Hello, Is there a statistics theory that confirms weather an occurrence is random or a valid pattern? Lets say when there is a situation "A", "B" will occur. How do I know if the occurrence "B" is random or not? If in 3/3 cases "B" occurs, is it random or "lucky"? 4/5 cases? 10/10 still random or is there a pattern? Thanks
I'm a statistician among other things, but I don't want to belabor this. There is no way to absolutely, definitively "prove" anything with statistics. All you can do is show the probability of something based on observations-and more observations are always better than fewer. So-called physical "laws" are only based on observations. So the question come back to you: which probability is "good enough" for what you want to know. In the medical/scientific statistics world, a 5% chance of occurring randomly is a commonly used cutoff, but you would use a much tighter one in other fields of endeavor, such as designing a bridge or a building to withstand natural conditions. I'm not a meteorologist, but I did take a meteorology class several years ago, and I recall the professor telling us he had just been to a meteorology conference at which the consensus was that no one really know how to predict weather very accurately. Of course, you can watch the news and learn that. I picture all the meteorologists agreeing to this the first day and then blowing off the rest of the conference in the bar. At least I hope that is what they did. I presume this question is prompted not by weather, but trading. Remember that you are not studying a natural science related to physical phenomena, but something subject to the ramifications of human behaviors such as fear and greed. The questions to ask would actually be about expected value (probability of an event times the prize or penalty associated with it, integrated over all the possible outcomes).
in addition the post by drcha above I like to look at it as follows: Statistical measures (calculated) of data, say prices or profits, allows me to make statements with a certain level of confidence. If I want higher degree of confidence, I generally need more data. The tricky thing is that the distribution of the underlying data is key to determining the "degree of confidence", and the distribution is often unknown or can only be estimated using the same data you want to use to make statements about. There are endless ways to fool yourself. There is thus no general answer to your question as its a function of the distributions, and the degree to which you want to make the inference.
Good question. Taleb "Fooled by Randomness" and probably some other texts show tests (coin toss etc.) indicating that you can have series of values seemingly indicating that the process is not random. According to the above series of 4/5, 10/10 can still occur in random process. One indication of random vs nonrandom would be distribution. If it is Gaussian then most probably you are dealing with random process. It is weak and questionable measure.
Look at the various "goodness of fit" tests, such as the chi square one mentioned above. There are others.
One should be clear about the fact that statistics are no rules themselves but rather indications of how probably it is that a certain something is going to happen. So if something happens in 10 out of 10 cases chances are that it will happen the 11th time as well. Especially in trading it is vital to keep an eye on statistics imho. When I watch the stock quotes on http://www.quotenet.com/stock-quotes I always compare developments to events that have happened in the past and try to picture and predict future developments. Since much speculation is involved in trading I would always rely on statistics to reinforce my decisions and actions.
So in a nutshell, I believe drcha is talking more or less about p-values here. In a coinflip example suppose have a coin in which it is unknown whether or not it's a fair coin. From there you want to set your null hypothesis, which would be the coin is not unbiased. You flip it and get 5 heads in a row. Now let's say you've set your significance level at 5%. The probability of getting 5 heads in a row is (.5)^5 = 3.125%. However, depending on how you setup the test, you probably want to also consider getting 5 tails in a row the same exact outcome. If you do so, then your p-value would then be 6.25%. Now philosophically speaking, you can't really say anything with 95% certainty here you can only fail to reject the null with 93.75% confidence but I digress. Now as this is applied to financial markets, there's a heavy underlying assumption here which is the distribution is known and not just that but that your RVs are independently identically distributed. We know this typically not the case, as financial time-series are generally non-stationary (in layman's terms, your distribution and/or moments are not the same at differing time levels) (note: this violates the central limit theorem!). Now if you want to test for stationarity, look into unit-root tests such as dickey-fuller. Generally speaking though, I try not to over complicate things with statistics. It's much more important to me that trades have a solid theoretical reason as to why they should work. They can certainly be there to help back up ideas in which you'd like to test but will not make or break strategies for me. If you focus too heavily on the statistics, I think you'll begin to run the risk of overfitting your model (i.e. generating equity curves that pick up noise).