In this paper, we consider subgeometric (specifically, polynomial) ergodicity of univariate nonlinear autoregressions with autoregressive conditional heteroskedasticity (ARCH). The notion of subgeometric ergodicity was introduced in the Markov chain literature in the 1980s, and it means that the transition probability measures converge to the stationary measure at a rate slower than geometric; this rate is also closely related to the convergence rate of $\beta $-mixing coefficients. While the existing literature on subgeometrically ergodic autoregressions assumes a homoskedastic error term, this paper provides an extension to the case of conditionally heteroskedastic ARCH-type errors, considerably widening the scope of potential applications. Specifically, we consider suitably defined higher-order nonlinear autoregressions with possibly nonlinear ARCH errors and show that they are, under appropriate conditions, subgeometrically ergodic at a polynomial rate. An empirical example using energy sector volatility index data illustrates the use of subgeometrically ergodic AR–ARCH models.

It is well known that stationary geometrically ergodic Markov chains are $\beta$ -mixing (absolutely regular) with geometrically decaying mixing coefficients. Furthermore, for initial distributions other than the stationary one, geometric ergodicity implies $\beta$ -mixing under suitable moment assumptions. In this note we show that similar results hold also for subgeometrically ergodic Markov chains. In particular, for both stationary and other initial distributions, subgeometric ergodicity implies $\beta$ -mixing with subgeometrically decaying mixing coefficients. Although this result is simple, it should prove very useful in obtaining rates of mixing in situations where geometric ergodicity cannot be established. To illustrate our results we derive new subgeometric ergodicity and $\beta$ -mixing results for the self-exciting threshold autoregressive model.

In this paper, we discuss how the notion of subgeometric ergodicity in Markov chain theory can be exploited to study stationarity and ergodicity of nonlinear time series models. Subgeometric ergodicity means that the transition probability measures converge to the stationary measure at a rate slower than geometric. Specifically, we consider suitably defined higher-order nonlinear autoregressions that behave similarly to a unit root process for large values of the observed series but we place almost no restrictions on their dynamics for moderate values of the observed series. Results on the subgeometric ergodicity of nonlinear autoregressions have previously appeared only in the first-order case. We provide an extension to the higher-order case and show that the autoregressions we consider are, under appropriate conditions, subgeometrically ergodic. As useful implications, we also obtain stationarity and $\beta $ -mixing with subgeometrically decaying mixing coefficients.

Poor dietary quality is one of the leading modifiable risk factor for premature mortality worldwide. People live longer than ever, but spend more years with illness and disability although the ultimate goal is to increase healthy years of life. Less research has considered the role of dietary habits in relation to health or cardiometabolic disesase-free life expectancy (LE). This study investigate the association of diet quality with healthy and cardiometabolic disease-free LE between ages 50 and 85. The study comprised 8,075 participants of the Whitehall II study. Diet quality was assessed with Alternative Healthy Eating Index (AHEI) 2010 at phases 3, 5 and 7 and took the measure of diet closest to age of 50 years for each participant. We utilized repeat measures of self-rated health and cardiometabolic disease from the first observation when participants were aged 50 years or older. In the analyses the AHEI-2010 total score was categorized in to quintiles, where the lowest quintile represents unhealthiest diet quality and highest quintiles healthiest diet. Multistate life table models were used to estimate healthy and cardiometabolic disease-free LE from age 50 to 85 years for each category of AHEI-2010 quintiles and three occupational position group. Participants in the highest AHEI-2010 quintile lived 3.6 years longer in good health and 2.7 years longer without cardiometabolic diseases than participants in the lowest quintile of the AHEI-2010. Higher diet quality associated with an increased healthy and cardiometabolic disease-free LE was observed across different occupational positions: Men in highest occupational position and highest AHEI-2010 quintile lived 9.4 years longer with good health compared to lowest occupational position and lowest AHEI-2010 quintile and for women the corresponding difference was 8.2 years. In terms of proportion of years spent without cardiometabolic diseases ranged from 77% (high occupational position and highest AHEI-2010) to 57% (low occupational position and lowest AHEI-2010) in men and from 82% to 70% in women. The difference in years lived healthy across AHEI-2010 quintiles was most remarkable in persons with low occupation status. Healthier dietary habits are associated with longer healthy and longer cardiometabolic disease-free LE between ages 50 and 85. Attention to poor diet should be paid especially among people in the lowest occupational position.

