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Prediction is a key issue in time series analysis. Just as classical mean regression models, classical autoregressive methods, yielding L$^2$ point-predictions, provide rather poor predictive summaries; a much more informative approach is…
In financial markets, low prices are generally associated with high volatilities and vice-versa, this well known stylized fact usually being referred to as leverage effect. We propose a local volatility model, given by a stochastic…
We present a new framework for modeling the statistical behavior of both fully developed turbulence and short-term dynamics of financial markets based on the nonextensive thermostatistics proposed by Tsallis. We also show that intermittency…
In this paper, we propose a new aperiodic formulation of model predictive control for nonlinear continuous-time systems. Unlike earlier approaches, we provide event-triggered conditions without using the optimal cost as a Lyapunov function…
This paper explores stochastic modeling approaches to elucidate the intricate dynamics of stock prices and volatility in financial markets. Beginning with an overview of Brownian motion and its historical significance in finance, we delve…
We study a pulse-coupled dynamics of excitable elements in uncorrelated scale-free networks. Regimes of self-sustained activity are found for homogeneous and inhomogeneous couplings, in which the system displays a wide variety of behaviors,…
Contemporary time series data often feature objects connected by a social network that naturally induces temporal dependence involving connected neighbours. The network vector autoregressive model is useful for describing the influence of…
Dynamical systems comprising of multiple components that can be partitioned into distinct blocks originate in many scientific areas. A pertinent example is the interactions between financial assets and selected macroeconomic indicators,…
In the realm of big data, discerning patterns in nonlinear systems affected by external control inputs is increasingly challenging. Our approach blends the coarse-graining strengths of centroid-based unsupervised clustering with the clarity…
This paper illustrates novel methods for nonstationary time series modeling along with their applications to selected problems in neuroscience. These methods are semi-parametric in that inferences are derived by combining sequential…
We construct a statistical indicator for the detection of short-term asset price bubbles based on the information content of bid and ask market quotes for plain vanilla put and call options. Our construction makes use of the martingale…
Many physical systems are formulated on domains which are relatively large in some directions but relatively thin in other directions. We expect such systems to have emergent structures that vary slowly over the large dimensions. Common…
Interaction graphs, such as those recording emails between individuals or transactions between institutions, tend to be sparse yet structured, and often grow in an unbounded manner. Such behavior can be well-captured by structured,…
We design a novel, nonlinear single-source-of-error model for analysis of multiple business cycles. The model's specification is intended to capture key empirical characteristics of business cycle data by allowing for simultaneous cycles of…
Financial time series exhibit a number of interesting properties that are difficult to explain with simple models. These properties include fat-tails in the distribution of price fluctuations (or returns) that are slowly removed at longer…
Many financial and economic variables, including financial returns, exhibit nonlinear dependence, heterogeneity and heavy-tailedness. These properties may make problematic the analysis of (non-)efficiency and volatility clustering in…
In this paper we propose a new model for volatility fluctuations in financial time series. This model relies on a non-stationary gaussian process that exhibits aging behavior. It turns out that its properties, over any finite time interval,…
Financial markets exhibit highly dynamic and complex behaviors shaped by both historical price trajectories and exogenous narratives, such as news, policy interpretations, and social media sentiment. The heterogeneity in these data and the…
In this paper we present a dimensional reduction to obtain a one-dimensional model to analyze localized necking or bulging in a residually stressed circular cylindrical solid. The nonlinear theory of elasticity is first specialized to…
The aim of this paper is to propose a heterogeneous agent model of stock markets that develop complicated endogenous price fluctuations. We find occurrences of non-stationary chaos, or speculative bubble, are caused by the heterogeneity of…