21–29 of 29 posts
It is quite a leap to go from 'not gaussian' to 'not random' as done here. All that has been falsified, as far as I can tell, is a very simple model of a random walk with normally distributed disturbances. It would be interesting how much better it becomes if higher moments, in particular kurtosis ('fat tails') are included.
The article clearly states that the test extends to many forms of randomness beyond Gaussian: "Nevertheless, the desired effect of stochastic volatility namely, fatter tailed distributions ..." "... we want a test for the random walk hypothesis which passes (it concludes the market is random) even if the returns demonstrate heteroskedastic increments and large drifts. Why? Because both of these properties are widely…
I did not read the link but Benoit Mandelbrot basically showed this 30 years ago. So what's the news?
Not sure why I get downvoted http://www.amazon.com/The-Misbehavior-Markets-Financial-Turb...
Earlier quoted context omitted.
[deleted]
https://news.ycombinator.com/newsguidelines.html > In Comments Be civil. Don't say things you wouldn't say in a face-to-face conversation. Avoid gratuitous negativity.
Earlier quoted context omitted.
The article clearly states that the test extends to many forms of randomness beyond Gaussian: "Nevertheless, the desired effect of stochastic volatility namely, fatter tailed distributions ..." "... we want a test for the random walk hypothesis which passes (it concludes the market is random) even if the returns demonstrate heteroskedastic increments and large drifts. Why? Because both of these properties are widely…
His model is not heteroskedastic. The log-error terms are i.i.d, so they have actually all the same variance. The distribution they are sampled from is a normal variance mixture.
No. That is the consequence of the efficient market hypothesis being true. The hypothesis itself is subtly different. Though most people miss it:
All information from past prices is in current prices.
That is a better formulation.
I spent five years studying it and I think it is robust if you remember that it takes time for information to be consumed. That is why HFT works, because it acts before the information can be processed.
" weak form of the efficient market hypothesis which states that: future prices cannot be predicted by analyzing prices from the past ..." No. That is the consequence of the efficient market hypothesis being true. The hypothesis itself is subtly different. Though most people miss it: All information from past prices is in current prices. That is a better formulation. I spent five years studying it and I think it is r…
All information from past prices is in current prices.
Duh!
Earlier quoted context omitted.
His model is not heteroskedastic. The log-error terms are i.i.d, so they have actually all the same variance. The distribution they are sampled from is a normal variance mixture.
Interesting. I'm no statistician but the blog post states that the authors of the original paper (Lo and Mckinlay) claim the test is heteroskedasticity-consistent. So what are you saying? Are you saying the original paper is wrong? That his example was wrong? (This seems more likely) And if the example is wrong, is it wrong to say it is heteroskedastic AND wrong to say it is a stochastic volatility model? Or just tha…
The model in the webpage however is not heteroskedastic (literally "unequal variance") because all the log-increments are iid. It could be legitimately considered a geometric Brownian motion with stochastic volatility, because the log-error is indeed normally distributed with variance picked from some stochastic distribution, in this case a normal distribution. This term however is normally used for models in which the volatility has more structure (e.g. the ARCH or GARCH models which are mentioned in the page).
I did not read the link but Benoit Mandelbrot basically showed this 30 years ago. So what's the news?
Do you have any links to Mandelbrot's work in this field?