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Yun Luo, Gloria González-Rivera, A Truncated Mixture Transition Model for Interval-Valued Time Series, Journal of Financial Econometrics, Volume 22, Issue 4, Fall 2024, Pages 1130–1169, https://doi.org/10.1093/jjfinec/nbad022
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Abstract
We propose a model for interval-valued time series that specifies the conditional joint distribution of the upper and lower bounds as a mixture of truncated bivariate normal distributions. It preserves the interval natural order and provides great flexibility on capturing potential conditional heteroscedasticity and non-Gaussian features. The standard expectation maximization (EM) algorithm applied to truncated mixtures does not provide a closed-form solution in the M step. A new EM algorithm solves this problem. The model applied to the interval-valued IBM daily stock returns exhibits superior performance over competing models in-sample and out-of-sample evaluation. A trading strategy showcases the usefulness of our approach.