Detecting Periodicity in Short Time Series

sample size n

15

frequency

0.23

phase

0.8

ϕ

1

0.

error variance

0.1

random seed

9379

distribution

Gaussian

Laplace

t

5

plot

time series and Fisher test

log periodogram

Bartlett test

cubic distortion

This Demonstration compares the performance of the Fisher and Bartlett periodicity tests for the random sinusoid

z

t

=cos(2πλt+φ)+

e

t

, where

t=1,…,n

and

e

t

is a random error that is independent and identically distributed with mean 0 and variance

2

σ

when

ϕ

1

=0

. The plot shows the sinusoid curve

cos(2πλt+φ)

and a simulated time series with parameter settings

n=15

,

λ=0.1

,

φ=0.8

,

2

σ

=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.