Example: Yule-Walker Estimates

  Data: Annual number of lynx trappings in the Mackenzie River
     District for the period 1821 to 1934.

  Let's plot the data, the sample ACF and the sample PACF functions.

################

par(mfrow=c(3,1))

tsplot(lynx)   

acf(lynx)

# Setting type = "par" as an option in acf tells Splus to plot the PACF

acf(lynx, type = "par")

########################

  From the plots, what potential ARMA models may this data follow?


  Next, get Splus to estimate the parameters in 3 possible AR models:

 (a) AR(1). The order.max = 1 tells Splus to use AR(1).  Don't worry 
     about the aic = F part for now (but make sure you use it)

 lynx.ar1 <- ar.yw(lynx, aic = F, order.max =1)   

 lynx.ar1$ar
 
, , 1
          [,1]
[1,] 0.7108186 

 (b) AR(2).  order.max = 2 

lynx.ar2 <- ar.yw(lynx, aic = F, order.max =2)

 lynx.ar2$ar
 
, , 1
           [,1]
[1,]  1.1287030
[2,] -0.5878917