Hwai-Chung Ho

ON THE ASYMPTOTIC JOINT DISTRIBUTION OF THE SUM AND MAXIMUM OF STATIONARY NORMAL RANDOM VARIABLES

Let X 1 , X 2 , ·· ·be stationary normal random variables with ρ n = cov( X 0 , X n ). The asymptotic joint distribution of and is derived under the condition ρ n log n → γ [0,∞). It is seen that the two statistics are asymptotically independent only if γ = 0.

Time series and related topics : in memory of Ching-Zong Wei

A major research area of Ching-Zong Wei (1949--2004) was time series models and their applications in econometrics and engineering, to which he made many important contributions. A conference on time series and related topics in memory of him was held on December 12--14, 2005, at Academia Sinica in Taipei, where he was Director of the Institute of Statistical Science from 1993 to 1999. Of the forty-two speakers at the conference, twenty contributed to this volume. These papers are listed under the following three headings.

Weak ties and contact initiation in everyday life: Exploring contextual variations from contact diaries

Abstract This study examines how the significance of weak ties varies by contact initiation and purposes of contact in everyday life. Based on data from 55 contact diaries, we analyze the extent to which diary keepers judge each of 104,361 specific contacts as beneficial after they occur, by how well they knew the target person beforehand. Our hypothesis testing and bootstrap resampling show that when a diary keeper initiates a contact, weak ties result in more gains. In contrast, when the other party starts the contact, it is strong rather than weak ties that turn out to be more beneficial to the diary keeper. Such effects vary by other contextual factors, however, particularly the purposes of contacts.

Contact Trees: Network Visualization beyond Nodes and Edges

Node-Link diagrams make it possible to take a quick glance at how nodes (or actors) in a network are connected by edges (or ties). A conventional network diagram of a “contact tree” maps out a root and branches that represent the structure of nodes and edges, often without further specifying leaves or fruits that would have grown from small branches. By furnishing such a network structure with leaves and fruits, we reveal details about “contacts” in our ContactTrees upon which ties and relationships are constructed. Our elegant design employs a bottom-up approach that resembles a recent attempt to understand subjective well-being by means of a series of emotions. Such a bottom-up approach to social-network studies decomposes each tie into a series of interactions or contacts, which can help deepen our understanding of the complexity embedded in a network structure. Unlike previous network visualizations, ContactTrees highlight how relationships form and change based upon interactions among actors, as well as how relationships and networks vary by contact attributes. Based on a botanical tree metaphor, the design is easy to construct and the resulting tree-like visualization can display many properties at both tie and contact levels, thus recapturing a key ingredient missing from conventional techniques of network visualization. We demonstrate ContactTrees using data sets consisting of up to three waves of 3-month contact diaries over the 2004-2012 period, and discuss how this design can be applied to other types of datasets.

Measuring the default risk of sovereign debt from the perspective of network

Recently, there has been a growing interest in network research, especially in these fields of biology, computer science, and sociology. It is natural to address complex financial issues such as the European sovereign debt crisis from the perspective of network. In this article, we construct a network model according to the debt--credit relations instead of using the conventional methodology to measure the default risk. Based on the model, a risk index is examined using the quarterly report of consolidated foreign claims from the Bank for International Settlements (BIS) and debt/GDP ratios among these reporting countries. The empirical results show that this index can help the regulators and practitioners not only to determine the status of interconnectivity but also to point out the degree of the sovereign debt default risk. Our approach sheds new light on the investigation of quantifying the systemic risk.

On the strong uniform consistency of density estimation for strongly dependent sequences

For a stationary, possibly strongly dependent sequence {Xi} of standard Gaussian random variables, the strong uniform consistency of the kernel density estimates for sequence {Yi} modeled by Yi = H(Xt1 + i, ..., Xtd + i) is proved.

Estimation errors of the Sharpe ratio for long-memory stochastic volatility models

The Sharpe ratio, which is defined as the ratio of the excess expected return of an investment to its standard deviation, has been widely cited in the financial literature by researchers and practitioners. However, very little attention has been paid to the statistical properties of the estimation of the ratio. Lo (2002) derived the

On limiting distributions of nonlinear functions of noisy Gaussian sequences

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On Empirical Distribution of Long-Memory Stochastic Volatility Processes

-normality of the ratios estimation errors for returns which are iid or stationary with serial correlations, and pointed out that to make inference on the accuracy of the estimation, the serial correlation among the returns needs to be taken into account. In the present paper a class of time series models for returns is introduced to demonstrate that there exists a factor other than the serial correlation of the returns that dominates the asymptotic behavior of the Sharpe ratio statistics. The model under consideration is a linear process whose innovation sequence has summable coefficients and contains a latent volatility component which is long-memory. It is proved that the estimation errors of the ratio are asymptotically normal with a convergence rate slower than

Estimation of Short- and Long-Term VaR for Long-Memory Stochastic Volatility Models

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