How to fit a time series model for a large dataset? I need to compare the accuracy of time series modeling and neural network techniques. As we all know, large data set is needed for neural networks. Since I'm comparing both techniques, I have to consider equal size for both. I have 5 years of daily exchange rates for the analysis. 
Time series plot of 5 years daily exchange rates which shows positive and negative trends is reproduced below.

So, my question is: Can I fit a single time series model for the entire data set? If not, what is the procedure to fit time series model to such data? I have heard that a data set can be divided into subsamples. If so what is the method to perform sampling of the original data set?
 A: This looks like a nonstationary time series.  In general if there are no known interventions I would try to model this as a single series.  However if interventions are expected to exist that cause the behavior of the time series to change there are models of the Box-Jenkins ARIMA variety that have change points in the time series at specific intervention time points.  The software product autobox produced by Dave Reilly's company will take a time series like this and automatically select the number and the locations for the interventions and fit an ARIMA models with changes at the intervention points. Typically interventions are assumed to change the level of the series without changing other characteristics but they can be more complicated as may be the case for your particular series.
A: It is difficult to fit single model for very long time series. Even if you are able to fit a model, it will perform poorly while doing multi step forecasting.
You can make use of sliding window method to fit the model to the most recent k observations and do single step forecasting. Then repeat the procedure.
Unlike Neural networks, regular time series forecasting method (like ARIMA) do not work well for studying long term temporal variations.
See this for some more details.
