R: Flow of the River Nile

Nile {datasets} | R Documentation

## Flow of the River Nile

### Description

Measurements of the annual flow of the river Nile at Ashwan 1871–1970.

### Usage

    Nile

### Format

A time series of length 100.

### Source

Durbin, J. and Koopman, S. J. (2001) Time Series Analysis by State Space Methods. Oxford University Press. http://www.ssfpack.com/DKbook.html

### References

Balke, N. S. (1993) Detecting level shifts in time series. Journal of Business and Economic Statistics 11, 81–92.

Cobb, G. W. (1978) The problem of the Nile: conditional solution to a change-point problem. Biometrika 65, 243–51.

### Examples

    require(stats); require(graphics)
    par(mfrow = c(2, 2))
    plot(Nile)
    acf(Nile)
    pacf(Nile)
    ar(Nile) # selects order 2
    cpgram(ar(Nile)$resid)
    par(mfrow = c(1, 1))
    arima(Nile, c(2, 0, 0))

    ## Now consider missing values, following Durbin & Koopman
    NileNA <- Nile
    NileNA[c(21:40, 61:80)] <- NA
    arima(NileNA, c(2, 0, 0))
    plot(NileNA)
    pred <-
       predict(arima(window(NileNA, 1871, 1890), c(2, 0, 0)), n.ahead = 20)
    lines(pred$pred, lty = 3, col = "red")
    lines(pred$pred + 2*pred$se, lty = 2, col = "blue")
    lines(pred$pred - 2*pred$se, lty = 2, col = "blue")
    pred <-
       predict(arima(window(NileNA, 1871, 1930), c(2, 0, 0)), n.ahead = 20)
    lines(pred$pred, lty = 3, col = "red")
    lines(pred$pred + 2*pred$se, lty = 2, col = "blue")
    lines(pred$pred - 2*pred$se, lty = 2, col = "blue")

    ## Structural time series models
    par(mfrow = c(3, 1))
    plot(Nile)
    ## local level model
    (fit <- StructTS(Nile, type = "level"))
    lines(fitted(fit), lty = 2)              # contemporaneous smoothing
    lines(tsSmooth(fit), lty = 2, col = 4)   # fixed-interval smoothing
    plot(residuals(fit)); abline(h = 0, lty = 3)
    ## local trend model
    (fit2 <- StructTS(Nile, type = "trend")) ## constant trend fitted
    pred <- predict(fit, n.ahead = 30)
    ## with 50% confidence interval
    ts.plot(Nile, pred$pred,
            pred$pred + 0.67*pred$se, pred$pred -0.67*pred$se)

    ## Now consider missing values
    plot(NileNA)
    (fit3 <- StructTS(NileNA, type = "level"))
    lines(fitted(fit3), lty = 2)
    lines(tsSmooth(fit3), lty = 3)
    plot(residuals(fit3)); abline(h = 0, lty = 3)

[Package datasets version 3.1.2 Index]