Which econometric models can be used to forecast security returns + ARIMA/GARCH questions I'm trying to write an undergraduate thesis wherein I test the predictive power of a given econometric model on a given financial time series. I need some advice on how I should go about doing this. To put matters into context, I have mostly self-studied econometrics; the only course I took on the subject stopped short of delving into time series models, so I am by no means an expert on the subject.  
To my dismay, I recently read that ARIMA models are very poor at predicting stock (and other security) returns. A professor in my school's economics department also confirmed this. All this time I was hoping they could perhaps be even remotely useful for forecasting some financial time series... Are there any other models I could look at? My goal is simply to learn some econometric modeling of time series in R or MATLAB and hopefully find statistically significant predictive results. Also, is there a particular market you would look at (energy, rates, equities)?
Lastly, is GARCH only used for forecasting volatility? The professor I mentioned seemed to suggest I should turn toward GARCH or ARIMA-GARCH models to model stock returns. I read some papers that seemed to imply it could also be used for actual returns... Perhaps I misunderstood. Would the AR and MA components in an ARIMA-GARCH model differ from those in an ARMA model? From what I vaguely understood, ARIMA and GARCH are two completely separate things (with the former being used to predict the actual time series and the other to predict its volatility). 
I hope that's not too many questions, but I just don't know where to turn to anymore, I've been researching this on my own for so long. Thanks a lot!
 A: 
My goal is simply to ... find statistically significant predictive results. Also, is there a particular market you would look at (energy, rates, equities)?

Most if not all the established and liquid financial markets will be very hard to predict whatever model you will use. If markets were relatively easy to predict, market participant would try to exploit that to make money. By doing that they would eliminate the predictability. This brings a contradiction, and thus the markets are not easy to predict.

Lastly, is GARCH only used for forecasting volatility? The professor I mentioned seemed to suggest I should turn toward GARCH or ARIMA-GARCH models to model stock returns. I read some papers that seemed to imply it could also be used for actual returns... 

GARCH model is used for modelling the conditional variance of the disturbance term of the conditional mean model for a dependent variable $y_t$. E.g. if you have a conditional mean model $y_t=\alpha+\epsilon_t$, the GARCH model will describe the conditional variance of $\epsilon_t$. Sometimes the conditional mean model is "empty" ($y_t=\epsilon_t$), then GARCH model is used to model the conditional variance of $y_t$ itself. 
Even if you are primarily interested in the conditional mean model (e.g. you want to predict stock returns using an ARMA model), a GARCH model combined with a model for the conditional mean can be useful. If the conditional variance of the dependent variable is time-varying, that should be accounted for, and a GARCH model does exactly that. If a time-varying conditional variance is neglected, the conditional mean model may (and likely will) be invalid.

Would the AR and MA components in an ARIMA-GARCH model differ from those in an ARMA model? 

Yes. That also illustrates my last remark above.

From what I vaguely understood, ARIMA and GARCH are two completely separate things (with the former being used to predict the actual time series and the other to predict its volatility). 

This is true. But as I have already explained, the two models can work together nicely.
A: I applaud your enthusiasm for the subject.  There is a lot of applications and methods to help with prediction but it is clear that there is no silver bullet.  Just like there is no one weather model that predict all weather in all locations with equal accuracy, there is not model that can predict financial time series. 
I would encourage you to look at a single sub-behavior of markets to see if you can understand it.  Some quick examples are 


*

*Month end price action 

*Price movements around earnings-releases / economic data

*influences of winter storms on US natural gas markets

*futures contract rolls


As for techniques, one new-classic method is Cointegration:


*

*http://en.wikipedia.org/wiki/Cointegration

*http://gekkoquant.com/2013/01/21/statistical-arbitrage-trading-a-cointegrated-pair/

*http://www.eforenergy.org/docpublicaciones/documentos-de-trabajo/WPFA05-2013.pdf
I am in no way endorsing the analysis and results in the above links.  They are simply some top google results to get you on the path to learn more about co-integration.  
