AirPassengers            package:datasets            R Documentation

_M_o_n_t_h_l_y _A_i_r_l_i_n_e _P_a_s_s_e_n_g_e_r _N_u_m_b_e_r_s _1_9_4_9-_1_9_6_0

_D_e_s_c_r_i_p_t_i_o_n:

     The classic Box & Jenkins airline data.  Monthly totals of
     international airline passengers, 1949 to 1960.

_U_s_a_g_e:

     AirPassengers

_F_o_r_m_a_t:

     A monthly time series, in thousands.

_S_o_u_r_c_e:

     Box, G. E. P., Jenkins, G. M. and Reinsel, G. C. (1976) _Time
     Series Analysis, Forecasting and Control._ Third Edition.
     Holden-Day. Series G.

_E_x_a_m_p_l_e_s:

     ## Not run: 
     ## These are quite slow and so not run by example(AirPassengers)

     ## The classic 'airline model', by full ML
     (fit <- arima(log10(AirPassengers), c(0, 1, 1),
                   seasonal = list(order=c(0, 1 ,1), period=12)))
     update(fit, method = "CSS")
     update(fit, x=window(log10(AirPassengers), start = 1954))
     pred <- predict(fit, n.ahead = 24)
     tl <- pred$pred - 1.96 * pred$se
     tu <- pred$pred + 1.96 * pred$se
     ts.plot(AirPassengers, 10^tl, 10^tu, log = "y", lty = c(1,2,2))

     ## full ML fit is the same if the series is reversed, CSS fit is not
     ap0 <- rev(log10(AirPassengers))
     attributes(ap0) <- attributes(AirPassengers)
     arima(ap0, c(0, 1, 1), seasonal = list(order=c(0, 1 ,1), period=12))
     arima(ap0, c(0, 1, 1), seasonal = list(order=c(0, 1 ,1), period=12),
           method = "CSS")

     ## Structural Time Series
     ap <- log10(AirPassengers) - 2
     (fit <- StructTS(ap, type= "BSM"))
     par(mfrow=c(1,2))
     plot(cbind(ap, fitted(fit)), plot.type = "single")
     plot(cbind(ap, tsSmooth(fit)), plot.type = "single")
     ## End(Not run)