Characterizing the Structure of Optimal Stopping Policies

This paper studies a stochastic model of optimal stopping processes, which arise frequently in operational problems (e.g., when a manager needs to determine an optimal epoch to stop a process). For such problems, we propose an effective method of characterizing the structure of the optimal stopping policy for the class of discrete‐time optimal stopping problems. Using this method, we also derive a set of metatheorems that can help identify when a threshold or control‐band type stopping policy is optimal. We show that our proposed method can determine the structure of the optimal policy for some stopping problems that conventional methods fail to do so. In some cases, our method also simplifies the analysis of some existing results. Moreover, the metatheorems we propose help identify sufficient conditions that yield simple optimal policies when such policies are not generally optimal. We demonstrate these benefits by applying our method to several optimal stopping problems frequently encountered in, for example, the operations, marketing, finance, and economics literatures. We note that with structural results, optimal‐stopping policies are easier to follow, describe, and compute and hence implement. They also help determine how a stopping policy should be adjusted in response to changes in the operational environment. In addition, as structural results are critical for the development of efficient algorithms to solve optimal stopping problems numerically, we hope that the method and results provided in the study will contribute to that effort.     

Bayesian automatic polynomial wavelet regression

This paper considers the problem of Bayesian automatic polynomial wavelet regression (PWR). We propose three different Bayesian methods based on integrated likelihood, conditional empirical Bayes, and reversible jump Markov chain Monte Carlo (MCMC). From the simulation results, we find that the proposed methods are similar to or superior to the existing ones.     

Double unit root tests for cross-sectionally dependent panel data

This paper proposes various double unit root tests for cross-sectionally dependent panel data. The cross-sectional correlation is handled by the projection method [P.C.B. Phillips and D. Sul, Dynamic panel estimation and homogeneity testing under cross section dependence, Econom. J. 6 (2003), pp. 217–259; H.R. Moon and B. Perron, Testing for a unit root in panels with dynamic factors, J. Econom. 122 (2004), pp. 81–126] or the subtraction method [J. Bai and S. Ng, A PANIC attack on unit roots and cointegration, Econometrica 72 (2004), pp. 1127–1177]. Pooling or averaging is applied to combine results from different panel units. Also, to estimate autoregressive parameters the ordinary least squares estimation [D.P. Hasza and W.A. Fuller, Estimation for autoregressive processes with unit roots, Ann. Stat. 7 (1979), pp. 1106–1120] or the symmetric estimation [D.L. Sen and D.A. Dickey, Symmetric test for second differencing in univariate time series, J. Bus. Econ. Stat. 5 (1987), pp. 463–473] are used, and to adjust mean functions the ordinary mean adjustment or the recursive mean adjustment are used. Combinations of different methods in defactoring to eliminate the cross-sectional dependency, integrating results from panel units, estimating the parameters, and adjusting mean functions yields various available tests for double unit roots in panel data. Simple asymptotic distributions of the proposed test statistics are derived, which can be used to find critical values of the test statistics.

We perform a Monte Carlo experiment to compare the performance of these tests and to suggest optimal tests for a given panel data. Application of the proposed tests to a real data, the yearly export panel data sets of several Latin–American countries for the past 50 years, illustrates the usefulness of the proposed tests for panel data, in that they reveal stronger evidence of double unit roots than the componentwise double unit root tests of Hasza and Fuller [Estimation for autoregressive processes with unit roots, Ann. Stat. 7 (1979), pp. 1106–1120] or Sen and Dickey [Symmetric test for second differencing in univariate time series, J. Bus. Econ. Stat. 5 (1987), pp. 463–473].     

Longitudinal trajectories of maternal parenting stress in Korean families: Children's executive function and school adjustment

A majority of mothers experience parenting stress in daily life; however high levels of maternal stress have been recognized as a risk factor for children's developmental outcomes. We examined trajectories of maternal parenting stress across childhood, and their longitudinal relations to children's executive function and school adjustment. Data were drawn from the Panel Study on Korean Children (PSKC), which included 1754 mothers across five waves measured at children ages 3, 4, 5, 6, and 7 (boys = 51%). Results of Latent Growth Curve Modeling (LGCM) revealed that, on average, maternal parenting stress decreased over time, but there were significant variabilities in the initial levels at age 3 and changes across early through middle childhood. High initial levels of stress and an increase in maternal parenting stress over time were associated with lower executive function at age 7 in planning-organizing and attention concentration. An increment in maternal parenting stress over time was related to poorer school adjustment at age 7, measured by classroom behavior, positive approach to learning, and child-peer and child-teacher relationships. These findings support cultural commonality and may contribute to the instantiation of culturally universal, early preventions and interventions to support mothers’ mental health. Efforts aimed at reducing maternal parenting stress early in development may promote better long-term developmental outcomes, including executive functioning and school adjustment of children in their first year of elementary school.     

On score vector- and residual-based CUSUM tests in ARMA–GARCH models

In this study, we consider the problem of testing for a parameter change in ARMA–GARCH models. We suggest two types of cumulative sum (CUSUM) tests, namely, score vector- and residual-based CUSUM tests. It is shown that under regularity conditions, their limiting null distributions are the sup of Brownian bridges. A simulation study and real data analysis are conducted for illustration.     

