Modeling interval trendlines: Symbolic singular spectrum analysis for interval time series

Abstract

In this article we propose an extension of singular spectrum analysis for interval-valued time series. The proposed methods can be used to decompose and forecast the dynamics governing a set-valued stochastic process. The resulting components on which the interval time series is decomposed can be understood as interval trendlines, cycles, or noise. Forecasting can be conducted through a linear recurrent method, and we devised generalizations of the decomposition method for the multivariate setting. The performance of the proposed methods is showcased in a simulation study. We apply the proposed methods so to track the dynamics governing the Argentina Stock Market (MERVAL) in real time, in a case study over a period of turbulence that led to discussions of the government of Argentina with the International Monetary Fund.

Interval time series forecasting: A systematic literature review

“…Forecasting process : During the forecasting process, interval‐valued numbers, triangular fuzzy numbers, and trapezoidal fuzzy numbers can be predicted using the upper and lower bounds (Carvalho & Martos, 2021; Chou et al, 2020; Maia & Carvalho, 2019; Souza et al, 2017; Sun, Han, et al, 2018; Yang et al, 2022) or transformed into a central radius (Francisco et al, 2021; Guo & Hao, 2017; Liu et al, 2022; Maté, 2022; Sun, Wang, & Wei, 2020). The forecasting of interval gray numbers can also be implemented using an upper‐lower boundary (Chen et al, 2019; Jiang et al, 2020; Xie, 2018; Xie & Liu, 2015; Xie et al, 2014; Zeng et al, 2016) or transformed into geometric features (Xiong et al, 2018, 2020; Yang & Xue, 2017; Ye et al, 2019).…”

“…The main idea of the hybrid framework based on the decomposition method is to use decomposition methods to divide the time series into regular sub‐modes and then use other models for forecasting. Sun, Wang, and Wei (2020), Carvalho and Martos (2021), Liu et al (2022), Yang et al (2022), and Wang, Li, et al (2022), Wang, Chudhery, et al (2023) demonstrated that decomposition techniques can effectively improve the forecasting accuracy.…”

“…Data from other sources also comprise interval‐valued type data. The difference is that models based on statistical forecasting methods tend to transform historical data and other interval‐valued information into center‐radius series before modeling (Domingues et al, 2010; Fagundes et al, 2016; Giordani, 2015; Xiong et al, 2018, 2020; Zeng et al, 2010, 2021), while artificial‐intelligence‐based forecasting methods model historical data and other interval‐valued information by constructing multiple‐input multiple‐output neural networks (Carvalho & Martos, 2021; Fang et al, 2006; Froelich & Salmeron, 2014; Hu et al, 2015; Huang, Tao, et al, 2021; Wang, Chen, & Chen, 2020). Text information is quantified into scores using sentiment analysis technology and then converted into interval‐type data (Hajek et al, 2020).…”

“…Current interval forecasting research is mainly focused on two‐source information based on historical data and influencing factors (comprising 27 of the target studies herein). This is because, in a complex economic system, the study of single‐source information is consistently unable to fully describe the data characteristics (Carvalho & Martos, 2021). Therefore, considering the influence of other factors on the forecasting process significantly improves the forecasting system (Zeng et al, 2019).…”

“…Information‐source‐based studies are aimed at improving the predictability of the interval time series by supplementing external information sources (Carvalho & Martos, 2021; Hajek et al, 2020; Xiong et al, 2018, 2020). These studies primarily include the use of historical models, influencing‐factor‐based models (Chang et al, 2022; Garda‐Martos et al, 2013; Huang, Sun, & Wang, 2021; Ji et al, 2022; Lu et al, 2022; Tan & Wang, 2017; Wang, Gao, et al, 2023; Xu & Qin, 2023), and unstructured models (Amuri & Marcucci, 2017; Fan et al, 2017; Huang & He, 2020; Ren et al, 2018; Sun et al, 2017; Sun, Wei, et al, 2019).…”