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Bayesian Fuzzy Clustering with Robust Weighted Distance for Multiple ARIMA and Multivariate Time-Series

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  • Pacifico, Antonio

Abstract

The paper suggests and develops a computational approach to improve hierarchical fuzzy clustering time-series analysis when accounting for high dimensional and noise problems in dynamic data. A Robust Weighted Distance measure between pairs of sets of Auto-Regressive Integrated Moving Average models is used. It is robust because Bayesian Model Selection methodology is performed with a set of conjugate informative priors in order to discover the most probable set of clusters capturing different dynamics and interconnections among time-varying data, and weighted because each time-series is 'adjusted' by own Posterior Model Size distribution in order to group dynamic data objects into 'ad hoc' homogenous clusters. Monte Carlo methods are used to compute exact posterior probabilities for each cluster chosen and thus avoid the problem of increasing the overall probability of errors that plagues classical statistical methods based on significance tests. Empirical and simulated examples describe the functioning and the performance of the procedure. Discussions with related works and possible extensions of the methodology to jointly deal with endogeneity issues and misspecified dynamics in high dimensional multicountry setups are also displayed.

Suggested Citation

  • Pacifico, Antonio, 2020. "Bayesian Fuzzy Clustering with Robust Weighted Distance for Multiple ARIMA and Multivariate Time-Series," MPRA Paper 104379, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:104379
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    File URL: https://mpra.ub.uni-muenchen.de/117391/1/Manuscript_AP.pdf
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    References listed on IDEAS

    as
    1. Maharaj, E.A., 1994. "A Significance Test for Classifying ARMA Models," Monash Econometrics and Business Statistics Working Papers 18/94, Monash University, Department of Econometrics and Business Statistics.
    2. Antonio Pacifico, 2019. "Structural Panel Bayesian VAR Model to Deal with Model Misspecification and Unobserved Heterogeneity Problems," Econometrics, MDPI, vol. 7(1), pages 1-24, March.
    3. Umberto Triacca, 2016. "Measuring the Distance between Sets of ARMA Models," Econometrics, MDPI, vol. 4(3), pages 1-11, July.
    4. J. Carroll & Jih-Jie Chang, 1970. "Analysis of individual differences in multidimensional scaling via an n-way generalization of “Eckart-Young” decomposition," Psychometrika, Springer;The Psychometric Society, vol. 35(3), pages 283-319, September.
    5. Antonio Pacifico, 2019. "International Co-movements and Business Cycles Synchronization Across Advanced Economies: A SPBVAR Evidence," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 8(4), pages 68-84, July.
    6. Domenico Piccolo, 1990. "A Distance Measure For Classifying Arima Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 11(2), pages 153-164, March.
    7. Gary Koop & Dimitris Korobilis, 2012. "Forecasting Inflation Using Dynamic Model Averaging," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 53(3), pages 867-886, August.
    8. Bradley P. Carlin & Alan E. Gelfand & Adrian F. M. Smith, 1992. "Hierarchical Bayesian Analysis of Changepoint Problems," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 41(2), pages 389-405, June.
    9. Ghysels, Eric & Santa-Clara, Pedro & Valkanov, Rossen, 2006. "Predicting volatility: getting the most out of return data sampled at different frequencies," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 59-95.
    10. Kadiyala, K Rao & Karlsson, Sune, 1997. "Numerical Methods for Estimation and Inference in Bayesian VAR-Models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 12(2), pages 99-132, March-Apr.
    11. Corduas, Marcella & Piccolo, Domenico, 2008. "Time series clustering and classification by the autoregressive metric," Computational Statistics & Data Analysis, Elsevier, vol. 52(4), pages 1860-1872, January.
    12. C. Horan, 1969. "Multidimensional scaling: Combining observations when individuals have different perceptual structures," Psychometrika, Springer;The Psychometric Society, vol. 34(2), pages 139-165, June.
    13. repec:ibn:ijspnl:v:8:y:2019:i:4:p:68 is not listed on IDEAS
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    More about this item

    Keywords

    Distance Measures; Fuzzy Clustering; ARIMA Time-Series; Bayesian Model Selection; MCMC Integrations.;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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