On Sampling and Reconstruction of Continuous Time Stochastic Systems

Many important factors affect the spread of childhood infectious disease. To better understand the fundamental drivers of infectious disease spread, several researchers have estimated seasonal transmission coefficients in discrete-time models. In this paper, we build upon this previous work and also develop a framework for efficient estimation using continuous differential equation models. We introduce nonlinear programming formulations to efficiently estimate model parameters and seasonal transmission profiles from existing case count data for the childhood disease, measles. We compare results from discrete time and continuous time models and address several shortcomings of the discrete-time method, including removing the need for the data reporting interval to match the time between successive cases in the chain of transmission or serial interval of the disease. Using a simultaneous approach for optimization of differential equation systems, we demonstrate that seasonal transmission parameters can be effectively estimated using continuous time models instead of discrete-time models.

American Option Pricing with Discrete and Continuous Time Models: An Empirical Comparison

Limitations record on a variable which have continuous variable changes make the 'time' attached to the data is discrete. That underlies development of continuous time model. Compared to discrete time model, the continuous time model has advantages that can make prediction at different lag. In addition, it still can perform continuous time model parameter estimation, although the objects observations do not always have the same time interval (irregular time). Thus, the purpose of this study is to examine the consistency of continuous time model coefficient parameter with structural equation model (SEM) approach in irregular time data. The method used is the Exact Discrete Model (EDM) with SEM approach. EDM is a model that connects the parameter to value which is underlying parameter of the continuous time model with non-linear relationships. The result analysis of the research indicated that the coefficients of continuous time model parameter are still consistent until 20% of irregular time with 5% consistency limits.

This article focuses on production planning in the metallurgical sector. This study undertakes a detailed comparative study of mixed-integer linear programming models using different time representations: continuous and discrete. The analysis shows that the continuous model consistently outperforms its discrete counterpart in all evaluated scenarios. The key difference between the continuous and discrete models is the continuous model’s ability to deliver better makespan results, achieving an improvement of up to 15% compared to the discrete model. This advantage holds even in complex environments with a high number of tasks and machines, where the continuous model consistently outperforms the discrete model by over 6% in the scenario with the highest number of tasks and machines. This preference extends beyond makespan considerations. The continuous model also maintains an edge in terms of runtime efficiency, achieving better times with a 99% improvement over the discrete model in all scenarios except one. These findings provide concrete evidence for the use of continuous models, which promise more effective production planning in analogous manufacturing domains.

New distribution theory for the estimation of structural break point in mean

In this chapter we review continuous time series modeling and estimation by extended structural equation models (SEM) for single subjects and N > 1. First-order as well as higher-order models will be dealt with. Both will be handled by the general state space approach which reformulates higher-order models as first-order models. In addition to the basic model, the extensions of exogenous variables and traits (random intercepts) will be introduced. The connection between continuous time and discrete time for estimating the model by SEM will be made by the exact discrete model (EDM). It is by the EDM that the exact estimation procedure in this chapter differentiates from many approximate procedures found in the literature. The proposed analysis procedure will be applied to the well-known Wolfer sunspot data, an N = 1 time series that has been analyzed by several continuous time analysts in the past. The analysis will be carried out by ctsem, an R-package for continuous time modeling that interfaces to OpenMx, and the results will be compared to those reported in the previous studies.

We study a scenario in which n mobile robots with a limited viewing range are distributed in the Euclidean plane and have to solve a formation problem. The formation problems we consider are the G athering problem and the C hain-Formation problem. In the G athering problem, the robots have to gather in one (not predefined) point, while in the C hain -F ormation problem they have to form a connected communication chain of minimal length between two stationary base stations. Each robot may base its decisions where to move only on the current relative positions of neighboring robots (that are within its viewing range); that is, besides having a limited viewing range, the robots are oblivious (they do not use information from the past), have none or only very limited identities, and they do not have a common sense of direction. Variants of these problems (especially for the G athering problem) have been studied extensively in different discrete time models. In contrast, our work focuses on a continuous time model; that is, the robots continuously sense the positions of other robots within their viewing range and continuously adapt their speed and direction according to some simple, local rules. Hereby, we assume that the robots have a maximum movement speed of one. We show that this idealized idea of continuous sensing allows us to solve the mentioned formation problems in linear time O( n ) (which, given the maximum speed of one, immediately yields a maximum traveled distance of O( n )). Note that in the more classical discrete time models, the best known strategies need at least Θ( n 2 ) or even Θ( n 2 log n ) timesteps to solve these problems. For the G athering problem, our analysis solves a problem left open by Gordon et al. [2004], where the authors could prove that gathering in a continuous model is possible in finite time, but were not able to give runtime bounds. Apart from these linear bounds, we also provide runtime bounds for both formation problems that relate the runtime of our strategies to the runtime of an optimal, global algorithm. Specifically, we show that our strategy for the G athering problem is log OPT-competitive and the strategy for the C hain -F ormation problem is log n -competitive. Here, by c -competitive, we mean that our (local) strategy is asymptotically by at most a factor of c slower than an optimal, global strategy.

