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Year 2025, Volume: 54 Issue: 3, 1206 - 1235, 24.06.2025

Emad Ashtari Nezhad

https://doi.org/10.15672/hujms.1586978

Abstract

References

  • [1] J.M. Amigó, S. Zambrano, and M.A. Sanjuán, True and false forbidden patterns in deterministic and random dynamics, EPL, 79, 50001, 2007.
  • [2] S. Anjali, N.R. Kaur, and B. Ghosh, GSSX method: A golden-section-based symbolic representation for time series analysis, Adv. Data Sci., 17, 2025.
  • [3] E. Ashtari Nezhad, Y. Waghei, G.R. Mohtashami Borzadaran, H.R. Nilli Sani, and H. Alizadeh Noughabi, The modified permutation entropy-based independence test of time series, Commun. Stat. Simul. Comput., 48(10), 28772897, 2019.
  • [4] E. Ashtari Nezhad, Y. Waghei, G.R. Mohtashami Borzadaran, H.R. Nilli Sani, and H. Alizadeh Noughabi, A Serial Independence Test by Kullback-Leibler via Quantile Symbolization, Accepted May 2024, REVSTAT Stat. J., 2024.
  • [5] V. Balakrishnan and L.D. Sanghvi, Distance between populations on the basis of attribute, Biometrics, 24, 859865, 1968.
  • [6] F. Betken, M. Li, and P. Zhao, Ordinal patterns for change point detection in time series, Comput. Stat. Data Anal., 129, 2025.
  • [7] W.A. Broock, J. A. Scheinkman, W.D. Dechert, and B. LeBaron, A test for independence based on the correlation dimension, Econom. Rev., 15, 197235, 1996.
  • [8] J.S. Cánovas and A. Guillamón, Permutations and time series analysis, Chaos, 19, 043103, 2009.
  • [9] J.S. Cánovas, A. Guillamón, and S. Vera, Testing for independence: Permutationbased tests vs. BDS test, Eur. Phys. J. Spec. Top., 222, 275284, 2013.
  • [10] A. Combettes, Symbolic representations for time series: Advances in pattern detection, Comput. Stat., 39(2), 2024.
  • [11] T.M. Cover and J.A. Thomas, Elements of Information Theory, Wiley, 2006.
  • [12] N. Cressie and T.R.C. Read, Multinomial goodness-of-fit tests, J. R. Stat. Soc. Ser. B, 46, 440464, 1984.
  • [13] H. Dehling, Limit theorems for dependent U-statistics, In Dependence in Probability and Statistics, Springer, 6586, 2006.
  • [14] J.J. Dik and M.C.M. de Gunst, The distribution of general quadratic forms in normal variables, Stat. Neerl., 39, 1426, 1985.
  • [15] A. Dionisio, R. Menezes, and D. A. Mendes, Mutual information: A measure of dependency for nonlinear time series, Physica A, 344, 326329, 2004.
  • [16] H.J. Elsinger, Independence tests based on symbolic dynamics, Oesterreichische Nationalbank, No. 165, 2010.
  • [17] E.F. Fama, L. Fisher, M.C. Jensen, and R. Roll, The adjustment of stock prices to new information, Int. Econ. Rev., 10, 121, 1969.
  • [18] K. Ghoudi, R.J. Kulperger, and B. Remillard, A nonparametric test of serial independence for time series and residuals, J. Multivar. Anal., 79, 191218, 2001.
  • [19] A. Gut, Probability: A Graduate Course, Springer, 2006.
  • [20] J.D. Hamilton, Time Series Analysis, Princeton University Press, 1994.
  • [21] A. Hassani, M.J. Mollah, and J.S. Lee, White noise misapplications in time series modeling: Implications for model diagnostics, Econom. Rev., 32, 2025.
