Related papers: Discrete $q$-exponential limit order cancellation …
Power law or generalized polynomial regressions with unknown real-valued exponents and coefficients, and weakly dependent errors, are considered for observations over time, space or space--time. Consistency and asymptotic normality of…
We analyze the price return distributions of currency exchange rates, cryptocurrencies, and contracts for differences (CFDs) representing stock indices, stock shares, and commodities. Based on recent data from the years 2017--2020, we model…
Zipf's power-law distribution is a generic empirical statistical regularity found in many complex systems. However, rather than universality with a single power-law exponent (equal to 1 for Zipf's law), there are many reported deviations…
We study the discrete-time linear-quadratic (LQ) control model using reinforcement learning (RL). Using entropy to measure the cost of exploration, we prove that the optimal feedback policy for the problem must be Gaussian type. Then, we…
Power-law distributions are ubiquitous in nature. Random multiplicative processes are a basic model for the generation of power-law distributions. It is known that, for discrete-time systems, the power-law exponent decreases as the…
Frequency-dependent acoustical loss due to a multitude of physical mechanisms is commonly modeled by multiple relaxations. For discrete relaxation distributions, such models correspond with causal wave equations of integer-order temporal…
In the regression problem, L1 and L2 are the most commonly used loss functions, which produce mean predictions with different biases. However, the predictions are neither robust nor adequate enough since they only capture a few conditional…
Linear temporal logic (LTL) offers a simplified way of specifying tasks for policy optimization that may otherwise be difficult to describe with scalar reward functions. However, the standard RL framework can be too myopic to find maximally…
We start with the idea that open quantum systems can be used to represent financial markets by modelling events from the external environment and their impact on the market price. We show how to characterize distinct orbits of the time…
We explore the applicability of the causal analysis based on temporally shifted (lagged) Pearson correlation applied to diverse time series of different natures in context of the problem of financial market prediction. Theoretical…
Many time series produced by complex systems are empirically found to follow power-law distributions with different exponents $\alpha$. By permuting the independently drawn samples from a power-law distribution, we present non-trivial…
Time series analysis is used to understand and predict dynamic processes, including evolving demands in business, weather, markets, and biological rhythms. Exponential smoothing is used in all these domains to obtain simple interpretable…
Natural language data follows a power-law distribution, with most knowledge and skills appearing at very low frequency. While a common intuition suggests that reweighting or curating data towards a uniform distribution may help models…
This paper focuses on some simple models of limit order book dynamics which simulate market trading mechanisms. We start with a discrete time/space Markov process and then perform a re-scaling procedure leading to a deterministic dynamical…
We investigate the probability distribution of order imbalance calculated from the order flow data of 43 Chinese stocks traded on the Shenzhen Stock Exchange. Two definitions of order imbalance are considered based on the order number and…
We introduce a new diffusion process Xt to describe asset prices within an economic bubble cycle. The main feature of the process, which differs from existing models, is the drift term where a mean-reversion is taken based on an exponential…
Motivated by the desire to bridge the gap between the microscopic description of price formation (agent-based modeling) and the stochastic differential equations approach used classically to describe price evolution at macroscopic time…
Real data are constrained to finite sampling rates, which calls for a suitable mathematical description of the corrections to the finite-time estimations of the dynamic equations. Often in the literature, lower order discrete time…
We show that hyperscaling and finite-size scaling imply that the probability distribution of the order parameter in finite size critical systems exhibit data collapse. We consider the examples of equilibrium critical systems, and a…
It is empirically established that order flow in the financial markets is positively auto-correlated and can serve as an example of a social system with long-range memory. Nevertheless, widely used long-range memory estimators give varying…