Related papers: High frequency sampling of a continuous-time ARMA …
This paper investigates the role of high-dimensional information sets in the context of Markov switching models with time varying transition probabilities. Markov switching models are commonly employed in empirical macroeconomic research…
In high-frequency financial data not only returns, but also waiting times between consecutive trades are random variables. Therefore, it is possible to apply continuous-time random walks (CTRWs) as phenomenological models of the…
Dynamic Complexity is a phenomenon exhibited by a nonlinearly interacting system within which multitudes of different sizes of large scale coherent structures emerge, resulting in a globally nonlinear stochastic behavior vastly different…
Manifold-valued functional data analysis (FDA) recently becomes an active area of research motivated by the raising availability of trajectories or longitudinal data observed on non-linear manifolds. The challenges of analyzing such data…
Cellular automaton (CA) approach is an important theoretical framework for studying complex system behavior and has been widely applied in various research field. CA traffic flow models have the advantage of flexible evolution rules and…
A general stochastic traffic cellular automaton (CA) model, which includes slow-to-start effect and driver's perspective, is proposed in this paper. It is shown that this model includes well known traffic CA models such as…
In this paper we present a robust estimator for the parameters of a continuous-time ARMA(p,q) (CARMA(p,q)) process sampled equidistantly which is not necessarily Gaussian. Therefore, an indirect estimation procedure is used. It is an…
Rank-Ordered Multifractal Analysis (ROMA), a recently developed technique that combines the ideas of parametric rank ordering and one parameter scaling of monofractals, has the capabilities of deciphering the multifractal characteristics of…
In the study of complex physical and biological systems represented by multivariate stochastic processes, an issue of great relevance is the description of the system dynamics spanning multiple temporal scales. While methods to assess the…
Pure-jump processes have been increasingly popular in modeling high-frequency financial data, partially due to their versatility and flexibility. In the meantime, several statistical tests have been proposed in the literature to check the…
This paper presents an algorithm for the simulation of Hawkes-type processes where the intensity is expressed in terms of a continuous-time autoregressive moving average model. We identify upper bounds for both the univariate and the…
As a special infinite-order vector autoregressive (VAR) model, the vector autoregressive moving average (VARMA) model can capture much richer temporal patterns than the widely used finite-order VAR model. However, its practicality has long…
We describe the asymptotic behavior of the number $Z_n[a_n,\infty)$ of individuals with a large value in a stable bifurcating autoregressive process. The study of the associated first moment $\mathbb{E}(Z_n[a_n,\infty))$ is equivalent to…
Classical Cellular Automata (CCAs) are a powerful computational framework widely used to model complex systems driven by local interactions. Their simplicity lies in the use of a finite set of states and a uniform local rule, yet this…
We consider the sampling problem for functional PCA (fPCA), where the simplest example is the case of taking time samples of the underlying functional components. More generally, we model the sampling operation as a continuous linear map…
The Hurst exponent $H$ of long range correlated series can be estimated by means of the Detrending Moving Average (DMA) method. A computational tool defined within the algorithm is the generalized variance $ \sigma_{DMA}^2={1}/{(N-n)}\sum_i…
We consider extended slow-fast systems of N interacting diffusions. The typical behavior of the empirical density is described by a nonlinear McKean-Vlasov equation depending on , the scaling parameter separating the time scale of the slow…
The collective risk model (CRM) for frequency and severity is an important tool for retail insurance ratemaking, macro-level catastrophic risk forecasting, as well as operational risk in banking regulation. This model, which is initially…
Discrete dynamical systems can exhibit complex behaviour from the iterative application of straightforward local rules. A famous example are cellular automata whose global dynamics are notoriously challenging to analyze. To address this, we…
Time series of matrix-valued data are increasingly available in various areas including economics, finance, social science, among others. These data may shed light on the inter-dynamical relationships between two sets of attributes, for…