how to find interesting points in time series

i have an array of date=>values, like this

"2010-10-12 14:58:36" =>13.4
"2010-10-17 14:58:36" =>12
"2010-10-22 14:58:36" =>17.6
"2010-10-27 14:58:36" =>22
"2010-11-01 14:58:36" =>10
[...]

I use this date-value combination to paint an graph in javascript. Now i like to mark those dates, who are "very special".

My problem (and Question) is, which aspect should consider to find those specific dates?

As an human, i prefer the date "2010-10-17 14:58:36", because "something" should be happens on this date, because the value on the next dates rises for 5.6 points, which is the biggest step up followed by one mor big step up. On the other hand, also the date "2010-10-27 14:58:36" is an "highlight", because this is

1. the top of all values and
2. after this date, there comes the biggest step down.

So as an human, i would be choose both dates.

My problem is: how could an algorithm look like?

1. I tried averages values for n dates before and after the current values, which results in an accumulation of those specifics dates at the beginning and at the end of the graph
2. So i tried to find the biggest percentage step up (depending on the date before), but I'm not sure, if i really find the specific dat开发者_开发问答es, I'm looking for?!

How would you tackle the problem?

Thank you.

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Looks like financial stocking issue :-) You are looking for Time series analysis - this is a statistical issue. I'd recommend to use R programming language to play with it (you can do complex statistical things very fast). There are tens of special packages, for sure financial one's too. Once you know what you want, you may implement the solution in any other language.

Just try to google time series analysis r.

EDIT: note that R is very powerful - I'd bet there is a tool how to use R packages from other languages.

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If you have information over a timeline you could use Inerpolation.

A Polynomial interpolation will give you an approximated polynomial that goes through the points.
What's nice about this is you can then use Mathematical analysis which is easy on polynomials to find interesting points (large gradients, min-max points etc...)

Also you get an approximation of how the function behaves, so you could "future" points and see what may happen in the near future.

Of course looking into the future isn't so accurate, but forms of interpolation are used in analytic to see trends and behaviors.

And of course, it's easy to plot a polynomial, which is always nice.

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This is really a question of Statistics http://en.wikipedia.org/wiki/Statistics and the context of your data and what you're looking to highlight, for example, the fact that between 12/10 and 17/10 the data moved negative 1.4 units may be more useful in some scenarios than a larger positive step change.

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You need sample data, on which build up a function which can calculate an expected value for any given date; for instance averaging the values of the day before, the same week day of the previous week, of the previous month and so on. After that decide a threshold: interesting date are those for which real value is outside expected value +- threshold