I have implemented a VAR in Eviews using log first differenced time series data for four stock market indices and the Baltic dry index. The model had autocorrelation when the VAR was calculated on one lag based on the AIC, SIC and HQ. So I added an extra lag to correct for autocorrelation. The resulting VAR has no signficant variables. Is it still possible to proceed with Impulse Response functions as well as variance decomposition?
Yes, it still is possible with the same caveats that ought to be applied whenever we look at insignificant variables. That is, we can interpret the impulse responses, but we need to keep in mind that the data is not sufficiently informative to distinguish the effects from the effects under the null hypothesis (typically, the null that there are no effects from a lagged variable). That is, the effects we observe in the impulse responses may also be driven by chance.
That does not make it wrong per se to look at insignificant variables, because it may also be the case that there actually is an effect, which cannot be detected with sufficient precision given low power of the test. That is often a concern in VAR studies with relatively small sample sizes and many parameters.