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RDocumentation: AirPassengers
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    Note that this notebook was automatically generated from an RDocumentation page. It depends on the package and the example code whether this code will run without errors. You may need to edit the code to make things work.

    if(!require('datasets')) {
        install.packages('datasets')
        library('datasets')
    }
    ## 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")