rank.est {LongMemoryTS}

Cointegration Rank Estimation using Model Selection.

Description

Model selection procedure to estimate the cointegrating rank based on eigenvalues of correlation matrix P suggested by Robinson and Yajima (2002).

Usage

rank.est(data, d.hat, m, m1, v_n = m^(-0.3))

Arguments

data

data matrix of dimension (qxT).

d.hat

the estimated d.vector

m

bandwith parameter specifying the number of Fourier frequencies. used for the estimation of d, usually floor(1+T^delta), where 0<delta<1.

m1

the bandwidth parameter used for estimation of d.vec with m1>>m

v_n

bandwidth parameter. Nielsen and Shimotsu (2007) use m^(-0.3) in their simulation studies, which s the default value. m^(-b) mit 0<b<0.5 can be used.

Details

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References

Robinson, P. M. and Yajima, Y. (2002): Determination of cointegrating rank in fractional systems. Journal of Econometrics, Vol. 106, No.2, pp. 217-241.

Nielsen, M. O. and Shimotsu, K. (2007): Determining the coinegrating rank in nonstationary fractional systems by the exact local Whittle approach. Journal of Econometrics, 141, pp. 574-596.

Examples

library(fracdiff)
T<-2000
d<-0.4
m1<-floor(1+T^0.75)
m<-floor(1+T^0.65)
xt<-fracdiff.sim(n=T, d=d)$series
yt<-xt+rnorm(T)
zt<-xt+rnorm(T)
X<-cbind(xt,yt,zt)
lW.wrap<-function(data,m){local.W(data,m)$d}
d.hat<-apply(X,2,lW.wrap, m=m1)
rank.est(data=X, d.hat, m=m, m1=m1)