freqdom (version 1.0.4)

reg.dim.est: Estimate the optimal dimension in linear regression problem

Description

Consider a linear regression problem for a multivariate stationary time series X_t: $$Y_t=P{X}_t+{\epsilon }_t.$$ Estimator based on formula $$E{Y}_0{X}_0(E{X}_0^2{)}^{-1}=P$$ is fragile on the eigendirections of $E{X}_0^2$ with small eigenvalues. It is therefore desired to truncate the inversion at a level where eigenvalues are estimated consistently. Procedure dim.est suggest such level by taking only the eigenvalues which are greater and equal than $1/\sqrt{n}{K}_{const}$. It is designed for $\sqrt{n}$ consistent matrix estimator and can serve as one of heuristics for matrix inverion problems.

Usage

reg.dim.est(eigenvalues, n, Kconst = 1)

Arguments

eigenvalues

vector of eigenvalues

n

used for estimation

Kconst

parameter for fitting the convergence rate to 1/(Kconst*n^1/2)

Value

number of 'safe' eigendirections

References

Siegfried Hormann and Lukasz Kidzinski A note on estimation in Hilbertian linear models Research report, 2012

See Also

reg.est, pseudoinverse

Examples

# NOT RUN {
n = 100
X = rar(n)
Y = rar(n)
CV = lagged.cov(X,Y)
E = eigen(CV)
K = reg.dim.est(E$values, n)
# }