Time series estimation in R vs. Mathematica -

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i'm fitting ima(1,1) [or arima(0,1,1)] model time series. tried using arima function in r, , estimatedprocess function in mathematica (ver. 10), , got different results. why? making different assumptions, valid in different situations? have advice on 1 should use?

example. first, in r.

> series <- c(-1.42377, 0.578605, -0.534659, -3.07486, -2.4468,  -0.508346, -0.216464, -2.7485, -1.93354, -1.07292,  -1.48064, -1.13934, -1.24597, 1.419, -1.22549,  -2.44651, 1.54611, 1.80892, -0.863338, 1.21636) > arima(series, order=c(0,1,1))  call: arima(x = series, order = c(0, 1, 1))  coefficients:           ma1       -0.7807 s.e.   0.1548  sigma^2 estimated 2.227:  log likelihood = -35.03,  aic = 74.07

now, in mathematica:

series = {-1.42377, 0.578605, -0.534659, -3.07486, -2.4468,  -0.508346, -0.216464, -2.7485, -1.93354, -1.07292,  -1.48064, -1.13934, -1.24597, 1.419, -1.22549,  -2.44651, 1.54611, 1.80892, -0.863338, 1.21636}; estimatedprocess[series, arimaprocess[{}, 1, {ma1}, s2]]

which yields:

arimaprocess[{}, 1, {-0.252596}, 3.30217]

as can see, both estimated ma1 coefficients (-0.7807 in r, -0.2526 in mathematica) , variances (2.227, 3.302) rather different.

thanks lot insight or advice, mark

ok, i've figured out. default, mathematica functions estimatedprocess , findprocessparameters use method of moments. r function arima, on other hand, uses maximum likelihood. if tell mathematica use maximum likelihood, so

series = {-1.42377, 0.578605, -0.534659, -3.07486, -2.4468,  -0.508346, -0.216464, -2.7485, -1.93354, -1.07292,  -1.48064, -1.13934, -1.24597, 1.419, -1.22549,  -2.44651, 1.54611, 1.80892, -0.863338, 1.21636}; estimatedprocess[series, arimaprocess[{}, 1, {ma1}, s2],  processestimator -> "maximumlikelihood"]

you exact same answer r:

arimaprocess[{}, 1, {-0.780677}, 2.22661]

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