ONLINE TRADING........
How do we approach this problem to get an answer, I tried the following strategy and fairly satisfied and wanted to share my views, if anyone fascinated to move on further.
The moving function in an online trading is related to time on x-axis and with respect trading value related to countless number of market fluctuations on y-axis. If we are successful to predict what will be the trend or behavior of this curve in the next hour or after a specified time then we can win the trading.
Let the trading value y is a function of time t, y=f(t), y will be for all time random in nature and cannot be predicted easily because of hundreds of uncertainties, t is current time and intervals of say one hour, two hours or even one day. Assuming current value of y will have an influence on the previous set of trading values. For example consider last 48 hours data to predict the next hour, longer periods may be required for acceptable forecasts, strategies varies depends on the type of trading we pick.
Let (t-48),(t-47).....(t-2),(t-1),t and corresponding trading values are y48,y47......y2,y1,y. Function y=f(t) is fully defined including the limits of y and t, however the nature of change on y is so random which cannot be assessed theoretically. The tendency or nature of unknown trading value of y=(y+1) with the time t=(t+1) to be predicted or probability of uptrend (y+1)-y >0 or downtrend of (y+1)-y <0 to be foretasted.
What is the probability of being (y+1)>y Or (y+1)-y >0 ?
I have used Monte Carlo simulation technique to find out the answer to above question, the answer is fairly satisfied. The complexity of the function can be dealt with numerical methods rather than analytical as no closed form solution is obtainable. In this method a set of values of the basic variables are generated with the appropriate probability distribution and the values of the reliability function determined. By repeating this process many times and storing, the reliability can be estimated as the proportion of the results for which the reliability function is positive.
The function y=f(t) tested for the reliability function f (t+1)-f(t) >0 between limits, million times to get the required accuracy. MathPrime built in Monte Carlo functions are used to simulate the above conditions with the Weibull probability distribution, considered as most appropriate as the function y is so random in nature very similar to sea waves.
The above approach may require for 6-12 hours testing continuously in order to set up a trading strategy before doing the actual trading. A strategy of 90% probability or more for the uptrend and less than 10% probability for downtrend can be adopted, no trading will be done for all other conditions, however the strategy to be set only after closely examining the trend on preceding trends used for testing.
Bear in mind Monte Carlo is famous for gambling.