ARIMA algorithm in C#

Question

I am trying to implement my own ARIMA model in C#. I don't need to use any "best model" selection code at this time, I just need to specify which model I want like ARIMA(p,d,q).

So far I have made an autoregressive method that uses gradient descent to learn the auto-regressive coefficients, however I have read this method is not necessarily suitable for determining the MA model coefficients. In my own attempts before I figured that out through reading I just ended up with models that would diverge very quickly. I may be doing something else wrong with my initialization and learning rate, however this leads me to my question at hand anyway.

Does anyone know of any good resources for an actual pseudo-code ARIMA algorithm? Or perhaps a good book on algorithms to read on the subject?

Are there any good learning rate selection methods you know of that would work with a MA model?

I understand the idea of ARIMA, what I am not sure on is what method to use to determine the MA model coefficients essentially. I've read many publications on this but most people seem to just use R or some other 3rd party tool with this all pre-made, and I want to program it myself.

Answer 1

I understand you want to start simple, but there are many problems in addition to just specifying a model and running. You need to search for outliers. See Tsay's work here Outliers, Level Shifts, and Variance Changes in Time Series