Linear regression technical analysis

http://www.fao.org/docrep/W5449E/w5449e04.htm

As for me the main model of the technical analysis is the linear regression. The oscillators are not intended to measurecycles, they are intended to measure the deviation from the central line of the linear regression. and yes, when you deviate from those center line there is an increase probability that you will reverse to the center line of the linear regression.

That is the true reason why oscillator tend to work (of course according to the theory).

That theory is completely different from the Ehlers theory of trend mode and cycle mode.



I am not sure that I am really clear, that is why I am giving to the introduction to the video of linear regression.

And yes that is the basic model. Imagine: trend lines, Andrew's Pitchfork theories (look here it is very revelative how he defines the linear regression manually).

The second important model is the heteroscedasticity of the volatility. All the patterns of the technical anlysis are driven by this phenomenon, it is related also with the market state analysis.
Definition of 'Heteroskedasticity'

In statistics, when the standard deviations of a variable, monitored over a specific amount of time, are non-constant. Heteroskedasticity often arises in two forms, conditional and unconditional. Conditional heteroskedasticity identifies non-constant volatility when future periods of high and low volatility cannot be identified. Unconditional heteroskedasticity is used when futures periods of high and low volatility can be identified.

Read more: http://www.investopedia.com/terms/h/heteroskedasticity.asp#ixzz1swlH5Cfh


Investopedia explains 'Heteroskedasticity'

In finance, conditional heteroskedasticity often is seen in the prices of stocks and bonds. The level of volatility of these equities cannot be predicted over any period of time. Unconditional heteroskedasticity can be used when discussing variables that have identifiable seasonal variability, such as electricity usage.

Read more: http://www.investopedia.com/terms/h/heteroskedasticity.asp#ixzz1swlOdQge



The Third important thing is coming from the chaos thoery by measuring the fundamental properties of the price time series. Fractal dimension and Lyapunov exponent.

Those measurements matters because imagine the third window when you are using a limit order. Knowing the fractal dimension will save you to prevent your stop to be hit when the limit order is activated.



So here we are. We can explain most of the common technical analysis by some mathematical models.

By this theory it is clear that the oscillators may be adapted according to the volatility arround the central tendancy.

Do you see really what they are doing ? They measure how far we are going away from the central tendancy. If the central tendacly is going up we are saying up trend, if the central tendancy is going down (down trand), and if it is horizontal we say (range).



Those posts are a little bit long but they are related to the general theories underlying the technical analysis.

We are looking for a kinf of unifiying theory. Why those efforts? Well that is because we see how the linerar regression together with the volatility models are expaining so much of the technical analysis.

We ask ourself what the creators of this or that technical method really see. What is the mathematical underlying reality of what the technical authors really see.

To this we can add the psychology we have seen how the psychology is creating an accumulation of orders at specific places. Then in turn those places act as attraction points and are activated.

All this is forming a very complex soup.

We can observe this but our knowledge as a speculative knowledge is limited.

Nonetheless, speculative knowledge is not perfect knowledge of the phenomenon under inquiry, on the contrary, speculative knowledge is precisely imperfect, partial, fragmentary, as such a knowledge is rooted in the necessity of contingency, which implies the knowledge that perfect knowledge is illusory (not in an epistemological sense but in an ontological one).
Read more: http://fractalfinance.blogspot.de/2011/04/possibility-of-cognition.html