An Example of Peak Finding in Univariate Data by Least Squares Approximation and Restrictions on the Signs of the First Differences

We consider an application of the least squares piecewise monotonic data approximation method to the problem of locating significant extrema in univariate observations that are contaminated by random errors. The piecewise monotonic approximation method makes the smallest change to the data such that the first differences of the smoothed values change sign a prescribed number of times, but the positions of the sign changes are unknowns of the optimization process. We present a numerical example in order to show the efficiency of the method for peak finding. The example is an application to 31959 noisy observations of daily sunspots. Our results suggest some subjects for future research in automatic peak finding.