MLWS: MLWS test for multivariate spurious long memory.
In FunWithR/LongMemoryTS: Long Memory Time Series

Description Usage Arguments References Examples

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)

`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`.

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.

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))