Nonlinearity and Temporal Dependence

Nonlinearities in the drift and diffusion coefficients influence temporal dependence in scalar diffusion models. We study this link using two notions of temporal dependence: beta-mixing and rho-mixing. We show that beta-mixing and rho-mixing with exponential decay are essentially equivalent concepts for scalar diffusions. For stationary diffusions that fail to be rho-mixing, we show that they are still beta-mixing except that the decay rates are slower than exponential. For such processes we find transformations of the Markov states that have finite variances but infinite spectral densities at frequency zero. Some have spectral densities that diverge at frequency zero in a manner similar to that of stochastic processes with long memory. Finally we show how nonlinear, state-dependent, Poisson sampling alters the unconditional distribution as well as the temporal dependence.Mixing, Diffusion, Strong dependence, Long memory, Poisson sampling

Trends, cycles, and co-integration: some issues in modelling long-term development in time series analysis

Auf der Grundlage der Arbeiten von Namenwirth und Weber (1987), die sich mit dem Langzeitzyklus von kulturellem Wandel befassen, diskutiert der Beitrag Problemstellungen im Zusammenhang mit Trends, Zyklen und möglichen strukturellen Beziehungen zwischen Variablen in der Zeitreihenanalyse. Besonderes Augenmerk wird dabei auf Zeitreihendaten gelegt, die deterministische und stochastische Komponenten enthalten. Mithilfe eines statistischen Konzepts ko-integrierter Prozesse werden die Bedingungen abgeklärt, unter denen eine gleichgewichtige Beziehung zwischen Variablen mit stochastischen Trends hergestellt werden kann. (ICH)'In this article, the work of Namenwirth and Weber on the long term cyclical nature of culture change has been taken as a starting point in a discussion of more general issues in identifying trends and cycles and structural relationships between variables in time series analysis. A brief introduction into the statistical concept of cointegrated processes is offered. This concept clarifies conditions under which equilibrium relationships between variables exhibiting stochastic trends can be modeled.' (author's abstract

Nonlinearity and Temporal Dependence

Nonlinearities in the drift and diffusion coefficients influence temporal dependence in scalar diffusion models. We study this link using two notions of temporal dependence: β−mixing and ρ−mixing. Weshow that β−mixing and ρ−mixing with exponential decay are essentially equivalent concepts for scalar diffusions. For stationary diffusions that fail to be ρ−mixing, we show that they are still β−mixing except that the decay rates are slower than exponential. For such processes we find transformations of the Markov states that have finite variances but infinite spectral densities at frequency zero. Some have spectral densities that diverge at frequency zero in a manner similar to that of stochastic processes with long memory. Finally we show how nonlinear, state-dependent, Poisson sampling alters the unconditional distribution as well as the temporal dependence. Les non-linéarités dans les coefficients de mouvement et de diffusion ont une incidence sur la dépendance temporelle dans le cas des modèles de diffusion scalaire. Nous examinons ce lien en recourant à deux notions de dépendance temporelle : mélange β et mélange ρ. Nous démontrons que le mélange β et le mélange ρ avec dégradation exponentielle constituent des concepts fondamentalement équivalents en ce qui a trait aux diffusions scalaires. Pour ce qui est des diffusions stationnaires qui ne se classent pas dans le mélange ρ, nous démontrons quâelles appartiennent quand même au mélange β, sauf que les taux de dégradation sont lents plutôt quâexponentiels. Pour ce genre de processus, nous recourons à des transformations des états de Markov dont les variations sont finies, mais dont les densités spectrales sont infinies à la fréquence zéro. Certains états ont des densités spectrales qui divergent à la fréquence zéro de la même façon que dans le cas des processus stochastiques à mémoire longue. En terminant, nous indiquons la façon dont lâéchantillonnage de Poisson qui est non linéaire et dépendant de lâétat modifie la distribution inconditionnelle et la dépendance temporelle.Mixing, Diffusion, Strong dependence, Long memory, Poisson sampling., mélange, diffusion, forte dépendance, mémoire longue, échantillonnage de Poisson.

