MLWS: MLWS test for multivariate spurious long memory.

Description Usage Arguments References Examples

View source: R/MLWS.R

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

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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

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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))

Example output

$B
     [,1] [,2]
[1,]    1    0
[2,]    0    1

$d
[1] 0.3716396 0.1049893

$W.stat
[1] 0.4425343

$CriticalValues
  alpha=.1  alpha=.05 alpha=.025  alpha=.01 
     1.022      1.155      1.277      1.426 

$B
     [,1] [,2]
[1,]    1    0
[2,]    0    1

$d
[1] 0.3717507 0.1038943

$W.stat
[1] 0.4361484

$CriticalValues
  alpha=.1  alpha=.05 alpha=.025  alpha=.01 
     1.022      1.155      1.277      1.426 

$B
     [,1] [,2]
[1,]    1    0
[2,]    0    1

$d
[1] 0.1801331 0.2701262

$W.stat
[1] 1.06821

$CriticalValues
  alpha=.1  alpha=.05 alpha=.025  alpha=.01 
     1.118      1.252      1.374      1.517 

$B
     [,1]       [,2]
[1,]    1 -0.8382144
[2,]    0  1.0000000

$d
[1] 0.03104957 0.41408915

$W.stat
[1] 0.466867

$CriticalValues
  alpha=.1  alpha=.05 alpha=.025  alpha=.01 
     1.118      1.252      1.374      1.517 

LongMemoryTS documentation built on May 2, 2019, 5:58 a.m.