MLWS {LongMemoryTS}

MLWS test for multivariate spurious long memory.

Description

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).

Usage

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.

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.

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))