sim_ex_cluster {ftsa} | R Documentation |
Simulated multiple sets of functional time series
Description
We generate 2 groups of m
functional time series. For each i
in {1, ..., m} in a given cluster c
, c
in {1,2}, the t
th function, t
in {1,..., T}, is given by
Yit(c)(x)=μ(c)(x)+∑k=12ξtk(c)ρk(c)(x)+∑l=12ζitl(c)ψl(c)(x)+υit(c)(x)
Usage
data("sim_ex_cluster")
Details
The mean functions for each of these two clusters are set to be μ(1)(x)=2(x−0.25)2
and μ(2)(x)=2(x−0.4)2+0.1
.
While the variates ξtk(c)=(ξ1k(c),ξ2k(c),…,ξTk(c))⊤
for both clusters, are generated from autoregressive of order 1 with parameter 0.7, while the variates ζit1(c)
and ζit2(c)
for both clusters, are generated from independent and identically distributed N(0,0.5)
and N(0,0.25)
, respectively.
The basis functions for the common-time trend for the first cluster, ρk(1)(x)
, for k
in {1,2} are sqrt(2)∗sin(π∗(0:200/200))
and sqrt(2)∗cos(π∗(0:200/200))
respectively; and the basis functions for the common-time trend for the second cluster, ρk(2)(x)
, for k
in {1,2} are sqrt(2)∗sin(2π∗(0:200/200))
and sqrt(2)∗cos(2π∗(0:200/200))
respectively.
The basis functions for the residual for the first cluster, ψl(1)(x)
, for l
in {1,2} are sqrt(2)∗sin(3π∗(0:200/200))
and sqrt(2)∗cos(3π∗(0:200/200))
respectively; and the basis functions for the residual for the second cluster, ψl(2)(x)
, for l
in {1,2} are sqrt(2)∗sin(4π∗(0:200/200))
and sqrt(2)∗cos(4π∗(0:200/200))
respectively.
The measurement error υit
for each continuum x is generated from independent and identically distributed N(0,0.22)
Examples
data(sim_ex_cluster)
[Package
ftsa version 6.4
Index]