[R] Simple AR(2)

[fabio]

Hi there, we are beginners in R and we are trying to fit the following time
series using ar(2):

> x <- c(1.89, 2.46, 3.23, 3.95, 4.56, 5.07, 5.62, 6.16, 6.26, 6.56, 6.98,
> 7.36, 7.53, 7.84, 8.09)

The reason of choosing the present time series is that the we have
previously calculated analitically the autoregressive coefficients using
the direct inversion method as 1.1, 0.765, 0.1173. Since those coefficients
fits well our time series, we wanted to learn how to do it in R and check
that it would give us the same autoregressive coefficients as the direct
inversion method.

So as first step in R we have initially applied the OLS method and obtained
the following autoregression coefficients:


> ar(x, method="ols", order.max=2, demean=FALSE, intercept=TRUE)

Call:
ar(x = x, order.max = 2, method = "ols", demean = FALSE, intercept = TRUE)

Coefficients:
     1       2  
0.8049  0.0834  

Intercept: 1.103 (0.2321) 

Order selected 2  sigma^2 estimated as  0.009756 


Those are very close to the ones obtained with the direct inversion method
so the fitting is good.

Then we tried to apply the other techniques available in R, namely
Yule/Walker, Burg, MLE, obtaining different coefficients, which do not give
a good fit of the series at all.

Since there isnt anything useful in the R help or its interpretation is very
complicated to beginners,
can anybody please help us telling how to get a reasonable good fit with YW,
Burg
and MLE, reporting also the code that needs to be used and commenting the
coefficients obtained by comparing those with the ones obtained with OLS.


Thanks in advance.



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