Nile | R Documentation |

Measurements of the annual flow of the river Nile at Aswan (formerly
`Assuan`

), 1871–1970, in *10^8 m^3*,
“with apparent changepoint near 1898” (Cobb(1978), Table 1, p.249).

Nile

A time series of length 100.

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

Balke, N. S. (1993).
Detecting level shifts in time series.
*Journal of Business and Economic Statistics*, **11**, 81–92.
\Sexpr[results=rd,stage=build]{tools:::Rd_expr_doi("10.2307/1391308")}.

Cobb, G. W. (1978).
The problem of the Nile: conditional solution to a change-point
problem.
*Biometrika* **65**, 243–51.
\Sexpr[results=rd,stage=build]{tools:::Rd_expr_doi("10.2307/2335202")}.

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)

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