This article builds on ethnomethodological, conversation analytic research on object transfers: how participants hand over objects to one another. By analyzing video recordings of mundane (cars) and institutional interactions (laboratories), we focus on situations where an object is central to and talked about in the joint course of action. We focus on different organizations of object transfer and show that one embodied move is decisive, either a sequentially implicative ‘give’ or an arm extension designed as a stand-alone ‘take’. We examine the interrelationship between the organization of the object transfer and the broader course of action (e.g. request or offer sequence), which is either overlapping or intersecting. We demonstrate that by making the decisive move, either the participant initially holding the object or her recipient critically influences the progression and trajectory of the activity, and displays agency. (Ethnomethodology, Conversation Analysis, multimodal interactions, objects in interaction, object transfers, agency)*

High-dimensional distributed semantic spaces have proven useful and effective for aggregating and processing visual, auditory and lexical information for many tasks related to human-generated data. Human language makes use of a large and varying number of features, lexical and constructional items as well as contextual and discourse-specific data of various types, which all interact to represent various aspects of communicative information. Some of these features are mostly local and useful for the organisation of, for example, argument structure of a predication; others are persistent over the course of a discourse and necessary for achieving a reasonable level of understanding of the content.

This paper describes a model for high-dimensional representation for utterance and text-level data including features such as constructions or contextual data, based on a mathematically principled and behaviourally plausible approach to representing linguistic information. The implementation of the representation is a straightforward extension of Random Indexing models previously used for lexical linguistic items. The paper shows how the implementedmodel is able to represent a broad range of linguistic features in a common integral framework of fixed dimensionality, which is computationally habitable, and which is suitable as a bridge between symbolic representations such as dependency analysis and continuous representations used, for example, in classifiers or further machine-learning approaches. This is achieved with operations on vectors that constitute a powerful computational algebra, accompanied with an associative memory for the vectors. The paper provides a technical overview of the framework and a worked through implemented example of how it can be applied to various types of linguistic features.

The effects of triboelectricity in a small-scale fluidized bed of polyethylene particles were investigated by imaging the particle layer in the vicinity of the column wall and by measuring the pressure drop across the bed. The average charge on the particles was altered by changing the relative humidity of the gas. A triboelectric charging model coupled with a computational fluid dynamics–discrete element method (CFD-DEM) model was utilized to simulate gas–particle flow in the bed. The electrostatic forces were evaluated based on a particle–particle particle–mesh method, accounting for the surface charge on the insulating walls. It was found that simulations with fixed and uniform charge distribution among the particles capture remarkably well both the agglomeration of the particles on the wall and the associated decrease in the pressure drop across the bed. With a dynamic tribocharging model, the charging rate had to be accelerated to render the computations affordable. Such simulations with an artificial acceleration significantly over-predict charge segregation and the wall becomes rapidly sheeted with a single layer of strongly charged particles.

The failure process of a Wedge-shaped ice edge is modelled by dividing the process in crushing failures at the contact and flaking failures initiating from high pressure in the contact. This type of approach has been shown earlier by Daley to give an explanation of the physical background of the line-like contact observed in ice-crushing tests and in full-scale measurements. Daley's model is developed further by studying the stress field in ice in more detail when applying the Coulomb macroscopic failure criterion to determine the force required for flaking failures. The analysis indicates that the shape of the flaking failure surface to minimise the force required to cause failure follows a logarithmic spiral. The shape of the spiral is related to the inner friction angle of ice and to the geometry of the ice edge. The curved flaking surfaces require considerably less force than straight surfaces used previously, especially with wide wedge angles. Finally, the model developed is used to simulate the time history of a crushing force measured in laboratory crushing tests and a good correspondence is obtained.

Ship traffic is the factor that presents in almost all of the existing grounding risk models. It is considered to be one of the main factors affecting the expected frequency of ship groundings. This is mostly accepted by experts as common sense. However, there is no research available on the actual dependency between ship traffic and grounding accidents. In this paper, we conduct a study aimed at determining the statistical dependency between the density and distribution of traffic, the number and frequency of grounding accidents and the dependency between the complexity of waterways and an actual accident. For this purpose we utilise statistical analysis of maritime traffic, obtained from Automatic Identification System (AIS) data and grounding accidents, enhanced with the expert elicitation techniques delivering the waterway complexity index. The sea area under investigation is the Gulf of Finland. The results show statistical dependency between frequency of grounding and waterway complexity as well as the traffic distribution. However, the study does not reveal any significant dependency between grounding and traffic density.

In this paper, we propose a new noncausal vector autoregressive (VAR) model for non-Gaussian time series. The assumption of non-Gaussianity is needed for reasons of identifiability. Assuming that the error distribution belongs to a fairly general class of elliptical distributions, we develop an asymptotic theory of maximum likelihood estimation and statistical inference. We argue that allowing for noncausality is of particular importance in economic applications that currently use only conventional causal VAR models. Indeed, if noncausality is incorrectly ignored, the use of a causal VAR model may yield suboptimal forecasts and misleading economic interpretations. Therefore, we propose a procedure for discriminating between causality and noncausality. The methods are illustrated with an application to interest rate data.