scholarly journals Discretizing nonlinear, non-Gaussian Markov processes with exact conditional moments

10.3982/qe737 ◽  
2017 ◽  
Vol 8 (2) ◽  
pp. 651-683 ◽  
Author(s):  
Leland E. Farmer ◽  
Alexis Akira Toda
Keyword(s):  
Markov Processes ◽  
Conditional Moments ◽  
Non Gaussian

scholarly journals Iterative Filtering and Smoothing in Nonlinear and Non-Gaussian Systems Using Conditional Moments

2018 ◽  
Vol 25 (3) ◽  
pp. 408-412 ◽  
Author(s):  
Filip Tronarp ◽  
Angel F. Garcia-Fernandez ◽  
Simo Sarkka
Keyword(s):  
Conditional Moments ◽  
Iterative Filtering ◽  
Non Gaussian

scholarly journals Understanding the Nature of the Long-Range Memory Phenomenon in Socioeconomic Systems

Entropy ◽  
2021 ◽  
Vol 23 (9) ◽  
pp. 1125
Author(s):  
Rytis Kazakevičius ◽  
Aleksejus Kononovicius ◽  
Bronislovas Kaulakys ◽  
Vygintas Gontis
Keyword(s):  
Financial Markets ◽  
Long Range ◽  
Markov Processes ◽  
Point Processes ◽  
First Passage Time ◽  
Moving Average ◽  
Social Systems ◽  
Passage Time ◽  
Stable Motion ◽  
Non Gaussian

In the face of the upcoming 30th anniversary of econophysics, we review our contributions and other related works on the modeling of the long-range memory phenomenon in physical, economic, and other social complex systems. Our group has shown that the long-range memory phenomenon can be reproduced using various Markov processes, such as point processes, stochastic differential equations, and agent-based models—reproduced well enough to match other statistical properties of the financial markets, such as return and trading activity distributions and first-passage time distributions. Research has lead us to question whether the observed long-range memory is a result of the actual long-range memory process or just a consequence of the non-linearity of Markov processes. As our most recent result, we discuss the long-range memory of the order flow data in the financial markets and other social systems from the perspective of the fractional Lèvy stable motion. We test widely used long-range memory estimators on discrete fractional Lèvy stable motion represented by the auto-regressive fractionally integrated moving average (ARFIMA) sample series. Our newly obtained results seem to indicate that new estimators of self-similarity and long-range memory for analyzing systems with non-Gaussian distributions have to be developed.

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