Multiple Periodicity in Time Series

s1 = a1 * sin(b1 + [2* π *t/c1]); s2 = a2 * sin(b2 + [2* π *t/c2]); s3 = a3 * sin(b3 + [2* π *t/c3])

We examine the use of periodograms to extract the main component frequencies.
The original idea ws taken from Data Science Central challenge of the week
You can control the variables for each of the 3 harmonic functions composing the final waveform that models the time series being analyzed.
The periodogram leverages R's implementation of the Discrete Fourier Transform. f1, f2 and f3 are the top-3 most significant spectra. We also show f1's 95% confidence interval on a chi-squared distribution.