I was just re-reading parts of Fractals and Scaling in Finance: Discontinuity, Concentration, Risk. Selecta Volume E by the great Benoit Mandelbrot where he says 2.3. Specialists' trades Section VI.B of M 1963b{EI4} pointed out that the discontinuities of the process Z(t) were unlikely to be observed by examining transaction data. They are either hidden within periods when the market is closed or the trading interrupted, or smoothed away by specialists who, in accordance with S.E.C. instructions, "ensure the continuity of the market" by per- forming transactions in which they are party. It is tempting to postulate that virtual transactions and the specialists' transactions are identical, though the latter presumably see where the prices are aimed and can achieve the desired llZ in less than U inde- pendent Gaussian steps. Thus, the Bochner representation is plausible and suggests a program of empirical research of the role of Specialists. The method of filters. The distribution of price changes between trans- actions has a direct bearing upon the "method of filters," discussed in Section VI.C of M 1963b{EI4}. which led me to dig deeper where behold this is right up my alley as its a good candidate for the next thing to implement now that i got the damned Fourier transform implemented ------====================================================================-------- Bochner's representation theorem is a fundamental result in the theory of characteristic functions, which are used to study random variables and stochastic processes. An L-stable process is a particular type of stochastic process that has a specific form of the characteristic function, exhibiting stable distributions. These processes are often used to model heavy-tailed phenomena in various fields like finance, physics, and engineering. Bochner's representation theorem states that for any continuous positive definite function, there exists a unique Borel measure such that the function can be represented as the Fourier transform of that measure. In the context of an L-stable process, the characteristic function is given by: Φ(t) = E[exp(i * t * X)] = exp(−c|t|^α * (1 + i * β * sign(t) * tan(πα/2))) Here, the parameters are as follows: t is a scalar argument representing time. X is the random variable associated with the L-stable process. α is the stability parameter (0 < α ≤ 2), which characterizes the tail behavior of the distribution. When α = 2, the process reduces to a Gaussian process. β is the skewness parameter (-1 ≤ β ≤ 1), which measures the asymmetry of the distribution. c is a scale parameter (c > 0), which influences the overall scale of the distribution. E denotes the expectation operator, and exp(x) is the exponential function e^x. i is the imaginary unit (√-1), and sign(t) is the sign function. The Bochner's representation of the L-stable process is essentially a way of expressing the process's characteristic function in terms of its stable distribution parameters. This representation is crucial in understanding the behavior of L-stable processes, their statistical properties, and their application in various domains.
We have Φ_Y(t), the characteristic function of Y, where Y = ln(X), and we want to find Φ_X(t), the characteristic function of X. Let's first express Φ_X(t): Φ_X(t) = E[e^(itX)]. Since Y = ln(X), we have X = e^Y. Substituting X: Φ_X(t) = E[e^(it*e^Y)]. Now, we can use the moment-generating function (MGF) approach to derive the characteristic function of X. Recall that the MGF of a random variable W is defined as M_W(t) = E[e^(tW)], and the characteristic function of W is Φ_W(t) = E[e^(itW)]. The relationship between the MGF and the characteristic function is that the MGF is the characteristic function with t replaced by -it: M_Y(-it) = E[e^(-itY)] = Φ_Y(-t). Now, we can write Φ_X(t) in terms of the MGF of Y: Φ_X(t) = E[e^(it*e^Y)] = M_Y(-it). Thus, to find Φ_X(t), we just need to replace t by -it in the characteristic function of Y: Φ_X(t) = Φ_Y(-it). In summary, given the characteristic function of Y = ln(X), you can find the characteristic function of X by replacing t with -it in the characteristic function of Y: Φ_X(t) = Φ_Y(-it).
You surely love mumbo jumbo. What do fractals and scaling have to do with SEC? Where did you copy this content from? Why does none of it make any sense due to the content being convoluted and unrelated content being mixed in? Your new NLP model you trained? ;-) In fact I hang myself out of the window in claiming that the entire content is pure and utter bullshit which makes zero financial nor logical sense.
After plugging all of this into your models, where does it say the SP will close on tomorrow, or Wednesday? If it cannot tell you that with any accuracy, then it is a waste of materiel.
While we are mere monkeys and as such not much is expected of us, still we should not throw shit at things we don't understand. Remember what you said about tape reading in the ES journal? Even with my limited intellect I can almost envision a possible application of the above information in the creation of a predictive model that attempts to quantify the effect of apparent market maker actions under certain market conditions.
If market makers are accumulating or distributing inventory while maintaining orderly markets in extreme conditions, it seems to follow there may be predictive value if one were able to track and quantify such activity. Generally, retail traders and perhaps urgent medium sized orders pay the spread. Larger orders, including market maker activity, make the spread. This can be most visible during high volume in a particular instrument. I believe the tape can be read, creating potentially profitable trading opportunities.
i might have at one point and totally forgot and to the fellow i yelled at for calling me a java programmer please forgive me my goddamn neck was hurting and i had flashbacks to when i worked in the corporate world doing shit not nearly as cool as what im doing now of my own accord, no excuse to yell at passersby who dont know that. @BeautifulStranger its something to consider if possible https://math.stackexchange.com/ques...lows-where-the-chain-rule-is-forgotten-yet-it semi-related.. on the topic of dynamical systems..