Detecting Periodicity in Short Time Series
Detecting Periodicity in Short Time Series
This Demonstration compares the performance of the Fisher and Bartlett periodicity tests for the random sinusoid =cos(2πλt+φ)+, where and is a random error that is independent and identically distributed with mean 0 and variance when =0. The plot shows the sinusoid curve and a simulated time series with parameter settings , , , =0.23 and initial random seed 9379 for Gaussian white noise and Fisher's periodicity test. The time series plot does not show the vertical axis, since it is not important in this context. See Details for further discussion and examples.
z
t
e
t
t=1,…,n
e
t
2
σ
ϕ
1
cos(2πλt+φ)
n=15
λ=0.1
φ=0.8
2
σ