MLWS function

MLWS test for multivariate spurious long memory.

Multivariate local Whittle Score type test for the null hypothesis of true long memory against the alternative of spurious long memory suggested by Sibbertsen, Leschinski and Holzhausen (2018).

MLWS(X, m, epsilon = c(0.02, 0.05), coint.elements = NULL, B = NULL,
  prewhite = c("none", "uni", "multi"), eta = rep(1/sqrt(min(dim(X))),
  min(dim(X))), rep = FALSE, approx = 100, split = 1,
  T_limdist = 1000, M_limdist = 5000)

Arguments

• X: data matrix
• m: bandwith parameter specifying the number of Fourier frequencies used for the estimation usually floor(1+T^delta), where 0.5<delta<0.8 for consistency.
• epsilon: trimming parameter epsilon=0.05 by default. Determines minimum number of Fourier frequencies used in test statistic. For T>500 it is recommended to use epsilon=0.02. Confer Sibbertsen, Leschinski, Holzhausen (2018) for further details.
• coint.elements: Vector specifying which elements in the vector series are in a cointegrating relationship. By default NULL. Cf details.
• B: cointegrating matrix, if known. Default is B=NULL.
• prewhite: specifies the form of pre-whitening applied. One of c("none","uni","multi"). If uni is selected the univariate a univariate of maximal order (1,d,1) is selected using the AIC. If multi is selected VARFIMA_est is used to fit a VARFIMA(1,d,1) in final equations form. Default is none.
• eta: vector of weights. Default is rep(1/sqrt(min(dim(X))),min(dim(X))).
• rep: if prewhite="multi" is selected, rep specifies whether the current parameter values are displayed to the user during optimization procedure. Default is rep=FALSE.
• approx: if prewhite="multi" is selected, approx specifies the order of the AR-approximation used in VARFIMA_est. Default is approx=100.
• split: if prewhite="multi" is selected, split whether the sample should be split into subsamples to speed up the estimation. Default is split=1, so that the whole sample is used.
• T_limdist: number of increments used in simulation if limit distribution. Only relevant for component-wise version of the test. Default is T_limdist=1000.
• M_limdist: number of replications for simulation of the limit distribution. Default is M_limdist=5000.

Examples

T<-500
m<-floor(1+T^0.75)
series<-FI.sim(T=T,q=2,rho=0.7,d=c(0.4,0.2))
ts.plot(series, col=1:2)
MLWS(X=series, m=m, epsilon=0.05)

shift.series<-series+ARRLS.sim(T=T, phi=0, sig.shift=2, prob=5/T)
ts.plot(shift.series, col=1:2)
MLWS(X=shift.series, m=m, epsilon=0.05)

T<-500
m<-floor(T^0.75)
series<-FI.sim(T=T,q=2,rho=0,d=c(0.1,0.4), B=rbind(c(1,-1),c(0,1)))
ts.plot(series, col=1:2)
MLWS(series, m=m)
MLWS(series, m=m, coint.elements=c(1,2))

References

Sibbertsen, P., Leschinski, C. H., Holzhausen, M., (2018): A Multivariate Test Against Spurious Long Memory. Journal of Econometrics, Vol. 203, No. 1, pp. 33 - 49.