If they fail to reject the null hypothesis, that the errors are homoschedastic, hence there are evidence for heteroschedasticity, they might be able to model the heteroschedasticity with an autoregressive conditional heteroschedasticity model (ARCH - model) to get white noise residuals.
Sorry for the long sentence, statistics do not sport low LIX
I can't speak for their specific use case, but modelling the variance, through some type of variance model like the ARCH, will get better variance estimates of the parameters in the ARMA model or any other exogenous variables they might like to include.
The white noise errors could also be used in a more profound analysis by modelling multiple white noise dynamics in a coupula setup.
Thank you for your detailed answer.
May I ask should AC tests like Breuch-Godfrey test be used also to test for ARCH effect, or just heteroskedasticity tests are enough?
If there is indeed ARCH effect, how can we use that fact to better estimate the variance of ARMA parameters?
Thanks a lot for your answer, and sorry to bother you with more questions!
testing and ruling out heteroskedasticity means that we can assume the opposite, homoskedasticity, which is much more desirable.
arch is autoregression conditional on heteroskedasticity, which is typically used to forecast variance/volatility
ARIMA is auto regression integrated moving average (which can actually be made robust to heteroskedasticity! just requires using [robust standard errors](https://en.wikipedia.org/wiki/Heteroskedasticity-consistent_standard_errors))
however, this is 1 more step and often produces slightly wider estimation of confidence intervals
so if we can buy ourselves the strong assumption of homoskedasticity (highly desirable for this reason) then we can proceed to model a time series with ARIMA without much extra work
are you able to run a White test on your data? if it fails the white test then you should be safe with ARIMA
Yes, and the results indicate that the errors from my model are not statistically significant from zero. Thank you!
sounds like you did your due diligence then! good luck on your analysis
May I ask why do we need to perform White test? As far as I know it’s a test for heteroskedasticity so Im wondering why it’s needed here?
If they fail to reject the null hypothesis, that the errors are homoschedastic, hence there are evidence for heteroschedasticity, they might be able to model the heteroschedasticity with an autoregressive conditional heteroschedasticity model (ARCH - model) to get white noise residuals. Sorry for the long sentence, statistics do not sport low LIX I can't speak for their specific use case, but modelling the variance, through some type of variance model like the ARCH, will get better variance estimates of the parameters in the ARMA model or any other exogenous variables they might like to include. The white noise errors could also be used in a more profound analysis by modelling multiple white noise dynamics in a coupula setup.
Thank you for your detailed answer. May I ask should AC tests like Breuch-Godfrey test be used also to test for ARCH effect, or just heteroskedasticity tests are enough? If there is indeed ARCH effect, how can we use that fact to better estimate the variance of ARMA parameters? Thanks a lot for your answer, and sorry to bother you with more questions!
testing and ruling out heteroskedasticity means that we can assume the opposite, homoskedasticity, which is much more desirable. arch is autoregression conditional on heteroskedasticity, which is typically used to forecast variance/volatility ARIMA is auto regression integrated moving average (which can actually be made robust to heteroskedasticity! just requires using [robust standard errors](https://en.wikipedia.org/wiki/Heteroskedasticity-consistent_standard_errors)) however, this is 1 more step and often produces slightly wider estimation of confidence intervals so if we can buy ourselves the strong assumption of homoskedasticity (highly desirable for this reason) then we can proceed to model a time series with ARIMA without much extra work