R: Examples for 'datasets::Nile'

### ** Examples

require(stats); require(graphics)
par(mfrow = c(2, 2))
plot(Nile)
acf(Nile)
pacf(Nile)
ar(Nile) # selects order 2

Call:
ar(x = Nile)

Coefficients:
     1       2  
0.4081  0.1812  

Order selected 2  sigma^2 estimated as  21247

cpgram(ar(Nile)$resid)

par(mfrow = c(1, 1))
arima(Nile, c(2, 0, 0))

Call:
arima(x = Nile, order = c(2, 0, 0))

Coefficients:
         ar1     ar2  intercept
      0.4096  0.1987   919.8397
s.e.  0.0974  0.0990    35.6410

sigma^2 estimated as 20291:  log likelihood = -637.98,  aic = 1283.96

## Now consider missing values, following Durbin & Koopman
NileNA <- Nile
NileNA[c(21:40, 61:80)] <- NA
arima(NileNA, c(2, 0, 0))

Call:
arima(x = NileNA, order = c(2, 0, 0))

Coefficients:
         ar1     ar2  intercept
      0.3622  0.1678   918.3103
s.e.  0.1273  0.1323    39.5037

sigma^2 estimated as 23676:  log likelihood = -387.7,  aic = 783.41

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"))

Call:
StructTS(x = Nile, type = "level")

Variances:
  level  epsilon  
   1469    15099

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

Call:
StructTS(x = Nile, type = "trend")

Variances:
  level    slope  epsilon  
   1427        0    15047

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"))

Call:
StructTS(x = NileNA, type = "level")

Variances:
  level  epsilon  
  685.8  17899.8

lines(fitted(fit3), lty = 2)
lines(tsSmooth(fit3), lty = 3)
plot(residuals(fit3)); abline(h = 0, lty = 3)

Examples for 'datasets::Nile'

Flow of the River Nile