Identifying change point in production time-series volatility using control charts and stochastic differential equations

The article focuses on volatility change point detection using SPC (Statistical Process Control) methods, specifically time-series control charts and stochastic differential equations (SDEs). Contribution will review recent advances in change point detection for the volatility component of a process satisfying stochastic differential equation (SDE) based on discrete observations, and also by using time-series control charts. Theoretical part will discuss methodology of time-series control charts and SDEs driven by a Brownian motion. Research part will demonstrate the methodologies in a simulation study focusing on analysis of the AR(1) process by means of time-series control charts and SDEs. The aim is to make use of change point detection in time series of production processes and highlight versatility of control charts not only in manufacturing but also in managing financial cash flow stability. © 2014, World Scientific and Engineering Academy and Society. All rights reserved

Nonlinearity and Temporal Dependence

Nonlinearities in the drift and diffusion coefficients influence temporal dependence in diffusion models. We study this link using three measures of temporal dependence: rho-mixing, beta-mixing and alpha-mixing. Stationary diffusions that are rho-mixing have mixing coefficients that decay exponentially to zero. When they fail to be rho-mixing, they are still beta-mixing and alpha-mixing; but coefficient decay is slower than exponential. For such processes we find transformations of the Markov states that have finite variances but infinite spectral densities at frequency zero. The resulting spectral densities behave like those of stochastic processes with long memory. Finally we show how state-dependent, Poisson sampling alters the temporal dependence.Diffusion, Strong dependence, Long memory, Poisson sampling, Quadratic forms

Complex-valued Time Series Modeling for Improved Activation Detection in fMRI Studies

A complex-valued data-based model with th order autoregressive errors and general real/imaginary error covariance structure is proposed as an alternative to the commonly used magnitude-only data-based autoregressive model for fMRI time series. Likelihood-ratio-test-based activation statistics are derived for both models and compared for experimental and simulated data. For a dataset from a right-hand finger-tapping experiment, the activation map obtained using complex-valued modeling more clearly identifies the primary activation region (left functional central sulcus) than the magnitude-only model. Such improved accuracy in mapping the left functional central sulcus has important implications in neurosurgical planning for tumor and epilepsy patients. Additionally, we develop magnitude and phase detrending procedures for complex-valued time series and examine the effect of spatial smoothing. These methods improve the power of complex-valued data-based activation statistics. Our results advocate for the use of the complex-valued data and the modeling of its dependence structures as a more efficient and reliable tool in fMRI experiments over the current practice of using only magnitude-valued datasets

Data Analytics and Managing Health and Medical Care

The purpose is to introduce the demand for the quality movement practice in problems associated with public health diagnostic testing and other health related problems We examine problems involving 1 Multivariate control charts which simultaneously monitor correlated variables 2 we explain why the scale on multivariate control charts is unrelated to the scale of the individual Variables control charts and 3 discover that out of control signals in multivariate charts do not reveal which variable or combination of variables causes the signal and application of quality monitoring New methods provide methods for MPC charts focus on the average run length as the decision factor We indicate that other decision criteria in multivariate control charts are availableand these methods can be useful in evaluating the design and implementation of multivariate charts in special circumstance

Detecting gradual changes in locally stationary processes

In a wide range of applications, the stochastic properties of the observed time series change over time. The changes often occur gradually rather than abruptly: the properties are (approximately) constant for some time and then slowly start to change. In many cases, it is of interest to locate the time point where the properties start to vary. In contrast to the analysis of abrupt changes, methods for detecting smooth or gradual change points are less developed and often require strong parametric assumptions. In this paper, we develop a fully nonparametric method to estimate a smooth change point in a locally stationary framework. We set up a general procedure which allows us to deal with a wide variety of stochastic properties including the mean, (auto)covariances and higher moments. The theoretical part of the paper establishes the convergence rate of the new estimator. In addition, we examine its finite sample performance by means of a simulation study and illustrate the methodology by two applications to financial return data.Comment: Published at http://dx.doi.org/10.1214/14-AOS1297 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org