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
δ
(1-ℬ)
-λ
z
t
a
t
a
t
λ>0
δ∈
n
0.01≤λ≤0.2
0≤δ≤1
n=100
Var()=1
a
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