Multicollinearity of lagged terms in ARIMA model I am new to ARIMA and I have been watching quite a number of video about ARIMA online. The instructions that I have received is we have to finally run the least square to estimate the coefficients of the lag terms.
This worries me because if the lag term is correlated with each other, then vif of the whole model should be high and hence too much interactive terms in the model to inflate the errors.
I wish to ask if I have misunderstanding of the ARIMA, should I just directly apply the idea least square of multiple regression to ARIMA?
 A: First, you cannot estimate ARIMA($p,d,q$) models with least squares unless $q=0$. If $q>0$, you need lagged error terms which are unobservable, thus you cannot form the regressor matrix to conduct OLS estimation. In such situations, ARIMA models are estimated using maximum likelihood estimation (but even with $q=0$, maximum likelihood estimation can stil be used).
Second, near multicollinearity can be a problem not only when using OLS but also with other forms of estimation such as maximum likelihood. But since ARIMA models are typically used for forecasting rather than causal inference, you do not really care about the parameter values and their confidence intervals as long as the forecasts are accurate. Since multicollinearity affects inference but not (that much) forecasting performance, it is not really a problem in the typical use of ARIMA models. 
Moreover, multicollinearity may be avoided by smart model selection. If you consider several models and some of them have higher multicollinearity than others, they will tend to have higher AIC and BIC values (and higher means worse here). It is because under high multicollinearity it is possible to build a parsimonious model with few parameters that has a fit nearly as good as that of a rich model with many parameters. The parsimonious model will be less prone to high multicollinearity than the rich model. If you use AIC or BIC for model selection, you will then select the parsimonious model because the improvement in fit from the parsimonious to the rich model will be more than outweighted by the penalty term for model complexity.
