Symbolic interval-valued data analysis for time series based on auto-interval-regressive models

Liang, Lin; Chien, Hsiang Lin; Lee, Sangyeol

doi:10.1007/s10260-020-00525-7

Cited by 9 publications

(22 citation statements)

References 11 publications

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“…Therefore, we can define further seasonal measurements to analyze tourism seasonality. As a future study, we could consider reviewing contribution factors for seasonality, although we might need to develop further statistical models [44,45].…”

Section: Discussionmentioning

confidence: 99%

New seasonal measurement with stability and clustering seasonal patterns: A case study in Japan from 2011 to 2019

Ogasawara

2022

PLoS ONE

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Seasonality of tourism demand witnesses fluctuations over multiple years. The fluctuations and seasonality often cause seasonal pattern changes. This study presents a new seasonal measurement that considers the stability of seasonal patterns. The measurement is based on a seasonal index and expressed interval-valued data, which are a kind of symbolic data. As a case study, the new measurements are calculated from Japanese overnight data from 2011 to 2019 and the results classify the seasonal patterns of 47 prefectures using a hierarchical clustering method for interval-valued data based on Ward’s method. The analysis results indicate that there are differences in not only seasonal patterns but also their stability between domestic overnight demand and inbound overnight demand. The analysis procedure suggested in this study could be helpful in organizing numerous other unstable seasonal patterns.

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Section: Discussionmentioning

confidence: 99%

New seasonal measurement with stability and clustering seasonal patterns: A case study in Japan from 2011 to 2019

Ogasawara

2022

PLoS ONE

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“…We set Y t = (Y u,t , Y l,t ) T . Lin et al 11 proposed an auto-interval-regressive model with lag p, abbreviated as the AIR(p) model, as follows:…”

Section: Interval-valued Time Series Modelmentioning

confidence: 99%

“…In this subsection, we propose a general heteroscedastic volatility model that extends 11 HVAIR model. Here, the heteroscedastic volatility property is designated as the innovation term instead of the observation term as shown in Lin et al 11 Thus, the proposed model can be flexibly combined with the IVMA and AIRMA models. Let A t = (A u,t , A l,t ) T be the error terms at time t, where A u,t and A l,t are largest and smallest order statistics of i.i.d.…”

Section: Heteroscedastic Volatility Modelsmentioning

confidence: 99%

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Comprehensive interval‐valued time series model with application to the S&P 500 index and PM2.5 level data analysis

Lin

Sung

Lee

2022

Appl Stoch Models Bus & Ind

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In this study, we develop comprehensive symbolic interval-valued time-series models, including interval-valued moving average, auto-interval-regressive moving average, and heteroscedastic volatility models. These models can be flexibly combined to adapt more effectively to various situations. To make inferences regarding these models, likelihood functions were derived, and maximum likelihood estimators were obtained. To evaluate the performance of our methods empirically, Monte Carlo simulations and real data analyses were conducted using the S&P 500 index and PM2.5 levels of 15 stations in southern Taiwan. In the former case, it was found that the proposed model outperforms all other existing methods, whereas in the latter case, the residuals deduced from the proposed models provide more intuitively appealing results compared to the conventional vector autoregressive models. Overall, our findings strongly confirm the adequacy of the proposed model.

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“…I NTERVAL-VALUED data have gained increasing attention across a variety of contexts, as they offer a systematic way to capture information complete with an intrinsic representation of range or uncertainty in each individual 'measurement', which is not possible using point-values, such as numbers or ranks. Such data may arise due to imprecision and uncertainty in measurement (e.g., sensor data), inherent uncertainty of outcome (e.g., estimations of stock prices [1], climate/weather forecasting [2]), or inherent vagueness or nuance (e.g., in linguistic terms [3]). A growing body of evidence also suggests that subjective judgement of humans (e.g., experts, consumers) may be better represented by intervals [4], [5], where the interval width/size captures the response range as a conjunctive set (e.g., the reals between 2 and 4), or degree of uncertainty in respect to an estimate or rating -a disjunctive set (e.g., confidence interval) [6].…”

Section: Introductionmentioning

confidence: 99%

Towards Handling Uncertainty-at-Source in AI -- A Review and Next Steps for Interval Regression

Kabir¹,

Wagner²,

Ellerby³

2021

Preprint

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Most of statistics and AI draw insights through modelling discord or variance between sources of information (i.e., inter-source uncertainty). Increasingly, however, research is focusing upon uncertainty arising at the level of individual measurements (i.e., within-or intra-source), such as for a given sensor output or human response. Here, adopting intervals rather than numbers as the fundamental data-type provides an efficient, powerful, yet challenging way forward -offering systematic capture of uncertainty-at-source, increasing informational capacity, and ultimately potential for insight. Following recent progress in the capture of interval-valued data, including from human participants, conducting machine learning directly upon intervals is a crucial next step. This paper focuses on linear regression for interval-valued data as a recent growth area, providing an essential foundation for broader use of intervals in AI. We conduct an in-depth analysis of state-ofthe-art methods, elucidating their behaviour, advantages, and pitfalls when applied to datasets with different properties. Specific emphasis is given to the challenge of preserving mathematical coherence -i.e., ensuring that models maintain fundamental mathematical properties of intervals throughout -and the paper puts forward extensions to an existing approach to guarantee this. Carefully designed experiments, using both synthetic and real-world data, are conducted -with findings presented alongside novel visualizations for interval-valued regression outputs, designed to maximise model interpretability. Finally, the paper makes recommendations concerning method suitability for data sets with specific properties and highlights remaining challenges and important next steps for developing AI with the capacity to handle uncertainty-at-source. 1 Impact Statement-Capturing information as intervals, rather than numbers, provides a powerful means for handling uncertainty and inherent range in data. This paper focuses on a basic building block of statistics and AI: linear regression. In recent years, regression for intervals has become a topic of interest in AI, and has been applied to domains ranging from marketing to cyber-security. It allows direct modelling of relationships not only between variables per-se, but also concerning their associated uncertainty. For example, we can infer not only how a snack's nutritional benefits impact consumer purchase intention, but also how uncertainty about these benefits impacts purchase intention and its own associated uncertainty. Nonetheless, while there are considerable upsides to interval-valued regression and AI, substantial challenges remain. This paper reviews, analyses and extends state-of-the-art interval regression methods, presenting in-depth experimental results and introducing novel visualisations, to enhance model interpretability and provide context and data-specific recommendations for algorithm selection.

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Symbolic interval-valued data analysis for time series based on auto-interval-regressive models

Cited by 9 publications

References 11 publications

New seasonal measurement with stability and clustering seasonal patterns: A case study in Japan from 2011 to 2019

New seasonal measurement with stability and clustering seasonal patterns: A case study in Japan from 2011 to 2019

Comprehensive interval‐valued time series model with application to the S&P 500 index and PM2.5 level data analysis

Towards Handling Uncertainty-at-Source in AI -- A Review and Next Steps for Interval Regression

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