Multivariate Arch Effects in BEKK model

[paldejong]

I am trying to fit a MV-GARCH BEKK model with two variables. The data is minute data with over 5000 observations. The problem I am facing is that the model consistently has significant residual multivariate ARCH effect . I tried different model specifications but it seems that one variable is creating the problems even though both of them behave well in univariate GARCH models (Q as all McLeod). You had mentioned in previous posts that large datasets could cause this problem to occur (I could not find those specific posts). I am not sure what justification I could use for my model choice and I could not find a documented argument for large sample size.

Thank you,

Pieter de Jong

[TomDoan]

That's not specific to a GARCH model. It's just generally the case that with a very large data set, you will (in practice) almost always reject a hypothesis at a fixed conventional significance level (such as .05). The problem is that with a fixed significance level, all the added information from the big data set goes towards reducing Type II error (since the Type I error is fixed). It may be particularly common in GARCH models because all GARCH models are approximations to the variance dynamics. The real question is whether the diagnostics point to a correctable problem in the model. Tiny but statistically significant residual ARCH effects generally don't allow for an obvious fix.

However, one thing to check is whether the multivariate mean model is adequate. Incorrect dynamics in the mean can show up in residual ARCH effects.

[paldejong]

Thank you, Tom. You were correct; after I adjusted the mean model the residual ARCH effects disappeared.

Best,

Pieter