Modeling Dependence in High Dimensions With Factor Copulas

This article presents flexible new models for the dependence structure, or copula, of economic variables based on a latent factor structure. The proposed models are particularly attractive for relatively high-dimensional applications, involving 50 or more variables, and can be combined with semiparametric marginal distributions to obtain flexible multivariate distributions. Factor copulas generally lack a closed-form density, but we obtain analytical results for the implied tail dependence using extreme value theory, and we verify that simulation-based estimation using rank statistics is reliable even in high dimensions. We consider “scree” plots to aid the choice of the number of factors in the model. The model is applied to daily returns on all 100 constituents of the S&P 100 index, and we find significant evidence of tail dependence, heterogeneous dependence, and asymmetric dependence, with dependence being stronger in crashes than in booms. We also show that factor copula models provide superior estimates of some measures of systemic risk. Supplementary materials for this article are available online.     

Shipping Fees or Shipping Free? A Tale of Two Price Partitioning Strategies in Online Retailing

In this article, we study the price partitioning decisions of online retailers regarding shipping and handling (S&H) fees. Specifically, we analyze two partitioning formats used by retailers in this context. In the first scenario, retailers present customers with a price that is partitioned into a product price and a separate S&H surcharge (the PS strategy); in the second, customers are offered free shipping through a non‐partitioned format where the product price already includes the shipping cost (the ZS strategy). We first develop a stylized game‐theoretic model that captures the competitive dynamics between (and within) these two formats. Analysis of the model provides insights into how both firm and product level characteristics drive a retailer's strategic choice regarding which partitioning format to adopt and, hence, determines the equilibrium market structure in terms of proportion of ZS and PS retailers. Subsequently, we conduct empirical analyses, based on product and S&H prices data for two different product categories (digital cameras and printers) collected from online retailers, to validate all the results of our theoretical model. We establish that PS retailers charge lower product prices than ZS ones, but the total price (product + S&H) charged is higher for the first group. The S&H charge for PS retailers can be significant—it is, on average, 5.4% (printers) and 3.0% (digital cameras) for our two product categories. Furthermore, retailers which are popular and/or face risky cost environment are more likely to opt for the ZS strategy, while retailers whose portfolio mostly includes large or heavy products with high cost (S&H)‐to‐price ratios usually choose the PS strategy. Lastly, our empirical study also illustrates that the price adjustment behavior of retailers is affected by their shipping‐fee policies—for example, ZS retailers change their product prices almost 1.5 times more frequently than PS ones.     

Some asymptotic properties in INAR(1) processes with Poisson marginals

The first-order integer-valued autoregressive (INAR(1)) process with Poisson marginal distributions is considered. It is shown that the sample autocovariance function of the model is asymptotically normally distributed. We derive asymptotic distribution of Yule-Walker type estimators of parameters. It turns out that our Yule-Walker type estimators are better than the conditional least squares estimators proposed by Klimko and Nelson (1978) and Al-Osh and Alzaid (1987). also, we study the relationship between the model andM/M/∞ queueing system.     

Limited Income Mobility: Empirical Evidence from Korea

Longitudinal child cohort studies collect large amounts of information about children’s families and the types of activities they participate in. With such a broad array of information to select from, researchers investigating aspects of the family environment may be overwhelmed by the choices available if they only need summary measures reflecting domains of the family environment. Using data from the Longitudinal Study of Australian Children, this study aimed to derive and assess summary indices of three domains of the family environment, including a Family Stress Index, Home Education Index and Parenting Index. Indices were derived by identifying a set of candidate indicators, dichotomising the indicators to determine elements of risk, then averaging across the dichotomised items to create measures that captured cumulative risk. Assessments of the three indices suggest that the measures are consistent across time, and have good predictive validity with socioeconomic measures and assessments of children’s social-emotional wellbeing and learning outcomes. Structural equation models estimating children’s outcomes suggested that models using the indices had comparable model fit to models using the broader array of variables used to construct the indices, but the Parenting Index in particular explained less variation in children’s problem behaviour outcomes. Overall, the family environment indices derived in this study may be useful for researchers wishing to simplify complex models or explore the circumstances of children exposed to multiple risks, but less useful in analyses where the primary goal is to explain variance in children’s developmental outcomes.     

Assessing the Social Bonds of Elderly Neighbors: The Roles of Length of Residence, Crime Victimization, and Perceived Disorder

Starting from the rationale that elderly urban residents tend to be “neighborhood‐bound,” this study examines the relationship between age or aging and local social bonds (friendship, social cohesion and trust, informal social control, and participation in local organizations). Specifically, is the level of local bonding among elderly urban residents (age 65 and over) greater than that of the younger cohorts (17–35, 34–49, and 50–64)? Additionally, two specific hypotheses are constructed to examine the determinants of local social bonds among elderly urban residents: the systemic approach, regarding length of residence; and the social‐disorganization approach, regarding crime victimization and perceived disorder. Using Chicago data collected in 1995, the analysis found a substantial difference between the elderly cohort and each of the younger cohorts in only the friendship category of local social bonds. The other results show that in a sample of elderly urban residents, length of residence is the only significant, positive factor in local friendship, and that the two disorder predictors, physical and social, play a substantial role in weakening two types of local social bonds, social cohesion and trust and informal social control.