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The Econometric Analysis of Interval-Valued Time Series


This dissertation covers three topics in modeling and forecasting interval-valued time series.

In Chapter 1, we propose a model for interval-valued time series (ITS) that aims to generate valid point-valued forecasts. We dispense with the positive constraint on the range by estimating a bivariate system of the center/log-range. However, a forecast based on this system needs to be transformed to the original units of center/range, which requires bias correction. We examine the out-of-sample forecast performance of naive transformed forecasts (biased), parametric bias-corrected forecasts, and semiparametric correction methods like smearing correction and bootstrap forecasts. Monte Carlo simulations show that the biased correction methods do not generate forecasts that are uniformly superior. We apply these methods to the daily low/high intervals of the SP500 index and Google prices.

In Chapter 2, we go beyond point forecasts to construct the probabilistic forecasts for interval-valued time series. We estimate a bivariate system of the center/log-range, which may not be normally distributed. Implementing analytical or bootstrap methods, we directly transform prediction regions for center/log-range into those for center/range and upper/lower bounds systems. We propose new metrics to evaluate the regions performance. Monte Carlo simulations show bootstrap methods being preferred even in Gaussian systems. We build prediction regions for daily SP500 low/high return intervals, and apply them to develop a trading strategy.

In Chapter 3, we develop an alternative model directly on the ITS (upper/lower bounds system). The model specifies the conditional joint distribution of the upper and lower bounds of the interval to be a mixture of truncated bivariate normal distribution. This specification guarantees that the natural order of the interval (upper bound not smaller than lower bound) is preserved. The model also captures the potential conditional heteroscedasticity and non-Gaussian features in ITS. We propose an EM algorithm for model estimation. We establish the consistency of the maximum likelihood estimator. Monte Carlo simulations show the new EM algorithm has good convergence properties. We apply the model to the interval-valued IBM daily stock returns and it exhibits superior performance over competing methods.

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