Ahmet Kaya , what do you want to do with the model? Some context will be helpful. Many applications can tolerate a level of model misspecification and some not. Typically, if you want to predict or filter (forecast or nowcast) the expected values/ average behaviour of your economic variables, you will generally be ok with a level of heteroskedasticity. If you want to predict/filter extreme quantiles (as happens in predicting Value at Risk, for example) or predict/ filter some nonlinear functions of variables (as happens in forecasting financial derivative prices, for example), you may get really poor results with a mis-specified model. That's an engineer's point of view. Whether an asymptotic result (CLT) applies or not 'in practice' has very little meaning for me - we never have infinite data.

Paresh Date dear Paresh, thank you for your answer. I am trying to examine the relationship between inflation and unemployment. And I am not even sure about my autocorrelation

You can use a VAR-GARCH model

I suggest you get rid of unrelevant lags by looking at autocorrelations and partial autocorrelations.

I understand that you are trying to fit a VAR model to two variables inflation and unemployment. This reminds me of a closed economy Philips curve. I would think that many other variables will also have an effect on both inflation and unemployment. (Candidate variables would include exchange rates, monetary policy, taxes, oil prices, real GDP growth rates, etc.). Your test results are probably indicating that your model is misspecified. With an open economy, you are definitely missing some variables. You should consider revising your model.

A VAR model is often mixed up with an economic model and used instead of carefully thinking about the specification. That seems to be also the case here. One just takes time series with enough data (I think quarterly) for inflation and unemployment and "throughs" them into a VAR estimation program. That has nothing to do with economics, it is rather the dontrary of good econometrics (neither economics nor sensible statistics).

After putting more brain effort into a good specication (considering other influences, too; see John's advice), you should also look to find out the main lags (see Joel's answer) and whether there are unlagged (in the same quarter) effects, too. You must also take attention that unemployment is a stock (measured at which point of time?), but inflation is a flow.