Re: Statistical test for equality ?

[stn021]

2014/1/3 pathematica <address@hidden>

Stock prices comprise time series, whose data cannot be modelled by
processes that assume independence of successive variables

 

Yes, if you take what I wrote literally that is true. Stockcharts have a high auto-correlation, lots of dependency on previous states, low entropy and essentially belong to the most boring phenomena on the face of the planet.

Unless of course you add moving averages, triangles, trend-channels and all that other information-elliciting stuff. Just analysing trends in a chart can be a science in itself.

If you do that then one of three things will happen:

1) you start buying stocks and after a while begin to wonder why your capital varies with a high standard deviation while only displaying a comparatively slow downward trend.

2) you become a professional and start buying stocks for other people who after a while begin to wonder why their capital varies with a high standard deviation while only displaying a comparatively slow downward trend.

3) you make statistical tests with a reasonable sample-size and find that your favourite method (and all the other methods) lead you nowhere except to a high standard deviation ... etc ... we already had that. (This is also what this thread is about)


So how can that be? Just look at a stock-chart and you can plainly see trends and patterns and signals. It is so easy to predict what will happen next. Just follow the trend with your favourite method and invest ! Don't be scared by high standard deviation etc.


So this is what happens if you try to predict stock-prices. You should not do that unless you choose option 2).

Instead look at the changes in the prices. It doesn't matter if you choose 5 minutes or 24 hours, you will notice no auto-correlation, maximum entropy and no time-dependence at all.

So you can safely analyse the series without any prior assumptions of time-dependence. Download any stock-history and try it. I used BMW.

What you find is essentially noise, not sure which color. Apply your favourite entropy-measure and see that the series usually has no structure at all. And no predictive value either. Which means to me: no value at all. Except decoration of course. For some other interesting uses see below.

That is the reason why all the fun things from technical analysis do not work. There is absolutely no information in the chart to begin with. And adding up no information leads to more no information.

It is exactly that what make a stock-chart one of the most exciting things on the face of the planet. Not the chart itself, see above. But it is one of the most powerful illusion-generators known to man. Millions are captivated by it devine power. Some life-long, others as determined by the comparatively slow downward trend. Depends.

So where do all the trends and patterns and resistances (is that the correct english word?) come from? To find out generate some random noise in your favourite color (octave can do that for you) and aggregate, simply add up the values, make a plot and print. Add some axis-ticks and take the chart to your investment-advisor. If he starts giving you advice based on the chart - fire him. Fast!

That is what makes stock-charts very educational. Not the chart itself, that is still completely free of any information, but the influence it has on its users. I have come to suspect that many observable phenomena come from aggregated noise. The origin is often not noticed because the series are simply too short. So I suspect that much of the modern (social) sciences deal with structures like that, random brownian motion attributed with some meaning. And preferrably attributed with some funding 8-)

As I said: stock-charts belong to the most exciting things on the face of the planet.

And of course: if contrary to what I said you do find predictable structures in the series of price-changes, then congratulations: you win. Bigtime! Then you can get rich with stocks after all. Sadly I have not been able to do so. Not so far anyway :-)

Cheers
stn