif-
     ferences between Easter Island and Darwin, Australia.
     This difference drives the trade winds in the southern
     hemisphere.  Fourier analysis of the data reveals 3
     significant cycles.  The annual cycle is the strongest,
     but cycles with periods of approximately 44 and 26
     months are also present.  These cycles correspond to
     the El Nino and the Southern Oscillation.  Arguments to
     the SIN and COS functions are in radians.

_S_o_u_r_c_e_:

     Kahaner, D., C. Moler, and S. Nash, (1989).  Numerical
     Methods and Software.  Englewood Cliffs, NJ: Prentice
     Hall, pp. 441-445.

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

     library(NISTnls)
     data(ENSO)
     plot(y ~ x, data = ENSO)
     plot(y ~ x, data = ENSO, type = "l")  # to see the pattern more clearly
     fm1 <- nls(y ~ b1 + b2*cos( 2*pi*x/12 ) + b3*sin( 2*pi*x/12 )
                           + b5*cos( 2*pi*x/b4 ) + b6*sin( 2*pi*x/b4 )
                           + b8*cos( 2*pi*x/b7 ) + b9*sin( 2*pi*x/b7 ),
                data = ENSO, trace = TRUE,
                start = c(b1 = 11.0, b2 = 3.0, b3 = 0.5, b4 = 40.0, b5 = -0.7,
                          b6 = -1.3, b7 = 25.0, b8 = -0.3, b9 = 1.4))
     fm2 <- nls(y ~ b1 + b2*cos( 2*pi*x/12 ) + b3*sin( 2*pi*x/12 )
                           + b5*cos( 2*pi*x/b4 ) + b6*sin( 2*pi*x/b4 )
                           + b8*cos( 2*pi*x/b7 ) + b9*sin( 2*pi*x/b7 ),
                data = ENSO, trace = TRUE,
                start = c(b1 = 10.0, b2 =  3.0, b3 =  0.5, b4 = 44.0, b5 = -1.5,
                          b6 =  0.5, b7 = 26.0, b8 = -0.1, b9 =  1.5))
     fm3 <- nls(y ~ cbind(1, cos( 2*pi*x/12 ), sin( 2*pi*x/12 ), cos( 2*pi*x/b4 ),
                         sin( 2*pi*x/b4 ), cos( 2*pi*x/b7 ), sin( 2*pi*x/b7 )),
                data = ENSO, trace = TRUE,
                start = c(b4 = 40.0, b7 = 25.0), algorithm = "plinear")
     fm4 <- nls(y ~ cbind(1, cos( 2*pi*x/12 ), sin( 2*pi*x/12 ), cos( 2*pi*x/b4 ),
                         sin( 2*pi*x/b4 ), cos( 2*pi*x/b7 ), sin( 2*pi*x/b7 )),
                data = ENSO, trace = TRUE,
                start = c(b4 = 44.0, b7 = 26.0), algorithm = "plinear")

