That depends on the nature of your problem, degree of dynamism in the parameters, and number of parameters.

Your question needs more details.

Hi! It's a sensible question, but Ali is right, it needs more details. I would start with, "What is an reliable way to forecast whether an expenditure will happen in a given time period?"

That suggests other questions:

* What kind of expenditure?

* What kind of time period?

* How far in advance do you need to know?

* What accuracy is acceptable?

* Are misses worse than false alarms?

* What other information do you have to predict from?

In some cases, you could ask the person/organization involved. If you don't know who to ask, you could run a prediction market. If you have data, and you think the future will resemble the past, you can fit a logistic regression or any other classifier that allows binary outcomes. (Almost any machine learner will.)

Hope that helps!

Try to consider machine learning techniques, which are simply said, an extension of statistical methods. ML techniques are capable to dig hidden information that is invisible to other commonly used methods: curves & regression, equations, differential equations, statistics, etc.

I recommend to google terms: " machine learning". You will get a starting point from which you can proceed. When lucky, you can find a similar solved problem to your problem this way.

'General Morhological Analysis' in a chavotic situation or when the data is in a highest level of disorder, the certainety of events are predictable. We still have to wait and see the depth of deep learning for the similar certainet predictions.y

One more idea of extending my previous answer. I would go for complexity measures. They are based on the work of Stefan Boltzmann and equation

H = SUM_i (p_i * ln_2(p_i)), over all I

Where I stay for slots which collects certain intervals of the measured value. You can, in this way, map even complex systems into a simple measured based on the Boltzmann equation.

This enables you to observe even subtle changes within the system, and in the tip of it, long time before their ma roscopic evidence.

Try to study how biosignals are processed using complexity measures: approximative, permutation, alphabetic, FFT, etc. Machine learning techniques are very useful in assessing complex systems measures as well.

Try to find good overviews of those issues. Very good level of complexity measures is developed in the field of processing EEG signals my field) and even EEGs.

Feel free to ask more. The area is very wide and deep and not easy to orientate.