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We know that dealing with model involving MA factors is not easy to estimate, since there are past values of errors to be computed recursively. And this recursive estimation requires preliminary (initial) estimates of the parameters. For example, an ARMA(1,2) $$z_t=\phi z_{t-1}-\theta_1 \varepsilon_{t-1}-\theta_2 \varepsilon_{t-2}+\varepsilon_t$$ To estimate the parameters, we need to compute first the values of $\varepsilon_{t-1}$ and $\varepsilon_{t-2}$, since these are not available yet. And they are computed using $$\varepsilon_t=z_t-\phi z_{t-1}+\theta_1 \varepsilon_{t-1}+\theta_2 \varepsilon_{t-2}$$ Procedures for obtaining preliminary estimates of the parameters is available in Box and Jenkins, Time Series: Forecasting and Control. And this estimation is already available in much statistical software. My question is, "Is there a function for obtaining a preliminary estimate of the parameters in R?"

I need this to obtain a preliminary estimate for my Space-Time ARIMA. Another question is, "How does arima function of R compute preliminary estimates of the parameters when there are MA factors involved?"

Thanks in advance!

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In base R's arima() take a look at the method= argument. From the help docs:

Fitting method: maximum likelihood or minimize conditional sum-of-squares. The default (unless there are missing values) is to use conditional-sum-of-squares to find starting values, then maximum likelihood.

From a little further down in the details:

Conditional sum-of-squares is provided mainly for expositional purposes. This computes the sum of squares of the fitted innovations from observation n.cond on, (where n.cond is at least the maximum lag of an AR term), treating all earlier innovations to be zero. Argument n.cond can be used to allow comparability between different fits. The ‘part log-likelihood’ is the first term, half the log of the estimated mean square. Missing values are allowed, but will cause many of the innovations to be missing.

If you just wanted those initial values, you could state method='CSS'. Of course, you could also just use the full 'CSS-ML' results as your starting values...

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  • $\begingroup$ Oh thank you for that! I got it now, I just hope I could apply this to Space-Time ARIMA. $\endgroup$ – Al-Ahmadgaid Asaad Jan 10 '13 at 14:27

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