In R, coefficients of MA function are wrong? I'm currently sifting through my copy of Analysis of Financial Time Series 2nd Edition by Ruey Tsay, and one of the sections involves fitting a MA model to certain data (data set is here). Here's the fit with exact maximum likelihood according to the text, with certain insignificant parameters removed:
rt = 0.013 + a(t) + 0.181a(t−1) − 0.121a(t−3) + 0.122a(t−9)
σ(a) = 0.0724
However, when I try to fit it with R...
> mew = read.table("m-ew.dat")
> arima(mew,order = c(0,0,9),fixed = c(NA,0,NA,rep(0,5),NA,NA),method = "ML")
Call:
arima(x = mew, order = c(0, 0, 9), fixed = c(NA, 0, NA, rep(0, 5), NA, NA), 
method = "ML")

Coefficients:
        ma1  ma2      ma3  ma4  ma5  ma6  ma7  ma8     ma9  intercept
      0.180    0  -0.1318    0    0    0    0    0  0.1373     0.0132
s.e.  0.031    0   0.0362    0    0    0    0    0  0.0327     0.0029

sigma^2 estimated as 0.005282:  log likelihood = 1039.1,  aic = -2068.21

As you can see, the ma1 coefficients are the same, but ma3 and ma9 are different, even with method = "ML", i.e. maximum likelihood. Why is this?
Also, from a practical standpoint, while ma2 and ma4-ma8 may be 0 (their 95% confidence intervals overlap with 0), removing them from the model raises the AIC, lowers the p-value with regards to the Ljung-Box test on the residuals, and also lowers the log-likelihood value. Is it even worth removing these parameters if such things happen?
 A: By comparing the timeplot in the book and a simple R plot, it looks as
though the file does not contain all the observations used in the
version of the book that you mention. If 864 monthly obs are starting
at jan-1926, the last one should be dec-1997 and not dec-2003 as
written and shown in the book. So 6 years seem to be missing at the
end of the file.
A: In general it's not the best model selection strategy to remove parameters just because their confidence intervals overlap zero.  This applies just as much to ARIMA modelling as to multiple regression (see e.g. here). Each one you remove changes the estimates of the ones remaining. Stepwise removal may be a better solution, but is still rather arbitrary. At the end of it there are combinations you won't have explored, for no good reason, & you can't say what the overall error rate or power of the selection process might be. Better, as you suggested, to use AIC, & keep hypothesis tests for use with some meaningful predetermined null hypotheses.  Better too, to confine your attention to a plausible set of models given prior knowledge. In this case what could be so special about lags 1, 3, & 9?  And the real test will come with out-of-sample forecasts.
