Do some trading firms recruit people who understand econometrics and time series, or Bayesian econometrics? I would like to be a trader, but I don't want to trade by technical analysis method, which I consider as man-made "technical", I prefer to calculate some beta, alpha, or correlation coefficient. Are there some trading firms doing this statistics trading? Thanks.

There are plenty of firms and hedge funds that use quantitative methods to trade. However, I doubt that just understanding econometrics and time series, or Bayesian econometrics is gonna cut it. They are looking for PhDs in maths and physics.

From your previous posts, I understand you're a M.S. Finance candidate. My advice is to continue to do well in school. If you haven't been doing well to this point, you better start now. Investment banks hire M.S. Finance students primarily as analyst if you lack experience to join their trading desk. Hedge funds such as D.E. Shaw and smaller quant funds will also hire M.S. Finance students. Most quant funds aren't looking for traders, they develop their own black box/automated trading systems. So you will be modeling and programming. Most traders on ET trade their own accounts and would never even be considered for positions with investment banks or billion dollar hedge funds. A few formed their own hedge funds, but will never see multi-million dollar yearly salaries.

I use a method of statistical analysis in addition to technical analysis and I can tell you statistical analysis has more flaws than technical. Even if you find a price movement that goes 3 or 4 sigma, for example, there's no gaurantee the market average won't catch up to the extreme price movement and render it non-extreme. Today's price action was a perfect example of that. It doesn't matter what type of analysis you choose. All of them have their merits but they all have their weaknesses. If you are aware of the weaknesses then you can develop strategies to handle the weaknesses. Choose a method that suits you and learn it inside and out. What are the strengths, the weaknesses, and how to you handle both situations. That will determine your success, or lack thereof.

Be aware that most quants, statisticians and econometrics are just a bunch of nerds who can't develop winning strategies, they just fool themselves with complex formulas. So be careful. If you want to get into professional level strategies, get into pair trading. A very simple yet effective pair trading idea: Long oil companies short home builders/mortgage troubled financials.