Detecting Directionality in Time Series

Abstract

Directionality can be seen in many stationary time series from various disciplines, but it is overlooked when fitting linear models with Gaussian errors. Moreover, we cannot rely on distinguishing directionality by comparing a plot of a time series in time order with a plot in reverse time order. In general, a statistical measure is required to detect and quantify directionality. There are several quite different qualitative forms of directionality, and we distinguish: rapid rises followed by slow recessions; rapid increases and rapid decreases from the mean followed by slow recovery toward the mean; directionality above or below some threshold; and intermittent directionality. The first objective is to develop a suite of statistical measures that will detect directionality and help classify its nature. The second objective is to demonstrate the potential benefits of detecting directionality. We consider applications from business, environmental science, finance, and medicine. Time series data are collected from many processes, both natural and anthropogenic, by a wide range of organizations, and directionality can easily be monitored as part of routine analysis. We suggest that doing so may provide new insights to the processes.     

Student budgets and widening participation: Comparative experiences of finance in low and higher income undergraduates at a northern red brick university

Drawing on a thematic analysis of longitudinal qualitative data (n_total = 118), this article takes a “whole student lifecycle” approach to examine how lower and higher income students at an English northern red brick university variously attempted to manage their individual budgets. It explores how students reconcile their income—in the form of loans, grants, and bursaries—with the cost of living. Four arenas of interest are described: planning, budgeting, and managing “the student loan”; disruptions to financial planning; the role of familial support; and strategies of augmenting the budget. In detailing the micro‐level constraints on the individual budgets of lower and higher income undergraduates, the article highlights the importance of non‐repayable grants and bursaries in helping to sustain meaningful participation in higher tariff, more selective, higher education institutions. It also supports an emerging body of literature that suggests that the continuing amendments to the system of funding higher education in England are unlikely to address inequality of access, participation, and outcome.     

Modeling Finite‐Time Failure Probabilities in Risk Analysis Applications

In this article, we introduce a framework for analyzing the risk of systems failure based on estimating the failure probability. The latter is defined as the probability that a certain risk process, characterizing the operations of a system, reaches a possibly time‐dependent critical risk level within a finite‐time interval. Under general assumptions, we define two dually connected models for the risk process and derive explicit expressions for the failure probability and also the joint probability of the time of the occurrence of failure and the excess of the risk process over the risk level. We illustrate how these probabilistic models and results can be successfully applied in several important areas of risk analysis, among which are systems reliability, inventory management, flood control via dam management, infectious disease spread, and financial insolvency. Numerical illustrations are also presented.     

论郭沫若《凤凰涅槃》的修订及其释义

《凤凰涅槃》作为收入诗集《女神》的一首白话新诗，它鲜明地表现了五四时代的不乏困惑的理想主义、革新精神和自我精神，同时也极好的融合中国古典的传统和西洋现代主义精神。郭沫若对该诗持续的修改表明了时代思潮的更替、诗人思想情感的变幻，以及诗歌形式的完善。“凤凰涅槃”是郭沫若创造的一个跨文化(诗意)新词。     

Quantal Risk Assessment Database: A Database for Exploring Patterns in Quantal Dose‐Response Data in Risk Assessment and its Application to Develop Priors for Bayesian Dose‐Response Analysis

Quantitative risk assessments for physical, chemical, biological, occupational, or environmental agents rely on scientific studies to support their conclusions. These studies often include relatively few observations, and, as a result, models used to characterize the risk may include large amounts of uncertainty. The motivation, development, and assessment of new methods for risk assessment is facilitated by the availability of a set of experimental studies that span a range of dose‐response patterns that are observed in practice. We describe construction of such a historical database focusing on quantal data in chemical risk assessment, and we employ this database to develop priors in Bayesian analyses. The database is assembled from a variety of existing toxicological data sources and contains 733 separate quantal dose‐response data sets. As an illustration of the database's use, prior distributions for individual model parameters in Bayesian dose‐response analysis are constructed. Results indicate that including prior information based on curated historical data in quantitative risk assessments may help stabilize eventual point estimates, producing dose‐response functions that are more stable and precisely estimated. These in turn produce potency estimates that share the same benefit. We are confident that quantitative risk analysts will find many other applications and issues to explore using this database.     

