Sat Nov 16 21:40:10 EST 2019

Financial transactions and density

Some posts in the past around 20120910.

The main idea:
- predict future based on past
- set targets, given a margin

I'm still not quite sure how to get the trend out of the noise, but a
key element seems to be to divide into categories (which is what gives
an idea where the money is going in rough terms), and apply smoothing
by filtering each category using a method that distributes reserves
while maintaining thresholds.

E.g. it is possible to take one paycheck and split it into one that is
payed at the original time, and one that is payed 1/2 of the period
later.  Or in the limit, spread the amount over the entire "future"
payment.  Same with expenses, but in the other direction: it is always
allowed to pay a debt early.

This is a reflection of the main property of money:

    You can always not spend money that you have avaiable, but you
    can't spend money that you do not have available.

That is the primary "shape" of the space we're dealing with.

The mangement of money is about managing those hard deadlines.  Now in
practice, deadlines are not completely hard, but debt does tend to
spiral.  So it is best to leave a safety margin.

Ideally, any partition of expenses and income can be smoothed by
performing time-distribution, in such a way that the resulting "curve"
is as smooth as possible, and can be used as a trend to make

So what this does is to give you smoothnes, but it consumes "buffer
space", i.e. there needs to be an amount of cash that can handle these
fluctuations without running out.

Essentially, we want to extract the following information:

- Trend: plot smoothed income vs. expenses.  This helps with planning
  future income, trading study vs. work.

- Buffer: what is the size of the variability, determining the need
  for reserves.  Note that smoothing might influence this.

- Feedback: if trends for categories can be clearly identified,
  optimization effort to reduce expenses can be directed.

Compared to previous insight related to "density" ideas: it is now
clear that apart from the need for smoothing to be directional, it
seems fairly straightforward to implement.  E.g. a piecewize linear
curve per year, quarter, or month is probably already enough.
Multiple scales could be used.  Other base functions could be used.

What is clear is that the main problem is introducing "goldy locks"
categories.  Too many or too few and no information can be extracted.