Quantocracy is the best quantitative finance blog aggregator with links to new analysis posted every day. Information about them has been moved off to my page on Egalite bets. This does not imply true randomness i. Non-cashable bonuses may be called "sticky" or "phantom" bonuses. In addition, behavior of these generators often changes with temperature, power supply voltage, the age of the device, or other outside interference.
This was a great article! I really enjoyed reading it. There was tons of stuff that went right over my head, but I love having exposure to such information! I will definitely come back for more. Thanks Rafeh, I'm happy to hear that you'll be coming back.
If this stuff interests you, you should also check out the NIST documentation because it is considerably more details and of a very high quality. I noticed today that some of their websites are down, but the Google cache system is still working. I will be reading this again and again, and I see your code as incredibly interesting and useful in the study of this and other processes. I am personally not a believer of global randomness, so it's no surprise that the percentage of passed tests decreased as the time window increased.
You can take several markets and notice by eye the long-term, non-random trends. I think it would be interesting to test the same experiment in very small time windows, which would also be interesting to high frequency traders. Take millisecond tick data for 1 year and make your windows on the order of seconds, minutes, hours, etc. Couldn't have said it better myself; like I said in the article the challenge comes in getting enough data to keep the results statistically significant. So, if you have high frequency data at your disposal let me know and I'd be happy to help with replicating the experiment on lower time-dimensions.
I think you are onto a really fantastic idea. A good source I often use is the millisecond level tick data from Duckascopy. They both download and process the tick data into CSV format, with some options such as weekend data, time zone conversion, etc. USD seem to be very reliable with tick data several years back. If I have time someday it would be interesting that I adapt the experiment to such data.
I have done some work with runs tests and I have noticed that results depend on timeframe and look-back period. For example, with a look-back period of n bars, in daily timeframe the result may be random state but in weekly timeframe it may be a trend. The fractal nature of markets allows for randomness inside trend and vice versa. Also, for runs tests, I have notice that as the look-back period increases, the results show trend no matter what.
First off, great blog. Secondly, let me get back to you later tonight. Doing so is quite easy, I just need to collapse the returns to a weekly frequency using the Quandl API. I didn't look at lower frequencies, because you need many data-point for some of the tests to get statistically significant results. That said, the runs test doesn't require a lot of data points, so for this test it should work fine.
I'm interested in the relationship between liquidity and entropy. Just yesterday, WSJ featured a chart showing how the ask-bid spread peaks at the market open and takes about a half-hour to decay to the usually steady state of high liquidity throughout the day. I think the data points you've examined differ in their information content. Some are a more accurate measure of "price" than others. What I'd expect is to find the highest liquidity market samples seem the most locally random.
The question then is whether, at their points of least liquidity, they become inefficient enough to show a "hackable signal". That's a really interesting idea I'd like to investigate this idea, so I'm sending you an email. You miss one very important and critical thing. Market randomness is different from other types of randomness. As soon as a "weakness" appears it is immediately exploited.
You mention the Malkiel book, but you did not get that part. He points out a large number of systems that worked until they were discovered and published. So this is not exactly like tossing a fair coin. The current market is "more random than random" so it is not unexpected that any tests will demonstrate it is not random. The market is random as it is not predictable [the basic definition of randomness].
If it was predictable [thus not random] it would very soon adapt so that it would be again unpredictable. This meta-randomness has to fail all randomness tests as it is a characteristic of a different type.
Thanks for the comment: I like your argument and I agree with some aspects of it. Where we disagree is semantics really because what you are describing is not randomness it is actually chaos. As I mentioned in the article, I like to believe that markets are actually complex adaptive systems which do exhibit the properties of randomness from time to time, but that does imply that they are random walks. This supports the argument that markets are complex adaptive systems. Perfect Imperfection, Agent Based Models 2.
The only other comment I have is that some patterns have existed for many decades and are highly stable. People have made, and are still making, tonnes of money off of these simple concepts and have managed to beat the market for decades. This empirical observations also supports the belief that markets are not random because, as per the definition of a martingale, it should be possible to devise a strategy which beats a random walk in the long run.
Thank you for your answer. The question of semantics is important. But the substance of my [hopefully] constructive criticism is not addressed.
Obviously that the market is a chaotic highly adaptive process, but also by their nature, random. And by "Random" I mean unpredictable.
Yet you say "People have made, and are still making, tonnes of money off of these simple concepts and have managed to beat the market for decades. This said, it does not mean that there are no such methods, but if they exist they are not up to scrutiny and it is far from clear if they would pass the test of time. This is an interesting discussion. Here I would like to concentrate on this interesting statement:. Some authors claim that momentum effects were due to some random events, such as the dot com bubble.