This paper presents some empirical evidence for a time series model of aggregate consumer' expenditure which is formulated in continuous time. It is argued that such models, expressed in terms of stochastic differential equations, are more realistic in representing the dynamic evolution of many economic time series, particularly at the aggregate level. However, such models impose complicated restrictions on the discretely observed data, which must be taken account of in estimation. The appropriate methodology is applied to a version of the consumption function for UK data, and is found to provide a good description of the data. The estimated continuous time model is compared with more popular discrete models, and is found to provide superior dynamic post-sample predictions over 16 quarters. The formulation of econometric models in continuous time may provide an alternative and potentially successful approach to the modelling of time series in many aspects of economics.

In the theoretical part of this article, we provide a brief introduction to differenttypes of repeated measure designs and methods to analyze repeatedly measured data, with aparticular focus on continuous time modelling of intensive longitudinal data (ILD) withN≥1 analysis. We built on the distinction betweenwithin-person versus between-person effects, and how this is addressed in static versusdynamic models. Further, we elaborate on the distinction between discrete time dynamicmodels versus continuous time dynamic models. In particular, we deal with continuous timestructural equation models (CTSEM), and we provide a brief introduction into theunderlying math. Since smart devices have become useful tools in monitoring health, we usethe applied part of this article for explaining how to retrieveN=1 bivariate ILD from popular smart watches and how toprepare them for CTSEM (including N>1 multivariateextensions). We show how to specify a cross-lagged panel CTSEM using the R package ctsem,how to fit the specified model to the retrieved data, and how to interpret the results.Limitations of CTSEM are discussed, too. Monitoring and forecasting industrial healthrepresent important issues for organizations.

An alternative method was proposed for identification of linear continuous time system with noisy output. Using Gaussian modulating filters, by numerical integration, a discrete equivalent identification model that was parametrized directly in continuous time model parameters was obtained, and the LS estimation algorithm was developed. The LS estimator is biased even with white measurement output noise, and the bias is determined by variance of output noise. On the basis of obtained output measurement noise variance, the bias was compensated and the consistent estimates of system parameters were given. Simulation which compares the standard LS with BCLS algorithm indicates that the proposed algorithm is an efficient method for noisy output continuous time system identification.

The Euro/Dollar exchange rate: Chaotic or non-chaotic? A continuous time model with heterogeneous beliefs

In this article, we provide empirical evidence of the recent financial crisis over 2007–2009 using discrete time multivariate GARCH (MGARCH) models and continuous time modelling approaches. Using daily data for 14 countries, we investigate the return and volatility spillovers among the US and other international markets. The MGARCH results reveal positive return spillovers from the US to a number of markets, and volatility transmission is verified. The US market is prone to return and volatility transmission from a limited number of markets. The continuous time analysis finds evidence of feedback effects in some cases. Evidence shows that spillover effects intensified during the financial crisis.

This paper describes the role of continuous components in linking the topological and measuretheoretic (or regenerative) analysis of Markov chains and processes. Under Condition $$\mathcal{T}$$ below we show the following parallel results for both discrete and continuous time models:

R. Garcia-Millan etal. [Phys. Rev. E 91, 042122 (2015)PLEEE81539-375510.1103/PhysRevE.91.042122] reported a universal finite-size scaling form of the survival probability in discrete time branching processes. In this comment, we generalize the argument to a wide range of continuous time branching processes. Owing to the continuity, the resulting differential (rather than difference) equations can be solved in closed form, rendering some approximations by R. Garcia-Millan etal. superfluous, although we work along similar lines. In the case of binary branching, our results are in fact exact. Demonstrating that discrete time and continuous time models have their leading order asymptotics in common, raises the question to what extent corrections are identical.

The exact discretisation of CARMA models with applications in finance