Interval-Valued Time Series Classification Using $D_K$-Distance
This work addresses classification for interval-valued time series, a problem relevant to fields like econometrics and finance, but it is incremental as it adapts existing imaging and deep learning techniques to a new data type.
The paper tackles the problem of classifying interval-valued time series, which had been overlooked in prior research, by extending point-valued time series imaging methods using the $D_K$-distance and applying deep learning models. The result demonstrates the method's superiority over existing point-valued classification approaches in simulations and real data applications.
In recent years, modeling and analysis of interval-valued time series have garnered increasing attention in econometrics, finance, and statistics. However, these studies have predominantly focused on statistical inference in the forecasting of univariate and multivariate interval-valued time series, overlooking another important aspect: classification. In this paper, we introduce a classification approach that treats intervals as unified entities, applicable to both univariate and multivariate interval-valued time series. Specifically, we first extend the point-valued time series imaging methods to interval-valued scenarios using the $D_K$-distance, enabling the imaging of interval-valued time series. Then, we employ suitable deep learning model for classification on the obtained imaging dataset, aiming to achieve classification for interval-valued time series. In theory, we derived a sharper excess risk bound for deep multiclassifiers based on offset Rademacher complexity. Finally, we validate the superiority of the proposed method through comparisons with various existing point-valued time series classification methods in both simulation studies and real data applications.