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Autoregressive Conditional Models for Interval-Valued Time Series Data

Event Type
Statistics Department & Econometrics
1000 Lincoln Hall
Apr 24, 2014   3:30 - 5:15 pm  
Statistics Seminar - Dr. Yongmiao Hong (Cornell University)

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 min-

imum 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 top 10% income and bottom 10% income of a

cohort in a year, etc. Interval forecasts may be of direct interest in practice, as it contains informa-

tion on the range of variation and the level or trend of economic processes. More importantly, 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-maximum likelihood 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.

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