T0stat function

Test for equality of all elements in an estimated d-vector based.

T0stat tests equality of all memory parameters simultaneously. Statistic was suggested by Robinson and Yajima (2002). Test statistic was denoted by T_0 in Nielsen and Shimotsu (2007).

T0stat(data, d.hat, m, m1, alpha = 0.05, s_bar = 1,
  h_n = 1/sqrt(log(max(dim(data)))))

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

• alpha: the desired significance level for the tests

• s_bar: number of subvectors to be tested in partitioning procedure. Default is s_bar=1, for independent use.

• h_n: bandwidth parameter. Default is h_n=1/sqrt(log(max(dim(data))))

  which is recommended by Nielsen and Shimotsu (2007) in their simulation study. Robinson and Yajima (2002) argue non-rejection with h_n=0 would imply non-rejection with any h_n>0.

Details

add details here.

Examples

library(fracdiff)
T<-1000
d1<-0.2
d2<-0.4
X<-cbind(fracdiff.sim(n=T,d=d1)$series,fracdiff.sim(n=T,d=d1)$series,
fracdiff.sim(n=T,d=d2)$series,fracdiff.sim(n=T,d=d2)$series)
alpha<-0.05
m1<-floor(1+T^0.75)
m<-floor(1+T^0.65)
lW.wrap<-function(data,m){local.W(data,m)$d}
d.hat<-apply(X,2,lW.wrap, m=m1)
T0stat(data=X, d.hat=d.hat, m=m, m1=m1)

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.