Basic Statistic/Probability Questions

[Omega Point]

Hi,

I'm investigating whether I can make money in the stock market based solely on past probabilities of the market having an up day or down day. (I know I'm probably not the first to try this but what the heck. I also know that past performance is no guarantee of future results but I'm looking at probabilities for an up or down day and I'm not too concerned with long-term appreciation since I don't plan on holding the stock for more than a few days at a time at the most).

I'm looking at a particular market index, which anyone can buy and one that follows the overall market. A market index is relatively safe and I don't need the index to move up very much in any given day to make a sizable amount.

The data set I have should be fairly representative, I've gone back to 1/2/02 (over 1,000 data points). Here's a brief summary of some of the data:

Total open market days: 1,029
Total up days: 536 or 52.1% chance
Total 2 consecutive up days: 137 or 13.3% chance
Total 3 consecutive up days: 67 or 6.5% chance
Total 4 consecutive up days: 32 or 3.1% chance
Total down days: 493 or 47.9% chance
Total 2 consecutive down days: 119 or 11.6% chance
Total 3 consecutive down days: 58 or 5.6% chance
Total 4 consecutive down days: 32 or 3.1% chance

Ok, here are my questions:

1) If there are two consecutive down days, what are the chances that the next day will be up? Is it 52.1% chance just like any other day, is it 94.4% (100%-5.6% for 3 consecutive down days), or something else?

2) Likewise, if there are two consecutive down days, what are the chances that the next two days will be up?

In your answer, please write the formula(s) you used since I plan on using for three consecutive days and so forth.

Thanks for your help, it's been long time since my college statistical class days.

 

[stapel]

1) If there are two consecutive down days, what are the chances that the next day will be up?

The point of a process being random is that past behavior cannot predict future behavior. The fact that the market has been "down" for two days in a row says pretty much nothing about what it might do on third.

Sorry.

Eliz.

 

[Omega Point]

Ok, then assume it's not a random process, then what would be the answers to my questions?

 

[stapel]

Ok, then assume it's not a random process, then what would be the answers to my questions?

Until you specify your parameters of and formulae for your non-random process, I see no way to make any predictions about it.

Eliz.

 

[Omega Point]

Ok,

Let's assume that this is a machine that produces widgets but it's not a very good machine and produces many defective widgets.

Let's assume the following data based on the machine's results over the past few years:

1,029 widgets produced per day.

52.1% chance of producing a non-defective widget
13.3% chance of producing 2 consecutive non-defective widgets
6.5% chance of producing 3 consecutive non-defective widgets
3.1% chance of producing 4 consecutive non-defective widgets

47.9% chance of producing a defective widget
11.6% chance of producing 2 consecutive defective widgets
5.6% chance of producting 3 consecutive defective widgets
3.1% chance of producing 4 consecutive defective widgets

If the machine produces a non-defective widget, what is the probability that the next widget is non-defective?

If it produces two defective widgets in a row, what is the probability that the next 2 widgets will be non-defective widgets?

 

[royhaas]

Check out the Markov Chain example of predicting the weather given in
Markov Example.