Using simpler models in place of more generalized and complex models I was reading about BATS (Box-Cox transformation,  ARMA errors, Trend and Seasonality) and TBATS (Trigonometric, Box-Cox transformation,  ARMA errors, Trend and Seasonality) models. I was wondering whether it's possible to get better forecasts with simpler models like standard Holt Winters than using BATS or TBATS?
 A: The Holt-Winters would not be applicable where those advanced and more complex proposals for multiple seasonalities would. There is, however, bigger room for errors by academic developers and misuses by practitioners with more complex methods. It is because of these potential problems simpler stuff, where it is applicable, may work better more often (and for more people). 
As to the performance of simpler methods, I would like quote O.D. Anderson "One would not train a modern soldier to  use a net and trident, but some gladiators did very well with them!"—it's not about methods only, but also about who uses them and more importantly how. In reality, advanced methods may perform only as well as their practitioners. 
As to forecasting competitions mentioned in another answer, I'd like to quote O.D. Anderson again "A  major point missed here is  that  the  success of a methodology is highly dependent on the person  applying it. Thus,  if  Mr  Merit does a  better job forecasting with  method  'A'  than Dr  Dud using 'B', this tells us little.  Moreover if,  instead, Professor  Passable employing both 'A'  and 'B' finds  that (for him) the former performs  superiorly, it may well be difficult  to  discount  the  fact  that  it  is just 'A' plus 
Passable which has outpointed the other combination, for the specific situation under investigation." 
Note the use of "for him" and "for the specific situation under investigation" to delineate the extent to which forecasting competitions are most useful. 
Anderson, O. D., A Commentary on 'A Survey of Time Series' International Statistical Review, 1977, 45, 273-297 (this is a critique of Spyros Makridakis  (1976) that some may find interesting).
A: No reason why a simpler method shouldn't give better forecasts for any particular series. Furthermore ...


*

*A complex model may include a simple model as a special case. It may still be true that it gives larger out-of-sample forecast errors than the simple model after fitting it to a finite sample from your time series. This is the phenomenon of over-fitting; applicable just as much to time-series models as to multiple regression. A larger sample lets you fit more complex models.

*One method may be better than another according to one way of measuring forecast error, yet worse according to a different way.
For the question as to what methods work better in general, it's hard to define "in general". The M3 competition compared various methods for many relatively short series of mainly "business" type data. The results (Makridakis (2000), International Journal of Forecasting, 16) showed simple methods like Holt–Winters & damped-trend exponential smoothing performing very well, often better than more complex methods.
A: I am trying to think through a few issues about time series modeling.
Are univariate time series methods enough? Do they extract all the relevant information from the particular time series? If they do not, then how you can continue your analysis?
There are of course well-known methods for univariate time series analysis but perhaps you have to account also some other information in other time series. Suppose that the expenditure for beer $y(t)$ is effected by many things like season, holidays, advertisiment etc. Your model might have to account these issues.
So in the end it could be that you have a model like this:
$$y(t)=A(L)y(t)+\mathrm{Seasonal\_deterministic\_effects}+\mathrm{various\_pulses}+B(L)x(t)+\varepsilon(t)$$
