Chapter 5: Building ARMA models

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)