Math Help - Solving Arima model using matrix equations.

Hey.
A few years ago I knew how to solve the Arima model using matrix equations. Seeing as it was a long time ago I have forgoten, would anyone be able to help me.
Im pretty sure I built some sort of matrix equation and then tried to find the minimum values using a calculators min function.

Ill try to explain the steps involved in finding the arima model values, and hope someone can help convert this into a matrix equation...

Ok, so this is what I do in excel.

1. A long list of numbers in column A, the statistical data.

2. I then make three fields of values which i call.
ksi fi1 fi2
These are the values im trying to predict.

3. I then create a new column of predicted values, Column B.
Each of these values are calculated by,
ksi + fi1*(val-1) + fi2 * (val-2)
if I am predicting the third value, then val1 is the datas second number and val2 is the datas first number.

4. Column C is equal to value of column A (row by row) minus column B

5. Column D is equal to column C * Column C (value by value)

6. I then try to minimize the sum of column D by using excels solver.

What im really looking for is the values for ksi, fi1 and fi2 that minimize the square sum of the different between the predicted values and the real values.

Including a picture from excel where Ive solved for the values.


As you've probably noticed math isen't my strongest area, but I would really appreciate the help. Reason im trying to do this is i want to make a program that can solve this for me in the future. Havent found any free libraries that can do this for me yet. Once it's done I'll gladly share it if anyone else finds it interesting.

think the solution method might have been called least squares.. dont know, its gnawing away at me =P

If anyone could show an example with numbers I would be very gratefull