The estimation of continuous time models

A sequential refinement approach for parameter optimization in continuous dynamic models

This is the first of a two-volume set of articles reflecting the current state of research in theoretical and applied econometrics. The topics covered include time series methods, semiparametric methods, seasonality, financial economics, model solution techniques, economic development, and labour economics. All the contributions were commissioned to be presented at the plenary sessions of the Sixth World Congress of the Econometric Society in Barcelona

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.

Introduction The previous four chapters emphasized the advantages of using discrete mass mathematicaxsl models wherein both the structural mass and the nonstructural mass is “lumped” at selected (usually a relatively few) finite element nodes or at short distances from those finite element nodes. The alternative in mass modeling is the seemingly more realistic mathematical model where the mass is distributed throughout each structural element. Such distributed or continuous mass models are not nearly as useful as discrete mass models. However, continuous mass models do have enough instructional value and occasional engineering value that they cannot be wholly ignored. Their instructional value resides in (i) seeing the results of dealing with what is essentially an infinite DOF system; (ii) the reinforcement, and perhaps deeper understanding, obtained through repetition of the same analysis procedures used with discrete mass systems in a different context; and (iii) discovering the very few types of structures which can be usefully described by this much more concise type of modeling. Therefore the purpose of this chapter is to discuss some of those situations where the use of continuous mass models is of some, albeit small, value in the study of structural dynamics. Again, continuous mass models are practical only in quite restricted circumstances. All cases examined here are limited to structures that are modeled as a single structural element (e.g., one beam or one plate).

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.

Modelling of voltage dependent load is always a current topic due to existence of an adequate load model is a prerequisite for calculation of steady states and the analysis of transient regimes of power systems. Given that it is important to know the load model parameters, we have performed the measurements in electric power system of Bosnia and Herzegovina (EPS BIH). The main idea is to identify the values of voltage parameters of dynamic load model. Therefore, this paper describes the dynamic load models and the methodology for exponential dynamic load model parameter identification. It also presents the voltage parameters of dynamic load model for a node in EPS BIH and compares them to similar published studies, concluding that the difference in given parameter values is the consequence of local load characteristics.

To realize high precision servo control for the extension pneumatic muscle (E-PM), the nonlinear dynamic model of the E-PM is established and the effect parameters of the nonlinear dynamic model are analyzed, according to the phenomenological dynamic modeling theory. Firstly, an E-PM is designed based on the basic principle of PMs. Secondly, based on the dynamic characteristics of the E-PM, the nonlinear dynamic model of the E-PM is established. Thirdly, the parameters of the nonlinear dynamic model are identified by the elasticity test. Lastly, in the Matlab\Simscape environment, the nonlinear dynamic model of the E-PM is simulated and the effect parameters of the nonlinear dynamic model are analyzed. The result shows that the nonlinear dynamic model by phenomenological dynamic modeling theory can accurately reflect the dynamic characteristics of the E-PM. In addition, when the damping parameter changes in the range of 0.35-0.55, the biggest difference between the rise time is 1.5s and the biggest difference between the stable time is 3.1s. It indicates that the damping parameter has a great effect on the dynamic characteristics of the E-PM.

This article extends recent work on the Gaussian or quasi-maximum likelihood estimation of the parameters of a closed higher-order continuous time dynamic model by introducing exogenous variables into the model The method presented yields exact maximum likelihood estimates when the innovations are Gaussian and the exogenous variables are polynomials in time of degree not exceeding two, and it can be expected to yield very good estimates under more general conditions. It is applicable, in principle, to a system of any order with mixed stock and iow data. The precise formulas for its implementation are derived, in this article, for a second-order system in which both the endog-enous and exogenous variables are a mixture of stock and flow variables.

Solid State Transformer (SST) is widely used in distribution renewable energy resources. SST includes AC-DC rectifier, DC-DC Dual Active Bridge (DAB) converter and AC-DC inverter. In this paper, continuous time average model and dynamic phasor model for combined Rectifier and DAB converter (R-DAB) are developed. Control scheme for R-DAB model is proposed for dynamic phasor based model, in which rectifier and DAB are being individually controlled using PI controller. The effect of controller has been analysed with change in input grid voltage variation. Stability analysis has performed using small signal stability analysis and Lyapunov's criterion. Developed model is verified with simulation in MATLAB/Simulink. Simulation result verifies the proposed modelling technique and controller performance.

