Adaptive Classification of Interval-Valued Time Series

In recent years, the modeling and analysis of interval-valued time series have garnered significant attention in the fields of econometrics and statistics. However, the existing literature primarily focuses on regression tasks while neglecting classification aspects. In this paper, we propose an adaptive approach for interval-valued time series classification. Specifically, we represent interval-valued time series using convex combinations of upper and lower bounds of intervals and transform these representations into images based on point-valued time series imaging methods. We utilize a fine-grained image classification neural network to classify these images, to achieve the goal of classifying the original interval-valued time series. This proposed method is applicable to both univariate and multivariate interval-valued time series. On the optimization front, we treat the convex combination coefficients as learnable parameters similar to the parameters of the neural network and provide an efficient estimation method based on the alternating direction method of multipliers (ADMM). On the theoretical front, under specific conditions, we establish a margin-based multiclass generalization bound for generic CNNs composed of basic blocks involving convolution, pooling, and fully connected layers. Through simulation studies and real data applications, we validate the effectiveness of the proposed method and compare its performance against a wide range of point-valued time series classification methods. Introduction Interval-valued time series have attracted significant attention in the fields of statistics and econometrics in recent years [1, 2, 3, 4, 5, 6], as they can simultaneously capture variation and level information. In practical applications, interval-valued time series are quite common. For example, in macroeconomics, the minimum and maximum annualized monthly GDP growth rates form interval-valued data for annual GDP growth rate. In meteorology, interval-valued time series are widely used to describe daily weather conditions, such as pollutant concentrations and temperature. In general, interval-valued time series modeling offers two main advantages over point-valued time series [6]. Firstly, within the same time period, interval-valued time series contain more variation and level information [4, 5, 6], which means that modeling interval-valued time series can lead to more efficient estimation and powerful inference. Secondly, specific disturbances, which may be considered noise in point-valued time series modeling and have adverse effects, can be addressed through modeling interval-valued time series. Over the past three decades, numerous methods for modeling and analyzing univari-ate and multivariate interval-valued time series, particularly focusing on regression, have been proposed.