'ARCH effects on the residuals

I using the AIC criterion to find the 'best fit' ARMA order for my logarithmic returns series.

I find that the best fit is MA(2) and from this model I retrieve the residuals. I perform residuals diagnostics on my residuals series using the Ljung Box test and I find that there is "no autocorrelation".

I want to use this residuals series to estimate volatility using a GARCH model. So to make sure that a GARCH model is 'good fit' I use the ARCH-LM test by Engle (1982) to find evidence of conditional heteroscedasticity. I do find evidence of heteroscedasticity at lag = 1 ( 5% significance level) and therefore I employ a GARCH(1,1) (I also do a model selection using AIC again to make sure this is the 'best fit' GARCH model) to model the conditional variance.

I have 2 questions:

  1. Why does the Ljung Box test says that there is no autocorrelation while the ARCH-LM test finds presence of ARCH effects?
  2. When I employ the GARCH model in R, should I use armaOrder = c(0,0) since the residuals are white noise? Or should I use armaOrder = c(0,2):

ugarchspec(mean.model = list(armaOrder = c(0,0), include.mean = FALSE), distribution.model = "norm", variance.model = list(model = 'sGARCH', garchOrder = c(1, 1))

or:

ugarchspec(mean.model = list(armaOrder = c(0,2), include.mean = FALSE), distribution.model = "norm", variance.model = list(model = 'sGARCH', garchOrder = c(1, 1))



Sources

This article follows the attribution requirements of Stack Overflow and is licensed under CC BY-SA 3.0.

Source: Stack Overflow

Solution Source