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.
Oh, not again... 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.