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Autoregressive Conditional Models for Interval-Valued Time Series Data

Friday 8 March 2013, 3.15PM to 5.00pm

Speaker(s): Dr. Ai Han, Chinese Academy of Sciences (Beijing)

This is a joint seminar with Professor Shouyang Wang and Dr. Xun Zhang also speaking. See department seminars for more details regarding their talks.

Abstract: An interval-valued observation in a time period contains more information than a point-valued observation in the same time period. Examples of interval data include the maximum and minimum temperatures in a day, the maximum and minimum GDP growth rates in a year, the maximum and minimum asset prices in a trading day, the bid and ask prices in a trading period, the long term and short term interests, and the 90%-tile and 10%-tile incomes of a cohort in a year, etc. Interval forecasts may be of direct interest in practice, as it contains information on the range of variation and the level or trend of economic processes. Moreover, the informational advantage of interval data can be exploited for more efficient econometric estimation and inference. We propose a new class of autoregressive conditional interval (ACI) models for interval-valued time series data. A minimum distance estimation method is proposed to estimate the parameters of an ACI model, and the consistency, asymptotic normality and asymptotic efficiency of the proposed estimator are established. It is shown that a two-stage minimum distance estimator is asymptotically most efficient among a class of minimum distance estimators, and it achieves the Cramer-Rao lower bound when the left and right bounds of the interval innovation process follow a bivariate normal distribution. Simulation studies show that the two-stage minimum distance estimator outperforms conditional least squares estimators based on the ranges and/or midpoints of the interval sample, as well as the conditional quasi-maximumlikelihood estimator based on the bivariate left and right bound information of the interval sample. In an empirical study on asset pricing, we document that when return interval data is used, some bond market factors, particularly the default risk factor, are significant in explaining excess stock returns, even after the stock market factors are controlled in regressions. This differs from the previous findings (e.g., Fama and French (1993)) in the literature.


Dr. Han is an assistant professor, affiliated with Academy of Mathematics and Systems Science/National Center for Mathematics and Interdisciplinary Science, Chinese Academy of Sciences. Dr. Ai Han’s research focuses on a novel interval-based methodology in econometrics and statistics. She was awarded for several prizes including Green Group Award of Computational Finance and Business Intelligence 2012, Omaha USA; Zhuli Yuehua Award in Management Sciences for Excellent PhD Student, Chinese Academy of Sciences, 2011, Beijing, China,; WPI Young Researcher, WPI Immunology Frontier Research Center, Osaka University, 2009, Osaka, Japan, First-place in GeLin Scholar, Chinese Academy of Sciences, 2009.

Research areas: Interval modelling, econometric theory, asymptotic theory, time series analysis.

Location: Economics Staff Room (EC/202)

Admission: For Staff and PhD students