Random Flow Theory and FOREX - page 65
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The moderators deleted the "options" joke. They're so fast.
Here we need to define what stationary process we are talking about. But frankly speaking I don't like this definition yet.
Let's not go to extremes. Let the process be stationary in the narrow sense, where we see a graph and not Everest and Mariana Trench.
I confess my ignorance on the subject of completeness and inconsistency. If I have offended you, faa1947, I apologise. But still, yours
- is a kind of nonsense... And the "Inverse Theorem" (which of course is not inverse to the Direct Theorem, but inverse to the theorem proved by Gödel) is valid only for sufficiently rich mathematical theories. I hope I didn't get it wrong here?
It just snapped a long time ago with Gödel, so you'll excuse me. None of us will develop a strictly formalized theory, but for us, practitioners, the most interesting conclusion of Gödel's theorem is that we must discuss first of all the initial premises of any statement. Since the beginning of 20th century we have accepted "BP is a random process with normal distribution".
Lyric. And that's why it fell apart. I dealt with graduates of the Faculty of Mechanics. My knowledge and abilities are not next to theirs. These people not only know a lot, but are able to master almost everything in a week. You give a job to such a genius, and he brings it back and says: "I proved that the sun rises in the west and sets in the east". I say in a worker peasant way: "It's 9am, let's take a compass and check". "No", he replies, "show me the mistake in the proof". And then comes the comment describing my education and mental capacity, that I am disproving their brilliant theory with a child's compass. All my acquaintances of mechmatovites are like that, maybe it's bad luck. Unfortunately, there are a lot of such people - clever and scholarly fools. They set up efficient boundaries and fool the suckers with portfolios with manageable risks. The forum is full of them. Writes: "I did the mathlab calculations". What he put on the input, how to understand the result, but stands firm - do not mess with the compass.
Constructive. It is best, initially, to consider the TS (the method on which it is built) as a black box. And if the output from the box more or less clearly, then the input is just a mess. Maybe it would be constructive to classify not BP, and methods of its processing (black boxes) and collect a list of these methods with reference to the appropriate sources and issue an article to ensure the accumulation of information.
Yes, I had it running, I was just about to use it to build a normal distribution. It worked, although it doesn't seem to do that.
Some people have already stated this here. Would you be so kind as to provide a scheme, algorithm, proof or whatever you like, but meaningful, to show how to do it. You can confine yourself to random rambling with a normal distribution. Pls.
Random walk is NOT a stationary process as it is time dependent and goes to infinity.
Weak or wide-sense stationarity A weaker form of stationarity commonly employed in signal processing is known as weak-sense stationarity, wide-sense stationarity (WSS) or covariance stationarity. WSS random processes only require that 1st and 2nd moments do not vary with respect to time. Any strictly stationary process which has a mean and a covariance is also WSS.
A stationary distribution with thick tails can play a cruel joke on such a strategy, as the notion of "far enough" is extremely vague or non-existent in this case (the second point is, say, infinite).
A stationary distribution doesn't play any jokes if you have estimated its parameters and type correctly. Don't get hung up on the normal distribution. If you are afraid of fat tails, use a stable distribution. The strategy will not change from this.
A stationary distribution is no joke if you have estimated its parameters and type correctly. Don't get hung up on the normal distribution. If you are afraid of fat tails, use stable distribution. This will not change the strategy.
Assume that our price process corresponds to a Cauchy distribution with constant parameters. This distribution is exactly a stable distribution that has not only no finite variance, but even no expectation. And this strategy is very dangerous for it.
Or are you talking about some particular cases of stable distribution?
Huh. It's working. I just didn't have "allow dll imports " checked in my MT settings. :)
So, apologies for my complaints to the strator :)
Suppose our price process corresponds to a Cauchy distribution with constant parameters. This distribution is just a stable distribution, which not only has no finite variance, but not even expectation. And this strategy is very dangerous for it.
Or are you talking about some particular cases of stable distribution?
I am talking about estimating process type and parameters with accuracy sufficient for practical purposes. If you've determined that your process has non-fixed parameters, then you need another process - go and find it. Personally, so far I'm satisfied with normal distribution, although my fellow wrestlers actively match me up with stable. Naturally these are special cases, as far as I know it has no general solution.