.......................？

et就是残差，如果采用OLS等方法估计，需要分多步。不过好象一般用的是极大似然估计。我没有编程手动处理ARMA的经验，因为软件都会代劳。建议楼主去下载Eviews自带的User's Guide看一下，一般按装了该软件，会自带这个手册的。

找到关于Eviews这方面的说明了。这些都是用条件最小二乘。
我已经看的萌萌的了。
谁能给详解一下。
Backcasting MA terms
Consider an MA() regression model of the form:
  (22.31)

for . Estimation of this model using conditional least squares requires computation of the innovations  for each period in the estimation sample.
Computing the innovations is a straightforward process. Suppose we have an initial estimate of the coefficients, , and estimates of the pre-estimation sample values of :
  (22.32)

Then, after first computing the unconditional residuals , we may use forward recursion to solve for the remaining values of the innovations:
  (22.33)

for .
All that remains is to specify a method of obtaining estimates of the pre-sample values of :
  (22.34)

By default, EViews performs backcasting to obtain the pre-sample innovations (Box and Jenkins, 1976). As the name suggests, backcasting uses a backward recursion method to obtain estimates of  for this period.
To start the recursion, the  values for the innovations beyond the estimation sample are set to zero:
  (22.35)

EViews then uses the actual results to perform the backward recursion:
  (22.36)

for . The final  values, , which we use as our estimates, may be termed the backcast estimates of the pre-sample innovations. (Note that if your model also includes AR terms, EViews will -difference the  to eliminate the serial correlation prior to performing the backcast.)
If backcasting is turned off, the values of the pre-sample  are simply set to zero:
  (22.37)

The sum of squared residuals (SSR) is formed as a function of the  and , using the fitted values of the lagged innovations:
  (22.38)

This expression is minimized with respect to  and .
The backcast step, forward recursion, and minimization procedures are repeated until the estimates of  and  converge.

ARMA一般用极大似然估计，给定et的初始值之后，et是计算出来的，具体的估计方法可以参考时间序列分析或金融计量的教材。

教材翻了很多了，基本都是给个公式还说不明白，然后就是各种软件操作。