Hello all,I have a question regarding momentum strategies and securities.Suppose we have a common stock. We can observe a whole ton of price movements, then we can see its behavior over that time, like it's distribution of returns, behavior at certain time periods, behavior when certain indicators go up / down / cross, etc. There are entire strategies devoted to taking a position whenever a certain event occurs, like the stock reaches a certain time (winter, for example), or the stock crosses a moving average (for example). Apparently, the basis for these strategies is: if this stock exhibited favorable price movements during a certain event in the past, then there is a good chance it will continue to exhibit a favorable price movement.However, the last statement can only be true if we have the probability density function, and that cannot be determined from simply taking the observation of price movements to be the intrinsic characteristic of the object. For example, just because we have observed a coin flip heads 3 times out of 4, we cannot say that the probability of heads is 3 / 4. We would need an infinite amount of samples to determine the parameters of the object.So, is there is any real, rigorous basis to these momentum strategies? Can the pdf (or an estimate) be calculated from simply the observations? What about securities with very little time history?jonsh

that infinite amount of samples is correct theoretically or else i refuse to believe that there is a 50% chance of a head or a tail i mean nobody has ever taken an infinite amount of samples for that as well.what u mean to say is that large enough samples need to be taken and that is correct. now the winter effect as u r talking about was actually observed over not 1-2 years but a long period of time.i don't know about the technical indicators, there is always a debate about them but if you see something like pairs trading, that has given huge profits and it works on the hypothesis that if the stocks have moved together in the past then they will do so now as well. what you have presented is a very crude form of a strategy like crossing of moving averages, but in general it is not as simple, i mean for starters not every moving average works, only some do, which are found out using backtesting and other methods, so when we are using these methods, we are finding out in a sense the probability of how good they are. its not necessary to have a probability density function always.from the observations what you can calculate is the empirical probability distribution functions of the given data, but the pdf exists only for certain distributions. and to find a pdf you have to go the other way round, first predict that a distribution fits a data and then use the pdf.also when you calculate stuff statistically, u use concepts like confidence intervals and standard errors which give you an estimate as to how accurate your predictions or estimations are, these are generally based on things like number of data points, so an estimation on a security with little time history will itself manifest as a huge possibility of error. so it is imperative that u actually resort to these statistical techniques instead of just u know caring about the parameters of the distribution or the density.