My own research shows that momentum profits are not significant and can be due to luck. Especially profits from time-series momentum are due to luck after the s top.
This is also related to a switch from momentum to mean reversion. One problem is that hypothesis testing is conditioned on historical data.
If the sample is not representative, then there is error when we find evidence against the null. It could be that we need an order of magnitude of more data to perform accurate hypothesis testing and that would lead to rejection of the alternative. Therefore, my conclusion is that markets are random and our tests are fooled by non representative samples due to some other random events that disturb randomness oxymoron but could be true and that opportunities exist in random markets due to temporary anomalies that appear and disappear and are related to similar patterns in participant reactions.
I have identified price patterns and published them in books that stayed profitable for 10 years. Everything is documented in my blog. I used algos that made tons of real money but suddenly stopped working. Popular mean-reversion and momentum algos will also stop working at some point without any warning. Like this simple mean-reversion system:. Thus, we are fooled by randomness into believing there is no randomness due to limited samples but that can work to our advantage as Stuart has written some place I can't find it now if we can identify a distribution with a positive mean and skew and maybe leptokurtic although this is debatable.
Congratulations on your new job. It sounds like a very exciting opportunity. Great article - very well written, and interesting conclusions. I will be sharing this with my quant friends. Hey Chiedza, fantastic thank you, I'd be interested to hear what they say. I hope you are keeping well! Now I'm beginning to wonder if any correlation with the British Pound is a result of insider trading I believe it would be better to use a random market model for comparison, instead of the Mersenne Twister output.
For example, you could include a row in your final tables for data produced by the Heston stochastic volatility model of the same length as the market data. I believe that would be a more accurate demonstration of your point, otherwise you're sort of comparing apples to oranges. Great post though, I enjoyed reading! I couldn't agree more. I came to this exact same realization sometime last year while reading Lo and MacKinlay's papers.
You live and you learn: The "problem" with the NIST suite in the context of markets is that it is testing for pure randomness My goal for this year is to publish an in-depth set of results on numerous stochastic process models as well as thousands of de-trended and discretized real-world financial time series. I'd like to also contrast the results of the NIST suite against more "purely quantitative" measures of randomness like the variance ratio test and the lempel-ziv compression algorithm.
It's in the works, my biggest constraint is time. Thanks again for the comment Michael! I am very greatful to see your pictures. The kids are adorable and I cant wait to see them in person during passover. I will be lergonvtimoarow afternoon. Eine angemessenere Definition der Entropie einer Zeichenkette liefert die bedingte Entropie und Quellentropie, die beide auf Verbundwahrscheinlichkeiten aufbauen.
Die Entropie wird hier als 1 bit definiert. Gemessen als Entropie liegt die Ungewissheit bei nur noch etwa 0, Dies wird im folgenden Bild dargestellt.
Die Grenze zwischen beiden Bereichen ist nicht scharf zu ziehen, sondern nur mit einem Wahrscheinlichkeitsniveau von z. Je weiter man von der Grenze weg ist, desto klarer ist die Zuordnung. Der Mathematiker und Zufallsforscher Chaitin hat 2 Beispiele genannt:.
Trotzdem unterscheiden sie sich fundamental. Dies ist Gegenstand der Informationstheorie, die erstmals von Claude Shannon formalisiert wurde. Die erste Reihe hat zum Beispiel eine Entropie von 0 oder nahe 0, die zweite Reihe hat eine Entropie von 20 bit.
Dann ergeben sich die allgemeinen Aussagen: Er ist mathematisch auf verschiedene Arten definierbar. Umgekehrt kann man mittels komplizierter Rechenverfahren Zufallszahlen erzeugen, die ausschauen wie echte z.
Selten findet man eine brauchbare mathematische Definition. Will man Ordnung wie es beispielsweise die Kristallchemie tut als Gegensatz von Entropie ansehen, dann kann man folgende Formel aufstellen. Die Ordnung ist hier der Kehrwert der Entropie. Mit dieser Definition gibt es ein Problem: Eigentlich hat Chaitin bei seinen treffenden Beispielen noch etwas vergessen: Zwischen perfekter Ordnung und kompletter Zufallsordnung, gibt es noch gemischt geordnete Strukturen.
Bis jetzt ist es nicht gelungen, in den Nachkommastellen der Kreiszahl Pi eine mathematische Ordnung oder periodische Wiederholung zu erkennen. Ansichten Lesen Bearbeiten Versionsgeschichte.
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