Automated guided vehicles (AGVs) in the U-shaped automated container terminal travel longer and more complex paths. The conflicts among AGVs are trickier. The scheduling strategy of the traditional automated container terminal is difficult to be applied to the U-shaped automated container terminal. In order to minimize the handling time of all tasks and avoid AGV conflicts simultaneously in the U-shaped automated container terminal, this paper establishes a hybrid programming model for conflict-free integrated scheduling of quay cranes, AGVs, and double-cantilever rail cranes in the unloading process. It consists of a discrete event dynamic model and a continuous time dynamic model. An improved genetic seagull optimization algorithm (GSOA) is designed. A series of numerical experiments are conducted to verify the effectiveness and the efficiency of the model and the algorithm. The results show that the proposed method can simultaneously realize the AGVs collision avoidance and multi-equipment integrated scheduling optimization in the U-shaped automated container terminal.

This paper explores in depth the nature of the conditional moment restrictions implied by log-linear intertemporal capital asset pricing models (ICAPMs) and shows that the generalized instrumental variables (GMM) estimators of these models (as typically implemented in practice) are inefficient.The moment conditions in the presence of temporally aggregated consumption are derived for two log-linear ICAPMs.The first is a continuous time model in which agents maximize expected utility.In the context of this model, we show that there are important asymmetries between the implied moment conditions for infinitely and finitely-lived securities.The second model assumes that agents maximize non-expected utility, and leads to a very similar econometric relation for the return on the wealth portfolio.Then we describe the efficiency bound (greatest lower bound for the asymptotic variances) of the CNN estimators of the preference parameters in these models.In addition, we calculate the efficient CNN estimators that attain this bound.Finally, we assess the gains in precision from using this optimal CNN estimator relative to the commonly used inefficient CMN estimators.

Compared with other harmonic source models, the dynamic parameter model (DPM) has the advantage of accuracy and good application prospects. Previous studies on the DPM have been carried out under ideal conditions. In order to improve the practicability of the DPM, for the first time, this paper studied the influence of some factors in practical system on the DPM, the corresponding solutions and suggestions were put forward. Firstly, the DPM was briefly introduced and the concept of nonlinear characteristic curve of harmonic source was put forward. Secondly, in order to deal with the time-varying of harmonic source in practical system, a method of dividing each working state and modeling separately was developed. Thirdly, the influence of the sampling quantity, range and error on the accuracy and parameters of the DPM were analyzed, the guidance on sampling for different kinds of harmonic sources were obtained. Finally, the practical research direction of the DPM in the future were discussed.

Chapter 34 - Hierarchical continuous time modeling

Stacked self-attention models receive widespread attention, due to its ability of capturing global dependency among words. However, the stacking of many layers and components generates huge parameters, leading to low parameter efficiency. In response to this issue, we propose a lightweight architecture named Continuous Self-Attention models with neural ODE networks (CSAODE). In CSAODE, continuous dynamical models (i.e., neural ODEs) are coupled with our proposed self-attention block to form a self-attention ODE solver. This solver continuously calculates and optimizes the hidden states via only one layer of parameters to improve the parameter efficiency. In addition, we design a novel accelerated continuous dynamical model to reduce computing costs, and integrate it in CSAODE. Moreover, since the original self-attention ignores local information, CSAODE makes use of N-gram convolution to encode local representations, and a fusion layer with only two trainable scalars are designed for generating sentence vectors. We perform a series of experiments on text classification, neural language inference (NLI) and text matching tasks. With fewer parameters, CSAODE outperforms state-of-the-art models on text classification tasks (e.g., 1.3% accuracy improved on SUBJ task), and has competitive performances for NLI and text matching tasks as well.

Spatial dynamic panel data (SDPD) models have received great attention in economics in recent 10 years. Existing approaches for the estimation and test of SDPD models are quasi-maximum likelihood (QML) approach and generalized method of moments (GMM). In this article, we introduce the empirical likelihood (EL) method to the statistical inference for SDPD models. The EL ratio statistics are constructed for the parameters of spatial dynamic panel data models. It is shown that the limiting distributions of the empirical likelihood ratio statistics are chi-squared distributions, which are used to construct confidence regions for the parameters of the models. Simulation results show that the EL based confidence regions outperform the normal approximation based confidence regions.