If you are using time series in levels, non-normality in the random errors would not seem to be a serious issue.

If you are investigating time series in returns and their associated volatilities, the distribution of the errors may be important in defining the log-likelihood function appropriately.

Normality is typically assumed, but a wide range of alternative distributions can also be considered, and then compared with the estimates using the normal distribution.

Dear Natale

It seems that you would have heteroskedasticity with the non-normal error terms.You can check for that with a variety of tests, one of which is Glejser. If you confirm there is heteroskedasticity then you can use a GLS technique to calculate your coefficients.

Hi there. I will copy the answer I gave to a similar question a few weeks ago. Hope it helps!!

Normality is desirable but it is not a requirement for many aspects of time series analysis.

For instance, if your objective is to obtain the best linear forecast for a given variable, simple OLS estimation in a regression model, or an ARDL model, will give you a consistent estimator of the BLP (Best Linear Predictor) irrespective of any assumption about normality.

Basic asymptotic theory for stationary time series does not require normality to hold true. Most of Wald tests, t-tests in traditional time-series regressions will have the "correct" asymptotic distribution even if errors are not normal.

So, my general answer is that normality in error terms is not necessarily a requirement, especially when you have a decent number of observations.

In most financial applications normality is rejected. It is not the end of the world and I would not be extremely concerned about it. I am mostly interested in forecasting, so what is the cost of non normality for your forecast?, confidence intervals will be tipically different than in the Gaussian case, but the forecast will be just fine.

Hi,

I agree with Pablo's comments. However, if you want to choose the correct distribution for error term of your time series model, you can try other distributions like Student's t or Genaralised Error Distribution (GED). Usually, Student's t distribution is appropriate when normality of the error term is rejected.

Kind regards

Thushara

@ NataIe: agree with 50% with Pablo's comments, I still believe you need to dummy some ith observation to minimize normality. I have discussed this issue somewhere so look for it. Simply, use standardized residual method to identify the biggest outlier in absolute term then dummy that as blip etc and then apply the automatic bandweight Newey-West estimator to contain the nonsphericalness of the residuals.

Thank You very much for your contributions, i think i will try to estimate the model through the GMM.

If you are using time series in levels, non-normality in the random errors would not seem to be a serious issue.

If you are investigating time series in returns and their associated volatilities, the distribution of the errors may be important in defining the log-likelihood function appropriately.

Normality is typically assumed, but a wide range of alternative distributions can also be considered, and then compared with the estimates using the normal distribution.

@Notice that Michael McAleer isn't saying non-normality is not a problem even in level time series data. He said WOULD NOT SEEM TO BE SERIOUS. Of course, a careful researcher would want to check the effect of this on his/her test statistic results.

Normality is assumed for convenience in linear regression models, but it is not necessary.

The Gauss-Markov Theorem, which is a sufficient condition for OLS to be BLUE, does not assume normality.

Kruskal's Theorem, which is a necessary and sufficient condition for OLS to be BLUE, does not rely on normality.

If one is concerned about non-normality, the Box-Cox transformation can be used as a filter to transform both non-normal and heteroskedastic errors.

I believe it is necessary and even Box-Cox transformation while minimizing the disease often lead to difficulty in interpretation of the obtained estimators

The Box-Cox transformation is a nonlinear model, and is straightforward to estimate and interpret.