Models for monthly penetrations with incomplete panel data*

The purchase behaviour of consumers is observed in a panel during a month. The quantity of interest is the penetration of a product. The problem is that this quantity has to be estimated on the basis of incomplete data. For some or all respondents some weeks are missing. To this end the purchasing process is modeled with a variety of stochastic processes. The performance of some existing models is compared for penetrations of the complete population, but also for Bayesian estimates in subpopulations.     

Estimating the stationary distribution of a Markov chain

Summary. Let be a Markov chain with a unique stationary distribution . Let h be a bounded measurable function. Write and . This paper explores conditions for the consistency and asymptotic normality of the estimate of of assuming the existence of a solution to the Poisson equation . Our framework covers the case of nonirreducible Markov chains arising in many growth models in economics. Received: October 8, 2001; revised version: April 8, 2002 RID="*" ID="*" Thanks are due to Professors Rabi Bhattacharya, Nicholas Kiefer and Timothy Vogelsang on an earlier draft for helpful conversations, and a referee for insightful comments. Correspondence to: M.Majumdar     

A semiparametric technique to estimate survival probabilities

The role of the so-called surplus processes in the assessment of probability of survival of a company is well-known in risk theory and applications thereof. However, the insurance models used in this regard ignore the fact that, in many situations, no relevant information is available for the assessment of survival after the company goes out of business. In this paper, we revisit the classical risk model in order to remedy this situation. Having stopped the deficit process, which is negative of the surplus process, at the time of ruin, under two different sampling schemes, we obtain inference procedure for ruin probabilities. As by products of our methodology, we also obtain procedures to assess the reliability of systems whose survival depends on a cumulative damage process, which is equivalent to the aggregate claim size process of the classical risk model.     

First-Order Integer-Valued Autoregressive (INAR (1)) Process: Distributional and Regression Properties

Some properties of a first-order integer-valued autoregressive process (INAR)) are investigated. The approach begins with discussing the self-decomposability and unimodality of the 1-dimensional marginals of the process {X_n} generated according to the scheme X_n=α° X _n-i +e_n, where α° X _n-1 denotes a sum of X_{n - 1}, independent 0 - 1 random variables Y^(n-1), independent of X _n-1 with Pr -( y ^{(n - 1)}= 1) = 1 - Pr ( y ^(n-i)= 0) =α. The distribution of the innovation process ( e _n) is obtained when the marginal distribution of the process ( X _n) is geometric. Regression behavior of the INAR(1) process shows that the linear regression property in the backward direction is true only for the Poisson INAR(1) process.     

中国享受美国普惠制待遇前景展望

美国是世界上31个普惠制给惠国中3个没有给中国普惠待遇的发达国家之一。其理由是共产党领导的中国不符合美国贸易法规定的三个条件之一－中国不是WTO的成员。现在，中国即将入世，提出享受美普惠制待遇的时机已成熟，但由于普惠制政策由给惠国单方面制定，中国能否享受其优惠关税待遇，前景还不容乐观，机遇与挑战并存。本文对中国面对的机遇与挑战进行了全面的分析。     

An Application of a Displaced Poisson Process*

Abstract A displaced Poisson process is presented as a reasonable model in describing the stages of certain chronic diseases. Although in some respects the model is an oversimplification of the true picture its feature is that it facilitates the easy estimation of some of the important parameters that arise in this area. Among the quantities estimated are the mean lead time and the distribution function of the time spent in the preclinical state. Properties of some of the estimators are obtained.     

A Forecasting Model for Stock Market Diversity

We apply the recently introduced generalized tree-structured (GTS) model to the analysis and forecast of stock market diversity. Diversity is a measure of capital concentration across a market that plays a central role in the search for arbitrage. The GTS model allows for different conditional mean and volatility regimes that are directly related to the behavior of macroeconomic fundamentals through a binary threshold construction. Testing on US market data, we collect empirical evidence of the model’s strong potential in estimating and forecasting diversity accurately in comparison with other standard approaches. In addition, the GTS model allows for the construction of very simple portfolio strategies that systematically beat the standard cap-weighted S&P500 index. Financial support by the Foundation for Research and Development of the University of Lugano and by the National Centre of Competence in Research “Financial Valuation and Risk Management” (NCCR FINRISK) is gratefully acknowledged. The authors thank four anonymous referees for helpful comments.     

Are international stock returns predictable?: An examination of linear and non-linear predictability using generalized spectral tests

This paper uses generalized spectral tests to examine whether international stock index returns are predictable using the history of the series. Unlike many other testing procedures, the generalized spectral tests used in this paper are robust to distributional assumptions, the presence of time-varying volatility, and allow for various forms of non-linear predictability. We find evidence of predictability in mean for over half of the international returns examined. In addition, we find most of the predictability to be non-linear in nature. The patterns of predictability are consistent with calendar effects and in some cases long-run dependence. Regardless of the implications of predictability of returns, this study is important because the generalized spectrum is defined for a range of different frequencies (corresponding to cycles of 2 days and greater), and we can therefore examine at what frequencies predictability occurs. This provides insight into whether there exists short-run, long-run, or both types of dependence.     

Sharp bounds on change in expected values and variances for single risk analysis in the flood catastrophe model

In the paper we propose a method how to assess sharp bounds on change in the expected value and variance of the individual loss distributions of the risks in the flood catastrophe model. The method does not involve the use of the whole model, only the river discharge distributions and above mentioned loss distribution moments are required. We present the method on a case study inspired by floods in Poland.     

Semiparametric Bayesian estimation of mixed count regression models

This paper develops semiparametric Bayesian estimation approach for Poisson regression models with unobserved heterogeneity of unknown density. This approach is computationally efficient and allows automatic adaptation of the approximating density to data during estimation. Simulations show the estimator performs well.