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Using the function MarchTest of package "MTS" in R, I am testing whether or not there are multivariate ARCH effects in my time series. I simulated some series without multivarate ARCH effects, so per definition there must be very high p-values. Running the MarchTest, there are high p-values only in small samples but they turn to 0 when the sample becomes bigger (1,000 or more observations). I am sure that there is no mistake in the construction of the time series.
Does anyone have an idea why there are such misleading results?

The underlying parameters are:

p<-3                    
mu<-c(0.28,0.17,0.34)                                   
phi<-matrix(c(-0.156,0.277,0.259,0.386,0.184,0.269,-0.265,0.191,0.376),3,3)     
psi<-matrix(c(-0.500, 0.612, 0.235, 0.597, 0.414, 0.169, 0.333, 0.273, 0.100),3,3)  
eps_t <-c(0,0,0)                            
n<-c(50,100,500,1000)

Then

Y_t<-matrix(0,ncol=3,nrow=n[4]) 
Y<-matrix(0,ncol=3,nrow=n[4]) 
set.seed(1234) 
Y_t<-(VARMAsim(nobs=n[4], arlags=1, malags=1, cnst=mu, phi=phi, theta=psi, skip=100, sigma=varcov)$series) 
head(Y_t) 
Y<-data.matrix(Y_t)

As you see, it is a pure VARMA process without any ARCH effects by construction.
The output with 1,000 observations is:

> MarchTest(Y)
Q(m) of squared series(LM test):  
Test statistic:  35.62607  p-value:  9.758118e-05 
Rank-based Test:  
Test statistic:  14.08036  p-value:  0.1693574 
Q_k(m) of squared series:  
Test statistic:  138.9744  p-value:  0.0007122924 
Robust Test(5%) :  100.2475  p-value:  0.215975

The output using the same parameters but only 50 observations is:

Q(m) of squared series(LM test):  
Test statistic:  14.46804  p-value:  0.152693 
Rank-based Test:  
Test statistic:  16.10272  p-value:  0.09672955 
Q_k(m) of squared series:  
Test statistic:  92.35173  p-value:  0.4116147 
Robust Test(5%) :  122.0541  p-value:  0.01385632
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  • $\begingroup$ There are four tests reported by MTS::MarchTest; which one is giving you the strange results? Could you include the output your are getting (and the code for generating the series, too)? (Here is a related question, although probably too basic to be useful for you.) $\endgroup$
    – Richard Hardy
    Apr 11, 2017 at 13:24
  • $\begingroup$ It is probably that there are differences that are only detected when the sample size gets large. Questions about the software should be asked at another site. $\endgroup$
    – Michael R. Chernick
    Apr 11, 2017 at 13:26
  • $\begingroup$ @MichaelChernick, I tend to view this question as of statistical nature rather than programming related. The question is, how to understand the counterintuitive results, not how to code something. But of course we need the question to be expanded to be able to answer it sensibly. $\endgroup$
    – Richard Hardy
    Apr 11, 2017 at 13:27
  • $\begingroup$ In large samples, I receive p values of 0 for all of the four tests. Depending on the simulation, this is the case sometimes already at 1000 observations. $\endgroup$
    – lirona
    Apr 11, 2017 at 13:29
  • $\begingroup$ @MichaelChernick as the poramming of the MarcgTest using the package is not difficult, I am not asking about the programming of this but about the conflicting results. $\endgroup$
    – lirona
    Apr 11, 2017 at 13:34

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