Nile
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dataset-80970.csv | 434 bytes |
Documentation |
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Flow of the River NileMeasurements of the annual flow of the river Nile at Aswan (formerly
UsageNile FormatA time series of length 100. SourceDurbin, J. and Koopman, S. J. (2001) Time Series Analysis by State Space Methods. Oxford University Press. http://www.ssfpack.com/DKbook.html ReferencesBalke, 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. Examplesrequire(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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