library(ggfortify)
Le chargement a nécessité le package : ggplot2
library(forecast)
Attachement du package : ‘forecast’
The following object is masked from ‘package:ggfortify’:
gglagplot
The lh
series
Recall that in Lab 1, we chose an AR(1). Here is a justification.

ggAcf(lh)

ggPacf(lh)

Let’s fit AR(1), AR(2), MA(1), MA(2) models
ar1 = Arima(lh,order = c(1,0,0))
ar2 = Arima(lh,order = c(2,0,0))
ma1 = Arima(lh,order = c(0,0,1))
ma2 = Arima(lh,order = c(0,0,2))
AICc, BIC
ar1 ar2 ma1 ma2
aicc 65.30378 65.43399 68.64934 63.99079
bic 70.37193 71.98856 73.71749 70.54537
Automatic procedure
auto.arima(lh)
Series: lh
ARIMA(1,0,0) with non-zero mean
Coefficients:
ar1 mean
0.5739 2.4133
s.e. 0.1161 0.1466
sigma^2 estimated as 0.2061: log likelihood=-29.38
AIC=64.76 AICc=65.3 BIC=70.37
Checks for residuals
Caution: available in version 8.0 of the forecast
package.
check = checkresiduals(ar1)
Ljung-Box test
data: residuals
Q* = 9.3564, df = 8, p-value = 0.3131
Model df: 2. Total lags used: 10

If you don’t have fortify
8.0, use the following code. autoplot(residuals.ar(ar1))
, ggAcf(residuals.ar(ar1))
and `Box.test(residuals.ar(ar1),lag = 10,type=“Ljung-Box”,fitdf=2)
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