Testing for a Unit Root with Near-Integrated Volatility

This paper considers tests for a unit root when the innovations follow a near-integrated GARCH process. We compare the asymptotic properties of the likelihood ratio statistic with that of the least-squares based Dickey-Fuller statistic. We first use asymptotics where the GARCH variance process is stationary with fixed parameters, and then consider parameter sequences such that the GARCH process converges to a diffusion process. In the fixed-parameter case, the asymptotic local power gain of the likelihood ratio test is only marginal for realistic parameter values. However, under near-integrated parameter sequences the difference in power is more pronounced.

Testing for Cointegration with Nonstationary Volatility

The paper generalises recent unit root tests for nonstationary volatility to a multivariate context. Persistent changes in the innovation variance matrix lead to size distortions in conventional cointegration tests, and possibilities of increased power by taking the time-varying volatilities and correlations into account. The testing procedures are based on a likelihood analysis of the vector autoregressive model with a conditional covariance matrix that may be estimated nonparametrically. We find that under suitable conditions, adaptation with respect to the volatility matrix process is possible, in the sense that nonparametric volatility estimation does not lead to a loss of asymptotic local power

Identifying, Estimating and Testing Restricted Cointegrated Systems: An Overview

The notion of cointegration has lead to a renewed interest in the identification and estimation of structural relations among economic time series, a field to which Henri Theil has made many pioneering contributions. This paper reviews the different approaches that have been put forward in the literature for identifying cointegrating relationships and imposing (possibly over-identifying) restrictions on them. Next, various algorithms to obtain (approximate) maximum likelihood estimates and likelihood ratio statistics are reviewed, with an emphasis on so-called switching algorithms. The implementation of these algorithms is discussed and illustrated using an empirical example.

The salient elephant in the room:exploring the concept of linguistic salience

The concept of linguistic salience is used differently in different subfields of linguistics. For example, in some subfields, linguistic salience has to do with the amount of attention a particular feature draws. In other subfields, linguistic salience relates to the prominence or frequency of a feature. Despite this variation, the meaning of this concept is assumed to be self-explanatory. When the concept is defined, in many cases the definition is circular. This is problematic because linguistic salience is used to explain multiple language related processes, such as language learning and language variation and change. It is no wonder, then, that the concept has been called ``notoriously difficult to quantify'' (Hickey, 2000). In this sense, the concept of salience is an elephant in the room. Accordingly, this dissertation addresses two questions. The first regards determining if there is a way to unify all the uses of linguistic salience in the literature. The second question involves identifying a quantifiable measure of linguistic salience. To answer these questions, I combine sociolinguistic theories with psycholinguistic methodologies. The research outcomes show that remarkability and complexity are underlying dimensions of linguistic salience. These operationalizations of linguistic salience can be explained through probability and context. Moreover, a feature’s salience can be measured through ERPs, but results are highly dependent on the situational context

Testing for periodic integration

A periodic autoregressive time-series model assumes that the autoregressive parameters vary with the season. This model can also be represented by a multivariate model for the annual vector containing the seasonal observations. When this multivariate model contains one unit root, a time-series is said to be periodically integrated of order 1. In this paper we propose tests for such a single unit root. These tests for periodic integration are applied to a periodic model for the quarterly German consumption series

Salience is in the brain of the beholder:ERPs reflect acoustically salient variables

A recent paper by Boswijk, Loerts & Hilton (Boswijk et al., 2020) in this journal discusses how technological advances allow us to explore the cognitive processing of so-called salient linguistic features, and how this could provide us with quantifiable measures of ‘salience’. The paper concludes that, although promising, the used measure of pupil dilation seems to be limited as a measure for linguistic salience, and therefore refers future research to other measures, specifically Event Related Potentials (ERPs). In this paper we therefore replicate the Boswijk et al. study using the ERP measure with the hypothesis that linguistic salience evokes distinct ERP components. We use the same materials that were used in the Boswijk et al. (2020) paper to observe changes in Dutch participants' pupil sizes when listening to stimuli containing salient and non-salient variants of linguistic variables. Using Generalized Additive Mixed Modelling (GAMM), we find distinct responses for five of six stimuli categories. We consider our findings in light of the literature on linguistic salience and discuss how our findings relate to the Boswijk et al. (2020) study. We find that ERPs provide a more fine-grained measure of theoretically salient stimuli

Salience is in the eye of the beholder:Increased pupil size reflects acoustically salient variables

‘Salience’ is a term frequently used in linguistics but an exact definition for the concept is lacking. Recent technological advances which allow us to explore the cognitive processing of so-called salient linguistic features could provide us with quantifiable measures of ‘salience’, and lead to a further understanding of the concept and its relationship to language acquisition and change. In this paper we measure pupil dilation with the assumption that auditory salience results in a change in pupil size, as an effect of cognitive load. We report an experimental study observing Dutch participants' pupil sizes when listening to stimuli containing salient and non-salient variants of linguistic variables (e.g. Dutch coda/r/; speech intensity, word frequency). Using Generalized Additive Mixed Modelling (GAMM), we find pupil size increases for three of six stimuli categories. We consider our findings in light of the speech processing literature, address the (dis)advantages of the technique, and formulate some recommendations for future advances in neurophysiological measures in (socio)linguistics

Adaptive wild bootstrap tests for a unit root with nonstationary volatility

Recent research has emphasised that permanent changes in the innovation variance (caused by structural shifts or an integrated volatility process) lead to size distortions in conventional unit root tests. Cavaliere and Taylor (2008) show how these size distortions may be resolved using the wild bootstrap. In this paper, we first derive the asymptotic power envelope for the unit root testing problem when the nonstationary volatility process is known. Next, we show that under suitable conditions, adaptation with respect to the volatility process is possible, in the sense that nonparametric estimation of the volatility process leads to the same asymptotic power envelope. Implementation of the resulting test involves cross-validation and the wild bootstrap. A Monte Carlo experiment shows that the asymptotic results are reflected in finite sample properties, and an empirical analysis of real exchange rates illustrates the applicability of the proposed procedures