what do you guys think about this?

I understand what he means, but I cannot explain this in a few words. Let me only explain the nonlinearity part.

Linearity means that the addition principle hold. If you have a linear operator L and it acts on something, let's call it x and y then here is what happens:

L(x+y)=Lx+Ly, acting on the sum of arguments (x+y) produces the sum of Lx and Ly.

This does not happen for nonlinear operators. Take the power operator, say x^2, let's call this operator N. Here is what we get in this case:

N(x+y)= (x+y)^2=x^2+y^2+2x*y=Nx+Ny+2x*y, as Nx=x^2 and Ny=y^2.

So as you see the addition rule does not hold here as:
N(x+y) /= Nx+Ny because we get some extra term 2x*y.

That's it, don't have time for more now.
 
options strategists have edges on this non-linear stuff. also if the distribution is not normal, then a better the options price model still need to be derived.

:p
 
Quote from Gordon Gekko:

i'm not smart enough to even understand it really.. for example, after reading the following, i could not in my own words explain it to someone else. lol can someone please explain this in simple terms? :(

http://vader.brad.ac.uk/finance/tfp.html

specifically, i'd like to understand this part:

"In spite of the volumes of rubbish in classical economics texts, the Efficient Market Hypothesis is NOT TRUE. There is now overwhelming evidence to the contrary. Moreover, mathematical analysis of financial time series shows that the market is NOT normally distributed, it is more like a Pareto-Levy distribution. Unlike normally distributed time series which have computable moments, the market distribution is NOT well behaved - for example, the Pareto-Levy distribution has INFINITE variance! In other words, financial time series are NOT STATIONARY and they are NOT LINEAR. Consequently, EVERY filter you will ever find in any book on signal processing, be it a simple moving average or an advanced Kalman tracking filter, is about as much use as a chocolate padlock in financial applications! What is not written in two inch high letters on the first page of these books (but what is always tacitly assumed), is that the signals are STATIONARY and hence LINEAR filtering is applicable. This is generally true for signals in communications equipment but it is NOT true for signals arising from natural phenomena, especially the markets.

What is required for the markets is NON-LINEAR analysis. This is, of course, MUCH more difficult both theoretically and practically than the simple linear cases, so textbooks don't bother with non-linear stuff; it is just too difficult. Likewise, vendors of technical analysis software generally use what they can find in the literature, at most tarting up the algorithms a little here and there. But these algorithms don't work! Gauss proved three hundred years ago that the best estimator of a random process is its moving average. If the markets are random, then moving averages should make you money every time. But they don't. Now you know why."
More...


Oh, not again... :D
Not another EMH battle. That guy has a few points but he's overdoing it b/c he seems to be plugging smth of his. Where he is wrong is that most EMH tests incorporate various non-parametric tests, and thus the distributional assumptions aren't that big a deal.
PS. Markets are generally pretty darn efficient. Aside from the manipulations, microstructural effects and some phycological repercussions. Unless you are in the know (e.g. see the order flow), you are like a blind sheep among wolves. I got my ass kicked today and am a bit more inclined to preach EMH than usual...
 
Hi GG,

Lets start at the start.

What is Linear Analysis? Historically Linear Analysis was concerned mostly with the behaviour of temperature, such as the weather, or the thermodynamic properties of materials such as metals etc.

Temperature is linear. For the temperature outside to go from 6 degrees to 10 degrees, it first must go through every point between 6 and 10 degrees. i.e 6.1, 6.2, 6.3 etc etc ect.

As you can see, each data point is connected and interrelated to the last data point.

Studying the interrelation between the data points in Linear Analysis.

Non-linear analysis is studying time series data where the data points do not always bare relation to each other. For example, the number of car crashes that occur each month.

Over a year the data may look like this January - 23, February - 45, March - 11, April -16, May -23, etc ect.

Non-linear essentially means chaotic.

See my previous posts on chaotic systems. (Chaotic, not to be confused with random)

Now are these car crashes completely random? By studying the data we may find that they are actually not. In fact over 10 years it appears that February has by far the most car crashes. Is the fact that more crashes occur in Feb completely random? The reason may be simple and obvious. For example the weather could make driving conditions worse. So while these is some randomess to the crashes, the distribution over a year in not competely random. Just like the stock market.



If we converted this data to a bell curve we would represent February at the top of the bell with the highest number of crashes. The months with the lowest number of crashes would be on the outside of the bell.

Now to the stockmarket. Stockmarket data in non-linear.

By applying a moving average to share price data for example, we make the data more linear.

Studies have been done on the distribution of share prices over the past hundred years and when plotted on a bell curve it has been found that the number of extreme changes in data i.e, crashes and bubbles for example occur too frequently to be regarded as just coincidence. This indicates that the markets are not completely random. There is some behavioural reason behind what is occurring.

So while markets remain chaotic that are not random.

In summary. All that long winded crap just means that the price of the market tomorrow bares some relation to today, but it is not completely controlled by yesterday.

Runningbear
 
About non-linearity, well the term can have different sense depending on the context, for example many people think that non linearity means that a model is just different from a straight line. But in the context of chaos theory, a model that does not give a straight line isn't necessarily non linear. To really understand I need to write that a linear model can be writen

x[n+1]=a*x[n]+b where a and b are parameters (not dependant on time whereas x is a variable whose value depends on time n)

You will remark the iterative form definition above.

For example the interest compounding is linear since

S[n+1] = S[n]*(1+r) where r is the interest rate (here b=0)

when a > 1 this give not a straight line and there is no limit to S which can tend to infinite !

A non linear model cannot be written as above. the most well known and studied is the logistic function where you "dump" the infinite growth of a*x[n] by a new term (x[n]-1) so that the growth is finite and cannot go higher than Xmax.

In that case you will have different behavior:

If a = 0 x will tend towards 0: it is the attraction point

If 1 < a < 3 the attraction point will depend upon a

When a > 3 you will have 2 or more attractions points. this is called bifurcation and give the image of a system be chaotic.
 
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