# Tempered Fractionally Differenced White Noise

Tempered Fractionally Differenced White Noise

Tempered fractionally differenced (TFD) white noise () can be defined using the backshift operator in the relation , where is Gaussian white noise, , and is the series length. In this Demonstration, we consider the ranges of values: , , and . This Demonstration explores the dependence on and .

z

t

t=1,…,n

ℬ

(1-ℬ)z=a

-λ

δ

t

t

a

t

λ>0

δ∈

n

0.01≤λ≤0.2

0≤δ≤1

n=100

Var(a)=1

t

λ

δ

The time series plot is shown on an arbitrary scale to emphasize the general shape, independent of scale and location. The initial parameter settings, and , provide an appropriate model for turbulent flow. You can generate a wide variety of random patterns using the "random seed" slider. You can display the associated spectrum and autocorrelation using the "plot" buttons. See Details.

λ=0.025

δ=0.833