Hello list,

we are beginners in R and we are trying to fit the following time series:


  *> 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 for choosing the present time series is that the we
have previously calculated analytically 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.

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

*Call:**ar(x = x, order.max = 2, method = "yw", demean = FALSE,
intercept = TRUE)*
*Coefficients:*
     *1  **0.9305  *

*Order selected 1 sigma^2 estimated as 5.368*


 Please can anybody 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.
Fabio

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