Hi,
This is boring,but as always i try to pass on my confussion to this forum which eventually gets corrected by more experienced traders.
Was exploring in context to 'Game Theory' the Price pattern.
Preamble:
In 1921, Emile Borel, a French mathematician, published several papers on the theory of games. He used poker as an example and addressed the problem of bluffing and second-guessing the opponent in a game of imperfect information. Borel envisioned game theory as being used in economic and military applications. Borel's ultimate goal was to determine whether a "best" strategy for a given game exists and to find that strategy. While Borel could be arguably called as the first mathematician to envision an organized system for playing games, he did not develop his ideas very far. For that reason, most historians give the credit for developing and popularizing game theory to John Von Neumann, who published his first paper on game theory in 1928, seven years after Borel.
My understandings:=
Von Neumann Analysis
Von Neumann analysis is used to verify the stability of a finite difference scheme (FDS). It only consider FDSs having one time dimension, but any number of spatial dimensions. ( Daily price discovery process)
1st Condition := (Selection of Filters)
The procedure, in principle, is to perform a spatial Fourier transform along all spatial dimensions, thereby reducing the FDS to a time recursion in terms of the spatial Fourier transform of the system. The system is then stable if this time recursion is at least marginally stable as a digital filter.
Now Digital Filter
This is now a second-order difference equation (digital filter) that needs its stability checked. This can be accomplished most easily using the Durbin recursion, or we can check that the poles of the recursion do not lie outside the unit circle in the "Z" plane. (We are now aware of Fourier transform & Z transform)
A method equivalent to checking the pole radii, and typically used when the time recursion is first order, is to compute the amplification factor as the complex gain in the relation or we can check that the poles of the recursion do not lie outside the unit circle in the "Z" plane.
2nd Condition:
An important tool for inverting the z transform and converting among digital filter implementation structures is the partial fraction expansion (PFE). The term "partial fraction expansion'' refers to the expansion of a rational transfer function into a sum of first and/or second-order terms. The case of first-order terms is the simplest and most fundamental:
Here spl. attention given to eliminate the unwanted in the 'Conditions' :
In summary, von Neumann analysis verifies that no spatial Fourier components in the system are growing exponentially with respect to time.
Exploring the Alternate Filter:
Impulse-Response Representation
In addition to difference-equation coefficients, any LTI filter may be represented in the time domain by its response to a specific signal called the impulse. This response is called, naturally enough, the impulse response of the filter. Any LTI filter can be implemented by convolving the input signal with the filter impulse response.
Here again eliminating the unwanted :
We normally require that the impulse response decay to zero over time; otherwise, we say the filter is unstable.
Exploring another Type Fourier:=
Discrete Time Fourier Transform (DTFT)
This can be viewed as the limiting form of the DFT when its length is allowed to approach infinity:
Thus, as , a continuous frequency axis must result in the limit along the unit circle in the "Z" plane. The axis is still finite in length, however, because the time domain remains sampled.
How to calculate the Impulse:= (which can be Pre Entry Trigger)
Time - Price :=
Asymmetry of Horizontal/Vertical Terminations :
It is common that horizontal and vertical transverse waves are transduced differently at the origin.(Impulse origin).
This unequal terminating impedance causes the horizontal component to decay slower than the vertical component of vibration. We can say that this happens because the vertical origin admittance is much greater than the horizontal admittance, giving rise to a faster rate of energy transfer from the vertical polarization into the origin--in other words, the origin is more "yielding'' in the vertical direction. The consequence of this unequal rate of decay is a two-stage amplitude envelope. The initial fast decay gives a strong onset to the rise/fall, while the slower late decay provides a long-lasting sustain--two normally opposing but desirable features.
Here 'Impedence' = force / velocity.
Now i am unable to decide ,whether my basic understanding is wrong ?
Which one to choose ?
All MACD / RSI gets validated ,but differentiating Noise is imp.
Looking for your guidance.
Asish
