Should I avoid mixed ARMA models? I have hourly demand data for taxi rides that spans several years into the past. I want to use it in order to forecast future demand (for the next day). Robert Nau warns against the usage of a mixed ARMA model 

you should generally avoid using both AR and MA terms in the same nonseasonal ARIMA model:  they may end up working against each other and merely canceling each other’s effects.

Not sure I understand why are they canceling each-other - can you explain the mathematical intuition? 
Also, I saw that Hyndman isn't paying attention to Nau's advice when dealing with demand data (much like my data), and simply uses auto.arima and searches for the best model (the one that's minimizing the AICc). 
I think that the source of my confusion is that I don't understand in what circumstances AR and MA processes are cancelling each other, and when should we avoid them. Is this a manifestation of a multicollinearity problem? or is it something else I should worry about?
 A: This is a comment, but too long. I looked at the cited paper by Robert Nau, and here is actual citations: (page 6 of pdf)

You should try to avoid using “mixed” models in which there are both
  AR and MA coefficients, except in very special cases.

with this footnote:   

An exception to this is that If you are working with data from physics
  or engineering applications, you may encounter mixed ARIMA(p, 0, p-1)
  models for values of p that are 2 or larger. This model describes the
  discrete-time behavior of a system that is governed by a p-order
  linear differential equation, if that means anything to you. For
  example, the motion of a mass on a spring that is subjected to
  normally distributed random shocks is described by an ARIMA(2, 0, 1)
  model if it is observed in discrete time. If two such systems are
  coupled together, you would get an ARIMA(4, 0, 3) model.

Also, among his list of typical models, he includes one model breaking this advice


*

*ARIMA(1, 1, 2) = linear exponential smoothing with damped trend (leveling off) 


showing the advice is meant to be tentative. The paper is an instructional one aimed for business students, and much advice is modified by ... for a
business application. 
Lot of other interesting advice, one example cite: (page 20 of pdf)

If you apply one or more first-difference transformations, the
  autocorrelations are reduced and eventually become negative, and the
  signature changes from an AR signature to an MA signature. An AR
  signature is often the signature of a series that is “slightly
  underdifferenced,” while an MA signature is often the signature of a
  series that is “slightly overdifferenced.” If you apply one difference
  too many, you will get a very strong pattern of negative
  autocorrelation.

