how to identify turning points in stock price data

Question

This question is a continuation of this one.

My goal is to find the turning points in stock price data.

So far I:

Tried differentiating the smoothed pri

Answer 1

Here's just an idea, sort of an idea from a different angle, and possibly a very bad idea, but since differentiation isn't working, something like this might be a thought.

First, you need to determine a minimum meaningful X-axis interval. In your figure, if you take this to be too small, you will get false positives from the bumps. This is conceptually similar to the idea of smoothing your data. Call this interval dx.

Next, using a sliding window of size dx, generate a moving average curve corresponding to your curve. There are lots of different ways you could think about doing this (to remove statistical outliers, or to use more or fewer points in the window). Call this curve g(x), and your original curve f(x). Additionally, make a curve h(x) which gives some measure of the variability of data in the sliding window which you use to compute g(x) (standard deviation should work fine if you're using a few points from the interval).

Now, begin computing curves of the form c_m(x) = |f(x) - g(x)| - m * h(x). You can start with m = 1. Any points x for which c_m(x) is positive are candidates for a local min/max. Depending on how many hits you get, you can begin increasing or decreasing m. You can do this in a way similar to binarys search: if you want more points, make m = (min + m) / 2, and if you want fewer points, make m = (max + m) / 2 (adjusting min and max accordingly).

So here's an example of what I'm suggesting. Let's say we have the following series:

f(x) = [  1,   2,   4,   3,   2,   3,   6,   7,   8,   7, 
          5,   4,   3,   2,   2,   3,   2,   3,   5,   8,   9]

We choose dx = 5. We construct g(x) by taking a simple average of the points around x:

g(x) = [2.3, 2.5, 2.4, 2.8, 3.6, 4.2, 5.2, 6.2, 6.6, 6.2, 
        5.4, 4.2, 3.2, 2.8, 2.4, 2.4, 3.0, 4.2, 5.4, 6.3, 7.3]

h(x) = [1.2, 1.1, 1.0, 0.7, 1.4, 2.4, 2.3, 1.7, 1.0, 1.5,
        1.9, 1.7, 1.2, 0.7, 0.5, 0.6, 1.1, 2.1, 2.7, 2.4, 1.7]

With m = 1 we get:

c(x) = [0.1, xxx, 0.6, xxx, 0.2, xxx, xxx, xxx, 0.4, xxx,
        xxx, xxx, xxx, 0.1, xxx, 0.0, xxx, xxx, xxx, xxx, 0.0]

This seems to have worked fairly well, actually. Feel free to share thoughts. Note that this might be more or less the equivalent of differentiation, given the mean value theorem.