Which math topics for analyzing stock market data?

[arzoo]

Hi,

I've been given a task to decipher patterns, cycles or any other trends within financial market data that will give a probable advantage in forecasting where prices will go, and possibly how big a magnitude a particular move can go.

I'm not a math major, and haven't really had too many math courses and I'm taking this intern job because I was curious about financial markets, which I finding very interesting so far. All I've got is 1 semester of calculus, plus the algebra, geometry, trigonometry, etc in high school so not really much to go on.

I've been scouring the web and found so many topics of math being used in finance my head is spinning. My question is if you guys could guide me as to which topics I should learn and in what order (if such is relevant). I've seen statistics, number theory, time series, and a boatload of others but am not sure which is relevant because some seen really way out there for my needs.

The data given me has been daily prices (open, high low, close) for the day for 20 years (certain instruments), from which I can also construct opens, highs, lows, closes for weekly, monthly, yearly basis.

The other is intraday data, so what I have is a log of all transactions for each day, something like asset name, time of trade, price, volume traded. For example MSFT (microsoft), 093011 (done at 9:30 am 11 sec), 132.9 (dollar price of trade), 300 (shares traded).

Each day yields something like 50,000 to 150,000 of such entries for each asset, depending on how many trade executions are made.

So what I'm trying to figure out is what I call 'statistical pattern recognition', or 'numerical patterns', but when I googled this phrase it came out to something that looked different, though I may be wrong. Meaning if 'so and so' pattern (for ex. if you have 3 consecutive days where the low of the day is lower than the previous day's low, the next day's close ends higher than the open 73% of the time), or something like for the intraday data, if you splice the time of the day 9:30-3:30, into x segements you'll see that segment y has on average the smallest range while segments z and w have larger ranges.

Another would be, for a given asset, if it's 15-min bars (which are reconstructing each 15 mins of a given day to a 'bar' with an open, high, low, close for that 15 mins), moves past standard deviation of 2.5 away from the mean, it is likely to revert to the mean.

Hope you guys can guide me as to which math topics I need to read up on. Very much appreciate any help.

In the end I hope to be able to build models the firm can use to get a statistical edge in the markets. Part of my goal is to see things from another point of view. To be able to treat the numbers as numbers and not stock prices, like arrays of experimental data or sets where you have all open prices are 1 set, the highs are 1 set, etc. or some other mathematical or statistical means.

Thanks.

 

[danago]

Many books and articles on security selection and market timing will divide methods into two broad classes--technical analysis and fundamental analysis; the former looking at patterns in price and volume data, and the latter looking at the intrinsic value of the underlying security. The method that you seem to be interested in is akin to technical analysis.

Try a google search for "technical analysis" and see if that is what you are looking for.

 

[romsofia]

PDEs (partial differential equations) play a big role, I believe.

 

[arzoo]

Thanks for the suggestions.

@Danago, you are correct. Technical analysis is what people use to look at price patterns. They have a number of people doing that in the firm I intern for. The head of the desk I am working for wants to come up with something different from the traditional things found in technical analysis because they do have a number of people doing it. An according to their experience strategies that aren't known to the world are the best since you don't have people or certain funds waiting on the opposite side to do something against you.

Since this all the information was basically a set of numbers, I wanted to ask you guys who are experts at math if there is a way or methods to extract certain patterns, cycles, correlations, etc from the data. Treating them more like statistical data or sets of numbers, rather than viewing them as stock prices.

@Romsofia, I'll look into PDEs and see if I can find anything there.

 

[romsofia]

You'll want to look at hyperbolic PDEs, I have a few economic grad students in my PDE class and my prof. said that'll be the most useful part of the class for them (but, I know economics isn't just the stock market, so hyperbolic PDEs might not apply to that).

http://mathworld.wolfram.com/HyperbolicPartialDifferentialEquation.html