I am new to time series modelling and I am trying to build a simple time series model using ARIMA methodology and forecast. I could write an R program to do the same, but I am more interested in writing my own arima(1,1,0) and predict() functions that R provides in Java / C++ / Python. While I can go about reading the theory behind ARIMA modeling and then implementing it, I still face a learning curve there, due to time constraints, I would like to take an approach where I can see a time series data sample, and a write up which walks me through the steps to compute arima() and predict() so that I can implement an algorithm. If someone can point me to a sourcecode / psedocode / step-by-step example via data, it would really be helpful.
Solved – ARIMA model fitting and forecasting implementation
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In response to your second question. I had found this paper a few months ago which is trying to exactly what you are proposing.
First of all … you should model what is observed NOT what is accumulated . Secondly an ARIMA model can evolve into a time trend model with Intervention Detection with the potential of detecting breakpoints in trend. Stay way clear of simple ols models with trend or trend squared unless theory ( domain knowledge )tells you so .
Closely review a piece I wrote contrasting and comparing ARIMA with Regression a few years back. https://autobox.com/pdfs/regvsbox-old.pdf
EDITED AFTER RECEIPT OF INTERMITTENT DEMAND DATA:
The data you have ( although daily ) does not have values for every day thus one can't build a daily model like Simple method of forecasting number of guests given current and historical data
Secondly you don't have data for each and every week of the year thus you can't build a weekly model as is done in these examples https://stats.stackexchange.com/search?q=user%3A3382+weekly
So all you have left is a monthly model. I propose that you reassemble your data into monthly buckets (totals by month) and repost your data to the web and I will try and help further.
EDITED AFTER RECEIPT OF 46 MONTHLY VALUES STARTING ATT 2012/3:
You say "how poorly ARIMA model is predicting my monthly data: . I say your chice of arima software and approach is performing poorly due to at least 3 Gaussian violations viz 1) There are identifiable pulses in the data ; 2) There is an identifiable level/step shift down in the data ; 3) there is an identifiable error variance reduction/change in the data. I used AUTOBOX which I have helped to develop which has features to deal with data like this.
Your data is here 
A useful arima model is here (2,0,0)(0,0,0)12 
and here 
A significant reduction in the model error variance was detected at period 27 
The Actual/Fit and Forecast graph is here 
Best Answer
Here's an open source ARIMA implementation. It's under GNU license. Not sure if they would mind you learning from it!
It's an ARIMA implementation in C++, windows executable and source available. I think going through it you should be able to learn ARIMA the quick way.