# Rank Transform in Harmonic Regression Time Series

Rank Transform in Harmonic Regression Time Series

Let =sin(2πωt)+, , where is the frequency and is a mean-zero error term with variance . The rank is =1+ℐ(>). The expected rank is given by where . In this Demonstration, . In the top panel, the dots show the simulated values when the normal distribution is used with and . The bottom panel shows the average empirical rank (points) based on 1000 simulations and expected rank (curve). The bottom panel demonstrates that the frequency in the original data can be determined using the ranks, provided that enough data is available.

z

t

e

t

t=1,…,n

ω

e

t

2

σ

r

t

∑

s≠t

z

t

z

s

{}=1+F(sin(2πωt)-A)

r

t

∑

s≠t

A=sin(2πωs)

n=100

z

t

ω=0.1

σ=1