  • [22] J. He, X. Liu, and S. Zheng, Non-parametric Symbolic Approximate Representation (NSAR) for time series classification in smart manufacturing, Ind. Eng. J., 45(2), 2024.
  • [23] Y. Hong and H. White, Asymptotic distribution theory for nonparametric entropy measures of serial dependence, Econometrica, 73, 837901, 2005.
  • [24] R. Hounyo and Y. Lin, Wild bootstrap inference with multiway clustering and serially correlated time effects, Stat. Inference J., 39(1), 2024.
  • [25] J. Jiang, L. Gao, and Z. Shao, Distance covariance for object-valued time series in metric spaces, J. Time Ser. Anal., 44(3), 2023.
  • [26] G.M. Ljung and G.E.P. Box, On a measure of lack of fit in time series models, Biometrika, 65, 297303, 1978.
  • [27] Z. Liu, X. Zhang, and P. Chen, Kernel-based joint independence tests for multivariate time series, J. Multivar. Anal., 153, 2023.
  • [28] F. López, M. Matilla-García, J. Mur, and M.R. Marín, A non-parametric spatial independence test using symbolic entropy, Reg. Sci. Urban Econ., 40, 106115, 2010.
  • [29] M. Matilla-García and M.R. Marín, A non-parametric independence test using permutation entropy, J. Econom., 144, 139155, 2008.
  • [30] M. Mohammadi, D. Li, and J. Kim, Model-free prediction approach for time series using nonparametric methods, J. Forecast., 44, 2024.
  • [31] L. Pardo, Statistical Inference Based on Divergence Measures, Chapman and Hall/CRC, Taylor & Francis Group, 2006.
  • [32] Y. Polyanskiy and Y. Wu, Information Theory: From Coding to Learning, Cambridge University Press, 2023.
  • [33] J.S. Racine and E. Maasoumi, A versatile and robust metric entropy test of timereversibility, and other hypotheses, J. Econom., 138, 547567, 2007.
  • [34] P.M. Robinson, Consistent nonparametric entropy-based testing, Rev. Econ. Stud., 58, 437453, 1991.
  • [35] A.L. Rukhin, Optimal estimator for the mixture parameter by the method of moments and information affinity, In Trans., 12th Prague Conference on Information Theory, 214219, 1994.
  • [36] H.J. Skaug and D. Tjøstheim, A nonparametric test of serial independence based on the empirical distribution function, Biometrika, 80, 591602, 1993.
  • [37] A. Wald and J. Wolfowitz, On a test whether two samples are from the same population, Ann. Math. Stat., 11, 147162, 1940.
  • [38] J. Wang, H. Xie, and L. Zhang, Foundation model with series-symbol data generation for sparse time series analysis, J. Comput. Stat., 39, 2025.
  • [39] J. Wang, L. Li, and Y. Chen, Detecting state correlations in heterogeneous time series using advanced methods, J. Time Ser. Econom., 16, 2024.
  • [40] L. Weiß and M. Schnurr, Generalized ordinal patterns for discrete-valued time series, Chaos, 34, 053109, 2024.
  • [41] J. Yu, S. Li, and H. Zhou, Semiparametric latent ANOVA model for event-related potentials analysis in time series, J. Neurosci. Methods, 223, 2024.
  • [42] Y. Zhou and P. Müller, Testing independence between random objects in metric spaces using profile association measures, Ann. Stat., 53, 2025.

