![]() ![]() Gabor’s atom is a product of sinusoidal wave with a finite risk symmetric window. Gabor atoms are given by the following form and are constructed by time translation by period and frequency modulation (frequency ) of the original time window In order to surmount the aforementioned problem, we will take idea from Hungarian physicist Gabor who defined, inspired by quantum physics, elementary time-frequency ‘atoms’ or ‘kernels’ that have minimal time-spread in the time-frequency plane. Los the risk spread of variable and Fourier time-frequency cannot be simultaneously small. ![]() In order to continue our analysis, we will repeat the uncertainty principle which states that there is no finite risk time series which is supported in time and frequency domains. The two equations look very similar, except that here Plack constant plays its role because of quantum phenomenon. Where represents the standard deviation of momentum while denotes the standard deviation of position of a particle. If we want to compare it to Heisenberg principle of uncertainty in quantum physics, we use the equation given by Earle Hesse Kennard and Herman Weyl. The conclusion is that Uncertainty principle in time-series analysis holds and the following equation proves it: Using these two equations, we obtain the following: Where Uncertainty principle by Heisenberg states that the product of equivalent spectral bandwidth and time duration of a time series cannot be less than a certain minimum value, which is given by the following equation. Where At the same time, we define the spectral bandwidth of by ![]() Firstly, we will demonstrate classical econometrical approach taken from Cornelis Los. ![]() One approach is classical quantum approach, where we will try to establish analogy between quantum physics and time series analysis and the other one is classical econometrical approach. In order to prove the following assertion, we will compare two approaches. Theoretical Background Heisenberg principle applied in risk management and time-series analysis can be formulated in the following way : The Uncertainty principle asserts that there are no time series with finite risk which is compactly supported both in the time and frequency domains. The uncertainty principle states the main characteristic of quantum systems. Uncertainty principle is defined as any variety of mathematical equations that provide limited knowledge of certain pairs of physical properties of complementary variables that can be known pertaining in that sense to complementary variables like position and momentum. In order to approach Heisenberg uncertainty principle, firstly we must define Heisenberg uncertainty principle in quantum mechanics. Uncertainty is defined as lack of certainty, not being able to make a decision on a safe basis. Introduction When considering uncertainty, the following concept must be applied: Schroeder said that one of the fundamental consequences of uncertainty is the very size of atoms, which, without it, would collapse to an infinitesimal point. ![]()
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