Description Usage Arguments Details Value References See Also Examples
It generates functional Moving Average, FMA, process of sample size n with a specific
number of basis functions where the eigenvalue decay of the covariance operator is given
by the defined vector Sigma. The norm of the functional moving average
operators are defined by the vector kappa
. The generic function uses Fourier basis in [0,1],
however one can define a different basis and different range values. If the order or kappa is not defined
then the function generates iid functional data by default.
1 2 |
n |
Sample size of generated functional data. A strictly positive integer |
nbasis |
Number of basis functions used to represent functional observations |
order |
Order of the FMA process |
kappa |
Vector of norm of the FMA operators. The length of this vector must be same as the
FMA |
Sigma |
Eigen value decay of the covariance operator of the functional data. The eigenvalues of
the covariance operator of the generated functional sample will mimic the behavior of |
basis |
A functional basis object defining the basis. It can be the class of
|
rangeval |
A vector of length 2 containing the initial and final values of the interval over which the functional data object can be evaluated. As a default it is set to be [0,1]. |
... |
Further arguments to pass |
This function should be used for a simple functional moving average data generation for a desired eigenvalue decay of covariance operator. The j-th FMA operator Θ[j] is generated by Θ[j] = κ[j]Θ, where Θ has a unit norm with Θ[i,j] = N(0, σ[i]σ[j]). For more details see Aue A., Rice G., Sonmez O. (2017+).
Functional Moving Average data sample (class fd
) containing:
coefs |
The coefficient array |
basis |
A basis object |
fdnames |
A list containing names for the arguments, function values and variables |
Ramsay, James O., and Silverman, Bernard W. (2006), Functional Data Analysis, 2nd ed., Springer, New York.
Aue A., Rice G., Sonmez O. (2017+), Detecting and dating structural breaks in functional data without dimension reduction (https://arxiv.org/pdf/1511.04020.pdf)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 | # FMA(1) data with 21 fourier basis with a geometric eigenvalue decay
fun_MA(n=100, nbasis=21, order=1, kappa=0.8)
# Define eigenvalue decay
Sigma1 = 2^-(1:21)
# Then generate FMA(2) data
fun_MA(n=100, nbasis=21, order=2, kappa= c(0.5, 0.3), Sigma=Sigma1)
# Define eigenvalue decay, and basis function
library(fda)
basis1 = create.bspline.basis(rangeval = c(0,1), nbasis=21)
Sigma1 = 2^-(1:21)
# Then generate FMA(1)
fun_MA(n=100, nbasis=21, order=1, kappa= 0.3,Sigma=Sigma1, basis=basis1)
# Not defining order will result in generating IID functions
fun_MA(n=100, nbasis=21) # same as fun_IID(n=100, nbasis=21)
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