Can I continue ARIMA model despite my time time series has heterodasticity? I estimated ARIMA model with daily gold time series. The residuals' corelogram is flat but its squared is not flat. Already I tried eVİEWS heterodasticity >> arch effect and ı found prob value 0.00 so there is heterodasticity. Can ı continue with ARIMA?
https://yadi.sk/i/rT6UHvOud338Xw
2009q3-2018 work days
 A: If, after estimating any time-series model including ARIMA, your estimated residuals are not independent (so in this case their squares are autocorrelated), then this likely means that there exists a better specification for the model, i.e. maybe you are not specifying the conditional mean structure appropriately or you are making the wrong assumption about the shape of the conditional covariances, or all of them.. If I understand your situation correctly, in this case since the squared innovations are correlated and the simple innovations are not, I would say the second one is likely.. therefore maybe you are right using an Arima because the true process does follow an Arima in its mean but you need to specify other parts of the model better. If your conditional mean specification of the Arima removes the non-stationarity in the process and the autocorrelation in its first difference, then it means that you are correctly specifying the conditional mean of the process and that the true problem lies elsewhere. Here likely in the conditional variance.
Try with simulated data and check that, when you don’t mispecify the model to be estimated, then retrieving the innovations leads to 1) uncorrelated innovations 2) uncorrelated squared innovations 3) innovations that follow the distribution that generate the data (so for example if you have simulated normal shocks then the estimated innovations/shocks should proxy a normal distribution, look for simplicity at a QQ Plot or test). Notice that here by innovations I mean the standardized residuals of the model (standardized based on the conditional mean and variance structures forecasted for each t)
A: Depending on the estimator, it is not necessarily a problem.
In the context of OLS the Gauss-Markov theorem will not apply, this means that the standard errors will be biased. However, the OLS estimator itself is consistent in the presence of heteroscedastic errors. A quick-fix for your problem could be to use a "robust" estimator of the standard errors, see e.g. the wikipedia page on the subject. 
A better fix would be to actively model the heteroscedasticity in the errors, e.g. using a GARCH model. One often finds that the GARCH(1,1) model is sufficient to remove ARCH effects from financial data, such as your return series for gold prices, see e.g.  the following working paper Hansen & Lunde 2001 (or the published version, Hansen & Lunde 2005)
A: I would not trust a model with evidented heteroscedastic errors ... thus my preferred approach is to .... (AFTER adjusting for pulses,level shifts,seasonal pulses and local time trends i.e. adjusting the conditional mean structure ) pursue this thread .
To treat heteroscedasticity consider employing the GLS approach suggested by TSAY http://docplayer.net/12080848-Outliers-level-shifts-and-variance-changes-in-time-series.html . The weights he generates lead directly to Weighted Least Squares. I have had success with this feature which I incorporated into AUTOBOX, a commercial time series package to treat deterministic change points in model error variance AFTER validating that the model parameters didn't change over time which surprisingly is generally ignored elsewhere ! 
If doesn't resolve your problem then
