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

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Abstract

This study considers interval-valued time series data. To characterize such data, we propose an auto-interval-regressive (AIR) model using the order statistics from normal distributions. Furthermore, to better capture the heteroscedasticity in volatility, we design a heteroscedastic volatility AIR (HVAIR) model. We derive the likelihood functions of the AIR and HVAIR models to obtain the maximum likelihood estimator. Monte Carlo simulations are then conducted to evaluate our methods of estimation and confirm their validity. A real data example from the S&P 500 Index is used to demonstrate our method.

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References

  • Arroyo J, González-Rivera G, Maté C (2010) Forecasting with interval and histogram data. Some financial applications. In: Ullah A, Giles D (eds) Handbook of empirical economics and finance. Chapman and Hall, pp 247–280

  • Billard L, Diday E (2000) Regression analysis for interval-valued data. Data analysis, classification, and related methods. Springer, Berlin, pp 369–374

    MATH  Google Scholar 

  • Billard L, Diday E (2002) Symbolic regression analysis. Classification, clustering, and data analysis. Springer, Berlin, pp 281–288

    MATH  Google Scholar 

  • Billard L, Diday E (2003) From the statistics of data to the statistics of knowledge. J Am Stat Assoc 98:470–487

    Article  Google Scholar 

  • Billard L, Diday E (2006) Symbolic data analysis: conceptual statistics and data mining, 1st edn. Wiley, Chichester, UK

    Book  Google Scholar 

  • Blom G (1958) Statistical estimates and transformed beta-variables. Wiley, Hoboken

    MATH  Google Scholar 

  • Brito P (2007) Modelling and analysing interval data. In: Decker R, Lenz HJ (eds) Advances in data analysis. Springer, Berlin, Heidelberg

    Google Scholar 

  • Brito P (2014) Symbolic data analysis: another look at the interaction of data mining and statistics. WIREs Data Minnowl Disc 4:281–295

    Article  Google Scholar 

  • Brito P, Duarte Silva AP (2012) Modelling interval data with normal and skew-normal distributions. J Appl Stat 39:3–20

    Article  MathSciNet  Google Scholar 

  • Eberhart RC, Kennedy J (1995). A new optimizer using particle swarm theory. In: Proceedings of the 6th international symposium on micro machine and human science. IEEE, pp 39–43

  • González-Rivera G, Lin W (2013) Constrained regression for interval-valued data. J Bus Econ Stat 31(4):473–490

    Article  MathSciNet  Google Scholar 

  • Lima Neto EA, De Carvalho FAT (2008) Centre and range method for ftting a linear regression model to symbolic interval data. Comput Stat Data Anal 52:1500–1515

    Article  Google Scholar 

  • Lin W, González-Rivera G (2016) Interval-valued time series models: estimation based on order statistics exploring the agriculture marketing service data. Comput Stat Data Anal 100:694–711

    Article  MathSciNet  Google Scholar 

  • Maia ALS, De Carvalho FAT, Ludermir TB (2008) Forecasting models for interval-valued time series. Neurocomputing 71:3344–3352

    Article  Google Scholar 

  • Rodrigues PM, Salish N (2011) Modeling and forecasting interval time series with threshold models: an application to S&P500 index returns. Banco De Portugal, Economics and Research Department

  • Su Z-G, Wang P-H, Li Y-G, Zhou Z-K (2015) Parameter estimation from interval-valued data using the expectation-maximization algorithm. J Stat Comput Simul 85:320–338

    Article  MathSciNet  Google Scholar 

  • Teles P, Brito P (2015) Modeling interval time series with space-time processes. Commun Stat Theory Methods 44(17):3599–3627

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

We would like to thank the editor, AE, and two anonymous referees for their valuable comments.

Funding

Funding was provided by Ministry of Science and Technology, Taiwan (Grant No. MOST 108-2118-M-006-010-MY2) and National Research Foundation of Korea (Grant No. No. 2018R1A2A2A05019433).

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Authors and Affiliations

  1. Department of Statistics, Institute of Data Science, National Cheng Kung University, Tainan, Taiwan

    Liang-Ching Lin & Hsiang-Lin Chien

  2. Department of Statistics, Seoul National University, Seoul, 08826, South Korea

    Sangyeol Lee

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  1. Liang-Ching Lin
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  2. Hsiang-Lin Chien
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  3. Sangyeol Lee
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Correspondence to Liang-Ching Lin.

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Lin, LC., Chien, HL. & Lee, S. Symbolic interval-valued data analysis for time series based on auto-interval-regressive models. Stat Methods Appl 30, 295–315 (2021). https://doi.org/10.1007/s10260-020-00525-7

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  • DOI: https://doi.org/10.1007/s10260-020-00525-7

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