A New Bivariate Random Coefficient INAR(1) Model with Applications

Excess zeros is a common phenomenon in time series of counts, but it is not well studied in asymmetrically structured bivariate cases. To fill this gap, we first considered a new first-order, bivariate, random coefficient, integer-valued autoregressive model with a bivariate innovation, which follows the asymmetric Hermite distuibution with five parameters. An attractive advantage of the new model is that the dependence between series is achieved by innovative parts and the cross-dependence of the series. In addition, the time series of counts are modeled with excess zeros, low counts and low over-dispersion. Next, we established the stationarity and ergodicity of the new model and found its stochastic properties. We discuss the conditional maximum likelihood (CML) estimate and its asymptotic property. We assessed finite sample performances of estimators through a simulation study. Finally, we demonstrate the superiority of the proposed model by analyzing an artificial dataset and a real dataset.

Dynamics of a Rumor Propagation Model with Stochastic Perturbation On Homogeneous Social Networks

The rapid development of information society highlights the important role of rumors in social communication, and its propagation has a significant impact on human production and life. The investigation of the influence of uncertainty on rumor propagation is an important issue in the current communication study. Due to incomprehension about others and the stochastic properties of the users' behavior, the transmission rate between individuals on social network platforms is usually not a constant value. In this paper, we propose a new rumor propagation model on homogeneous social networks from the deterministic structure to the stochastic structure. Firstly, a unique global positive solution of rumor propagation model is obtained. Then, we verify that the extinction and persistence of stochastic rumor propagation model are restricted by some conditions. IfR *0< 1 and the noise intensity s i (i = 1,2,3) satisfies some certain conditions, rumors will extinct with a probability one. If R *0 > 1, rumor-spreading individuals will continue to exist in the system, which means the rumor will prevail for a long time. Finally, through some numerical simulations, the validity and rationality of the theoretical analysis are effectively verified.

Optimisation of absorber parameters in the case of stochastic vibrations in a bridge with a deck platform for servicing pipelines

The paper focuses on the problem of optimising the cooperation between a dynamic vibration absorber (DVA) and a structure. The authors analyse a road beam bridge equipped with a working platform (deck) used to service pipelines installed on the structure. The paper studies the problem of choosing the optimal parameters for damping absorbers that reduce the random vibration of a beam subjected to a random sequence of moving forces with a constant velocity. The stochastic properties of the load are modelled by means of a filtering Poisson process. A single-degree-of-freedom (SDOF) absorber model with a multi-degree-of-freedom (MDOF) primary structure model are is considered.

Analysis and Prediction of High Frequency Foreign Exchange Data

<p>This thesis investigates the stochastic properties of high frequency foreign exchange data. We study the exchange rate as a process driven by Brownian motion, paying particular attention to its sampled total variation, along with the variance and distribution of its increments. The normality of its increments is tested using the Khmaladze transformation-2, which we show is straightforward to implement for the case of testing centred normality. We found that while the process exhibits properties characteristic of Brownian motion, increments are non-Gaussian and instead come from mixture distributions. We also introduce a technical analysis trading strategy for predicting price movements, and employ it using the exchange rate dataset. This strategy is shown to offer a statistically significant advantage, and provides evidence that exchanges rates are predictable to a greater extent than current mathematical models suggest.</p>

Analysis and Prediction of High Frequency Foreign Exchange Data

<p>This thesis investigates the stochastic properties of high frequency foreign exchange data. We study the exchange rate as a process driven by Brownian motion, paying particular attention to its sampled total variation, along with the variance and distribution of its increments. The normality of its increments is tested using the Khmaladze transformation-2, which we show is straightforward to implement for the case of testing centred normality. We found that while the process exhibits properties characteristic of Brownian motion, increments are non-Gaussian and instead come from mixture distributions. We also introduce a technical analysis trading strategy for predicting price movements, and employ it using the exchange rate dataset. This strategy is shown to offer a statistically significant advantage, and provides evidence that exchanges rates are predictable to a greater extent than current mathematical models suggest.</p>

