Peak Detection in Time Series

Question

I\'m currently working on a little project in which I want to compare two time-series. The similarity measure is really vague, they are considered to be similar if the two time

Answer 1

You seem to simply look for slope inversion (from positive to negative and vice versa). A rough java algo could be (not tested):

List points = ... //all the points in your curve
List extremes = new ArrayList ();
double previous = null;
double previousSlope = 0;

for (Point p : points) {
    if (previous == null) { previous = p; continue; }
    double slope = p.getValue() - previous.getValue();
    if (slope * previousSlope < 0) { //look for sign changes
        extremes.add(previous);
    }
    previousSlope = slope;
    previous = p;
}

Finally, a good way to measure similarity is correlation. In your case, I would look at % move correlation (in other words, you want your 2 series to go up or down at the same time) - that's typically what is done in finance where you calculate the correlation between 2 assets returns for example:

• create 2 new series with the % move for each point of the 2 series
• calculate the correlation between those 2 series

You can read more about returns correlations here for example. In summary, if your values are:

Series 1  Series 2
 100        50
 98         49
 100        52
 102        54

The "returns" series will be:

Series 1  Series 2
 -2.00%     -2.00%
 +2.04%     +6.12%
 +2.00%     +3.85%

And you calculate the correlation of those 2 returns series (in this example: 0.96) to get a measure of how much the 2 curves look alike. You might want to adjust the result for variance (i.e. if one shape has a much wider range than the other).