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I have an extremely volatile series (capital flows). Due to heteroskedasticity I tried to estimate GARCH type models.

However, none of the variants (I tried altering process equation, as well as GARCH specification and errors distributions) resulted with an adequate model.

In all variants conditional variance is extremely large (Omega is equal 5554.52) and sum of coefficients in garch model is above 1 so the unconditional variance is not defined.

Another peculiarity to the series is that the in the Ljung-Box test for squared residuals - first lag is not statisticaly significant. I applied Ljung-Box test for squared residuals for different model specifications (interecept only; ar(1); ma(1); arma(1,1)...).

I always get that the first lag is statistically not significant with p-values of 0.5 and higher. At all other lags p-values are 0.000.

What could this statistical insignificance of the first lag mean? If it wasnt for the first lag it would be clear conditional HTSK but the first lag confuses me...

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