A proficient trader could tell you which of the two charts was the real market data in the vast majority of instances. In a few instances all that could be stated is that there is no trade on either chart. Curiously, it would be possible (but unlikely) for the randomly generated chart to resemble an actual market condition, but only by coincidence. We would therefore need to run a large sample size to make any work valid. I would think that given 100 pairs of charts, a proficient trader could correctly identify the random data chart in at least 80 of 100 cases. Yes.
Evidently, the question in the opening post is a subject of a lot of modern academic research. See, for example NONPARAMETRIC STATISTICAL TESTS FOR THE RANDOM WALK IN STOCK PRICES or a longer list from google.
All good questions, but I will just touch on the notion of random data. A typical way to do this is using the spectral function, http://en.wikipedia.org/wiki/Spectral_density The energy of a random signal is spread out over all bands. The problem with this sort of analysis is that it assumes the signal is stationary, an assumption that is simply not true in financial data. I will also point out that the whole notion of random is a very sophisticated mathematical concept. What may appear random to a given technique, can be shown not to be random with more powerful techniques. Note that some prediction is easier than other. For example, if two firms announce an M/A, it is easier to make money trading this M/A, then it is to try to predict general pair trades. Only the most sophisticated traders try predictive trading, but there are easier ways to make money.
So many responses but only one person so far has answered the question with a link to a list. The random walk index I presume is probably designed for the task. If I recall so are the vertical horizon filter and perhaps more common r-squared. Doesn't mean they are reliable indicators at least not alone or in the most basic form.
I don't understand what your problem is. Academics actually try to study things in precise, quantifiable ways and most make steady income well above the average American. A typical professor makes between 70-120k a year, they have job security since they have tenure, and they get awesome retirement and medical benefits. Not to mention they get to actually do research on topics that benefit society, such as cancer treatments or more efficient engines. So why don't you stop using medical science, vehicles, airplanes, bridges, computers, cell phones, the internet, and all the stuff mined from the earth that technology allows since us stupid "academics" are worthless failures. Furthermore, professors get to have a relatively easy workload compared to most traders and office workers. However, they earned it because, as a PhD student, I can tell you its hard as **ck to get one. In industry, PhD holders can make well over 120k. This includes the Finance industry where they have the potential due to education and ability to make more money than you will ever dream of. Those that do this are sitting fat on Wallstreet and you probably have never heard of them because you are too worthless of a human being to be worth their time. Have you ever heard of a Quant? All of the aforementioned being the case, academics are hardly "Failures" ***hole. Most day traders go off of gut feelings or technical analysis that is barely mathematical at all. Any idiot can watch the news and be like, "wow, the market will go this direction because these numbers came out this way" or look at historical support and resistance lines. My friend and I made 150k for our account over two years doing this with and trend lines. As a mathematician-in-training, I didn't use any of my more advanced knowledge to do it other than I programmed some indicators and a few automated things to assist manual trading. From a mathematical perspective, there IS randomness in the market, however using various mathematical topics including probability you can make fairly accurate predictions in the short term. You will always get some surprises, but probability theory allows for it since you will know however unlikely an event, it will happen sometimes. The financial system is more accurately described as a "chaotic system". Don't let the words mean more than they are to your feeble mind. It just means incredibly complex, were small changes in conditions can have major results. So, stop pissing on other people and go continue to trade using your "superior' techniques by yourself.