Time Series Methods and Repeated Sample Surveys

<p>When applied to a sequence of repeated surveys, the traditional sample survey estimators of means or totals for one time period only, fail to take advantage of any time series structure. Such structure may result from correlation between successive responses for resampled individuals, or from time series properties in the parameters of interest. Historically, the initial published papers on time series improvement of repeated sample survey estimates allowed only the first possibility, treating the sum over the population of the individual responses as fixed; individual responses were seen as having stochastic properties only with respect to the sampling scheme. The alternative and later development allowed that both individual responses and their sum have stochastic properties with respect to a superpopulation from which the population of individual responses are drawn. Superpopulations allowed the application of mainstream time series techniques, including signal extraction and stochastic least squares, to repeated sample survey data. These developments in their historical perspective are the topic of Chapter 1. Superpopulation models may also be applied to sample surveys from a single time period, and superpopulation and design properties of the one period linear non-homogeneous sample survey estimator form the topic of Chapter 2; this estimator is sufficiently general to subsume almost all single period non-informative sample survey estimators, and Chapter 2 allows systematisation of a wide range of previously disparate results. This linear estimator may also be extended beyond one time period to include the known estimators for repeated surveys, and this topic, together with a consideration of the effects of data agqregation on non-stochastic and stochastic least squares, is the subject of Chapter 3. Given the central role of the general linear model, and the time series nature of repeated surveys, projection and parameter updating formulae for linear models should form an integral part of repeated survey analysis. The correlation of sample survey errors however, invalidates the formulae appropriate to the known iid error case, and Chapters 4 and 5 develop the general formulae to allow correlated error structure. Chapter 4 considers parameter vectors of fixed length, as for example, for polynomial models, and provides formulae for estimating the length of the parameter vector, and for calculating independent recursive residuals and cusums when further data are added to the model. Chapter 5 considers updating and projection formulae in a wider context, and allows that the parameter vector may be stochastic or non-stochastic and that its length may increase with additional data; it consequently provides a general extension of the Kalman filter to the case of coloured noise over time. The paucity of suitable data has limited data analysis to that contained in Chapter 6, where a simulation study and an analysis of medical data gauge the efficacy of polynomial models in time with multiple observations per time point and autocorrelated errors. The formulae of Chapter 4 allow testing for the constancy of the regression relationships over time. The appendix details SAS computer programs for fitting the polynomial models of Chapter 6.</p>

Time Series Methods and Repeated Sample Surveys

<p>When applied to a sequence of repeated surveys, the traditional sample survey estimators of means or totals for one time period only, fail to take advantage of any time series structure. Such structure may result from correlation between successive responses for resampled individuals, or from time series properties in the parameters of interest. Historically, the initial published papers on time series improvement of repeated sample survey estimates allowed only the first possibility, treating the sum over the population of the individual responses as fixed; individual responses were seen as having stochastic properties only with respect to the sampling scheme. The alternative and later development allowed that both individual responses and their sum have stochastic properties with respect to a superpopulation from which the population of individual responses are drawn. Superpopulations allowed the application of mainstream time series techniques, including signal extraction and stochastic least squares, to repeated sample survey data. These developments in their historical perspective are the topic of Chapter 1. Superpopulation models may also be applied to sample surveys from a single time period, and superpopulation and design properties of the one period linear non-homogeneous sample survey estimator form the topic of Chapter 2; this estimator is sufficiently general to subsume almost all single period non-informative sample survey estimators, and Chapter 2 allows systematisation of a wide range of previously disparate results. This linear estimator may also be extended beyond one time period to include the known estimators for repeated surveys, and this topic, together with a consideration of the effects of data agqregation on non-stochastic and stochastic least squares, is the subject of Chapter 3. Given the central role of the general linear model, and the time series nature of repeated surveys, projection and parameter updating formulae for linear models should form an integral part of repeated survey analysis. The correlation of sample survey errors however, invalidates the formulae appropriate to the known iid error case, and Chapters 4 and 5 develop the general formulae to allow correlated error structure. Chapter 4 considers parameter vectors of fixed length, as for example, for polynomial models, and provides formulae for estimating the length of the parameter vector, and for calculating independent recursive residuals and cusums when further data are added to the model. Chapter 5 considers updating and projection formulae in a wider context, and allows that the parameter vector may be stochastic or non-stochastic and that its length may increase with additional data; it consequently provides a general extension of the Kalman filter to the case of coloured noise over time. The paucity of suitable data has limited data analysis to that contained in Chapter 6, where a simulation study and an analysis of medical data gauge the efficacy of polynomial models in time with multiple observations per time point and autocorrelated errors. The formulae of Chapter 4 allow testing for the constancy of the regression relationships over time. The appendix details SAS computer programs for fitting the polynomial models of Chapter 6.</p>

Ergodic Stationary Distribution of Hepatitis C Virus Model Incorporating Two Treatment Effects

In this paper, the dynamics of Hepatitis C infectious disease model with two treatment effects are studied through the Ito Stochastic Differential Equations (SDEs). While the first treatment rate reduces the reproduction of virion, the other mitigates the new infections. Though the deterministic behaviour of the model has been extensively studied, little is known about its stochastic properties. Thus, we examine sufficient conditions for the existence and uniqueness of the ergodic stationary distribution of the model via stochastic Lyapunov approach. The existence of a unique positive solution is also studied. The numerical simulations of the SDE model are performed through the Euler-Maruyama method and compared with their deterministic counterparts. The results obtained by SDEs are found to conform to those reported through their deterministic analogues.

EVALUATION OF THE RELIABILITY OF BUILDING STRUCTURES IN SIMULIA ABAQUS: MODELING OF STOCHASTIC MATERIAL PROPERTIES

This article describes a software module component integrated with the SIMULIA Abaqus engineering analysis software package and designed to simulate random values of material parameters in a finiteelement model based on specifiedstatistical characteristics, with the possibility of taking into account the physical nonlinearity of material behavior under various combinations of loads and influences.The target group of materials under study is materials of load-bearing elements of building structures, such as concrete, stone, steel. This software module can be recommended for use by specialists, engineers and scientists engaged in probabilistic analysis of the reliability of structures of buildings and structures, apparatus, machines, devices, with the combined use of complexes of computer modeling and engineering analysis. Has a certificateof state registration of the computer program "AS for modeling stochastic properties of materials" No. 2019667439 dated 12.24.2019.