Joe...

I'm not sure about Stata commands on this issue. However, you can test for residual heteroskedasticity in VAR models using R packages (https://cran.r-project.org/web/packages/het.test/het.test.pdf).

See also http://www.doornik.com/research/vectest.pdf. It could help you.

Best regards!

Sophia's advice is useful. However, she is rather unfair to Stata. Stata is a general econometrics package – the best, in my opinion – but is rooted in cross-section and panel econometrics and medical statistics. Betraying these origins, it is still patchy in its coverage of time-series econometrics. In contrast, JMulTi is a specialist package designed to close the gap between theoretical developments and availability to practitioners in a narrow range of time-series estimators. It is also brilliantly supported by Lütkepohl, H. and Krätzig, M. (2004). Applied Time Series Econometrics. Cambridge: Cambridge University Press. In the case of VAR/VECM, JMulTi offers a range of tests and estimators not available in Stata (e.g. tests for cointegration and the ability to estimate VECMs in the presence of up to two structural breaks, which is particularly important when dealing with macroeconomic time series that typically bridge structural divides such as before/after the global financial crisis). Also, for this type of modelling, JMulTi is quicker and easier to use.

 Although JMulTi does not provide an explicit test for heteroskedasticity for the VECM, it does offer relevant tests for ARCH effects (especially useful if you are working with high-frequency data). In addition – as noted above – the ability to estimate a VECM allowing for structural breaks is relevant; if breaks are not controlled for, they could influence the results of heteroskedasticity tests.  

 In addition, Microfit – which is not free – enables researchers to examine each equation in the VECM individually and, to do so, provides a full menu of standard diagnostic tests.

 Please allow me a final word in defence of Stata. Stata’ deficiencies are compensated by the availability of a huge range of superb and well-documented user-written programmes, which are often explained and demonstrated in the Stata Journal. For example, user-written programmes make Stata the leader in the emerging field of time-series panel analysis, which is closely related to the VECM approach.

Best wishes, Geoff

Dear check my detailed video on heteroskedasticity with practical help. 

Follow the link below:

https://www.youtube.com/watch?v=evJ5JpBHMGQ

Best

Meraj.

You know that the variance are not constant across the observation you are taking the Y hat ( combining all the explanatory variables). The medians are not constant, for instant B hat are still being constant, B hat are linear, B hat are unbiased, yet B hat are not efficient because of the violation of minimum variance assumption. Then we can apply GLS Estimator in place of OLS Estimator 

The application of OLS estimator with heteroskedasticity:-

-the t and F tests are likely to spurious results

-B hat will be inefficient then under or over estimates likely to happen 

-SE of the constant will be too high while the SE slope is low 

** Detecting it will be looking for:-

        - Outliers with observation 

       - Examine the residual condition after a simple regression

Other methods of detection that can be applied are:-

     1. application of two variable model ( by plotting the squared residual against the independent variable)

      2. As the predicted of dependent Y is a linear combination of the independent X

the plot against Xs or the predicted Y

        3. Graphing methods 

*** if you see the evidence heteroskedasticity then there is a probability of applying different testes like:

                  Park test; GoldFeld-Quandt test; etc 

the solution will be best to apply GLS or WLS