Reconceptualizing the generation in a digital(izing) modernity: digital media,social networking sites,and the flattening of generations

As digitalization binds society to an apparently perpetual acceleration, questions about the nature of time and speed have gained new urgency in the social sciences. Yet, theorizations of these issues have neglected their implications for social life and generations. Linking these lacunae, this article articulates how digital media and social networking sites (SNS) shape social life through cultural transformations in the generation. This article rationalizes predominant patterns of SNS user behaviors in the context of social theoretical and philosophical frameworks informed by Mannheim, Simmel, Adorno, Benjamin, Arendt, social presence, action, and acceleration theories to offer a relational reconceptualization of the generation as a set of social relations and processes for visualizing changing conceptions of time and speed in a digital (izing) modernity. This article introduces the concept of general and local generationing processes to articulate the processual nature of the generation and to assert that trends in SNS use and content production are underwritten by grammatical logics that collectively “flatten” separate traditional generations to form a cross-demographic and cross-temporal digital generation.     

Test of parameter changes in a class of observation-driven models for count time series

Abstract

This paper investigates the parameter-change tests for a class of observation-driven models for count time series. We propose two cumulative sum (CUSUM) test procedures for detection of changes in model parameters. Under regularity conditions, the asymptotic null distributions of the test statistics are established. In addition, the integer-valued generalized autoregressive conditional heteroskedastic (INGARCH) processes with conditional negative binomial distributions are investigated. The developed techniques are examined through simulation studies and also are illustrated using an empirical example.     

Bayesian sample size determination for phase IIA clinical trials using historical data and semi‐parametric prior's elicitation

The Simon's two‐stage design is the most commonly applied among multi‐stage designs in phase IIA clinical trials. It combines the sample sizes at the two stages in order to minimize either the expected or the maximum sample size. When the uncertainty about pre‐trial beliefs on the expected or desired response rate is high, a Bayesian alternative should be considered since it allows to deal with the entire distribution of the parameter of interest in a more natural way. In this setting, a crucial issue is how to construct a distribution from the available summaries to use as a clinical prior in a Bayesian design. In this work, we explore the Bayesian counterparts of the Simon's two‐stage design based on the predictive version of the single threshold design. This design requires specifying two prior distributions: the analysis prior, which is used to compute the posterior probabilities, and the design prior, which is employed to obtain the prior predictive distribution. While the usual approach is to build beta priors for carrying out a conjugate analysis, we derived both the analysis and the design distributions through linear combinations of B‐splines. The motivating example is the planning of the phase IIA two‐stage trial on anti‐HER2 DNA vaccine in breast cancer, where initial beliefs formed from elicited experts' opinions and historical data showed a high level of uncertainty. In a sample size determination problem, the impact of different priors is evaluated.     

Time varying long memory parameter estimation for locally stationary long memory processes

The semiparametric estimators of time varying long memory parameter are investigated for locally stationary long memory processes. The GPH estimator and the local Whittle estimator are considered. Under some mild regularity assumptions, the weak consistency and the asymptotic normality of the estimators are obtained. The finite sample performance of the estimators is discussed through a small simulation study.     

Expansion and estimation of Lévy process functionals in nonlinear and nonstationary time series regression

In this article, we develop a series estimation method for unknown time-inhomogeneous functionals of Lévy processes involved in econometric time series models. To obtain an asymptotic distribution for the proposed estimators, we establish a general asymptotic theory for partial sums of bivariate functionals of time and nonstationary variables. These results show that the proposed estimators in different situations converge to quite different random variables. In addition, the rates of convergence depend on various factors rather than just the sample size. Finite sample simulations are provided to evaluate the finite sample performance of the proposed model and estimation method.