I am not at all sure i understand your post above, but if the success of your intended method depends on the expectation that the variance of price over one time period be equal to the variance of price in another time period, then i would think you will be disappointed in the results of say the the F-test applied to these to variances. In fact i think you will discover that the F-test values are themselves distributed, and that the real movement of price is not entirely random walk, even though the movement of markets in academic textbooks may very well be.. In other words, i would be rather astounded if you were able to predict future price movement magnitude (even if not the direction) by the amount of additional variance you would have to introduce to one time period to force it to have a variance equal to that of another. Please do keep us posted.
Thanks for your post piezoe.. In a typical variance ratio test, we are testing the following: Var(x) = k * Var(y) Where length of period x = k * length of period y. There are different ways to improve the power of this basic test (for example: multiple VR test). I am not really sure that what you mentioned about VR is correct. The VR test has its own problems and I can easily construct a long nonrandom time series which will pass the VR test. One of the VR test problem is the distribution assumption and there are many other tests for randomness that take care of the distribution assumption problem. One example is the RUNS test. Regardless of the details of how you measure randomness, the basic question here is whether there is a randomness reversion? If yes, then let's start thinking about ways to identify and benefit from such behavior.
An assumption is the root of all screw-ups. If you build a trading system on that assumption, you will get your head (and wallet) handed to you at some point. I've come to believe that you need to pick setups (i.e. patterns)that you think have a greater than 50/50 odds, and then place your bet. Use money management and stops. These types of trading strategies generally have less than 50% winners, but can get you in on the big moves, and thus more likely to give positive expectancy. Strategies based on Gaussian assumptions often have a high winning percentage, but usually blow-up at some time.
Let's see... the assumption was do not assume an outcome with certainty. So you are saying that is a bad assumption? That doesn't sound like what the rest of your post advocates. I'll assume you were not directly responding to the quote you referenced.
Did you even read the quote I was referencing? Here, I'll repeat the salient points for you: "It's best to assume that markets are random in the simple sense that you should not try to predict the future outcome with any type of certainty, and devise a way to profit under that assumption." Now that's a text book quote on trading the markets, and if it isn't, it should be. ... and it sounds like you took it to heart, because that's the exact approach you are using in your trading methodology. You're using patterns based on past experience (which aren't worth much more than a 50/50 toin coss, btw) and protecting yourself with stops. ... and as far as that Gaussian bullshit is concerned, here's some really good advice - KISS
An assumption that the markets are completely random means I can enter at any time and always have 50/50 odds of being right about a given directional bet. Pattern recognition is an attempt to get better than 50/50 odds on a given directional bet. I could certainly take non-directional bets under a random movement assumption, and sell OTM strangles. However, that type of strategy almost always blows-up at some point. The markets are certainly Gaussian alot of the time, but not always. It's those times when it transitions from random to non-random, and vice versa that makes the purely random assumption strategy a weak one. Pattern recognition assumes correctly, that the markets are not always random.
You CAN get a coin to land heads 12 times in a row - just start with a few hundred coins flip them all at once, remove the ones that landed tails, flip again, remove the tails, until you are down to one. I use that metaphor to explain the world's largest skimming operation, err, I mean the mutual fund industry. That last coin (or last few coins) are those mutual fund managers that have had good returns over some time given time period.
Many on this thread seem to have lost sight of the most important thing about trading.' IT AIN"T HOW YOU GET IN THATS PARAMOUNT.IT'S HOW YOU GET OUT!!! If it's not totally random there may be some ways to enter propitiously. Even in this case it's still how you get out that determines success or failure.
There are no random markets. There are "seemingly random aspects", as there are equally "seemingly predictable" markets. An elementary example would be issues about the scope of viewing something. Taking a compressed bar chart then testing and concluding that Tick Charts are random doesn't make any sense. (You exclude and compress data between the OHLC and trying find what you just compressed is irrational.) There are lots of fallacies and things to consider when testing and concluding a point out of a test. It seems to me that most of what is discussed in this thread is based on irrational conclusions. ... hrmmm....