Tempered Fractionally Differenced White Noise

λ

0.025

δ

0.833

random seed

1503

plot

time series

ACF

log SDF

loglog SDF

Tempered fractionally differenced (TFD) white noise

z

t

(

t=1,…,n

) can be defined using the backshift operator

ℬ

in the relation

δ

(1-

-λ



ℬ)

z

t

=

a

t

, where

a

t

is Gaussian white noise,

λ>0

,

δ∈

and

n

is the series length. In this Demonstration, we consider the ranges of values:

0.01≤λ≤0.2

,

0≤δ≤1

,

n=100

and

Var(

a

t

)=1

. This Demonstration explores the dependence on

λ

and

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,

λ=0.025

and

δ=0.833

, 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.