Utilizing symmetric Phi-divergence in serial independence testing

Year 2025, Volume: 54 Issue: 3, 1206 - 1235, 24.06.2025

Emad Ashtari Nezhad

https://doi.org/10.15672/hujms.1586978

Abstract

This manuscript introduces a novel class of time series independence tests based on Phi-divergence and quantile-based symbolization. We derive the asymptotic distribution of the test statistic and propose a bootstrap version. Simulations identified optimal parameter values and compared the test performance to existing methods, demonstrating higher size-corrected power for specific Phi-divergence cases. Furthermore, we investigate Rukhin and power divergence, revealing Pearson’s divergence as optimal. The proposed tests were applied to financial (Tehran Stock Exchange, S\&P 500) and ecological (Lynx population) datasets, effectively detecting dependence on the data and confirming the adequacy of the model through independent residuals, demonstrating the robustness and versatility of the method in diverse domains.

Keywords

Serial independence test Phi-divergence simulation studies quantile symbolization time series

References

  • [1] J.M. Amigó, S. Zambrano, and M.A. Sanjuán, True and false forbidden patterns in deterministic and random dynamics, EPL, 79, 50001, 2007.
  • [2] S. Anjali, N.R. Kaur, and B. Ghosh, GSSX method: A golden-section-based symbolic representation for time series analysis, Adv. Data Sci., 17, 2025.
  • [3] E. Ashtari Nezhad, Y. Waghei, G.R. Mohtashami Borzadaran, H.R. Nilli Sani, and H. Alizadeh Noughabi, The modified permutation entropy-based independence test of time series, Commun. Stat. Simul. Comput., 48(10), 28772897, 2019.
  • [4] E. Ashtari Nezhad, Y. Waghei, G.R. Mohtashami Borzadaran, H.R. Nilli Sani, and H. Alizadeh Noughabi, A Serial Independence Test by Kullback-Leibler via Quantile Symbolization, Accepted May 2024, REVSTAT Stat. J., 2024.
  • [5] V. Balakrishnan and L.D. Sanghvi, Distance between populations on the basis of attribute, Biometrics, 24, 859865, 1968.
  • [6] F. Betken, M. Li, and P. Zhao, Ordinal patterns for change point detection in time series, Comput. Stat. Data Anal., 129, 2025.
  • [7] W.A. Broock, J. A. Scheinkman, W.D. Dechert, and B. LeBaron, A test for independence based on the correlation dimension, Econom. Rev., 15, 197235, 1996.
  • [8] J.S. Cánovas and A. Guillamón, Permutations and time series analysis, Chaos, 19, 043103, 2009.
  • [9] J.S. Cánovas, A. Guillamón, and S. Vera, Testing for independence: Permutationbased tests vs. BDS test, Eur. Phys. J. Spec. Top., 222, 275284, 2013.
  • [10] A. Combettes, Symbolic representations for time series: Advances in pattern detection, Comput. Stat., 39(2), 2024.
  • [11] T.M. Cover and J.A. Thomas, Elements of Information Theory, Wiley, 2006.
  • [12] N. Cressie and T.R.C. Read, Multinomial goodness-of-fit tests, J. R. Stat. Soc. Ser. B, 46, 440464, 1984.
  • [13] H. Dehling, Limit theorems for dependent U-statistics, In Dependence in Probability and Statistics, Springer, 6586, 2006.
  • [14] J.J. Dik and M.C.M. de Gunst, The distribution of general quadratic forms in normal variables, Stat. Neerl., 39, 1426, 1985.
  • [15] A. Dionisio, R. Menezes, and D. A. Mendes, Mutual information: A measure of dependency for nonlinear time series, Physica A, 344, 326329, 2004.
  • [16] H.J. Elsinger, Independence tests based on symbolic dynamics, Oesterreichische Nationalbank, No. 165, 2010.
  • [17] E.F. Fama, L. Fisher, M.C. Jensen, and R. Roll, The adjustment of stock prices to new information, Int. Econ. Rev., 10, 121, 1969.
  • [18] K. Ghoudi, R.J. Kulperger, and B. Remillard, A nonparametric test of serial independence for time series and residuals, J. Multivar. Anal., 79, 191218, 2001.
  • [19] A. Gut, Probability: A Graduate Course, Springer, 2006.
  • [20] J.D. Hamilton, Time Series Analysis, Princeton University Press, 1994.
  • [21] A. Hassani, M.J. Mollah, and J.S. Lee, White noise misapplications in time series modeling: Implications for model diagnostics, Econom. Rev., 32, 2025.
  • [22] J. He, X. Liu, and S. Zheng, Non-parametric Symbolic Approximate Representation (NSAR) for time series classification in smart manufacturing, Ind. Eng. J., 45(2), 2024.
  • [23] Y. Hong and H. White, Asymptotic distribution theory for nonparametric entropy measures of serial dependence, Econometrica, 73, 837901, 2005.
  • [24] R. Hounyo and Y. Lin, Wild bootstrap inference with multiway clustering and serially correlated time effects, Stat. Inference J., 39(1), 2024.
  • [25] J. Jiang, L. Gao, and Z. Shao, Distance covariance for object-valued time series in metric spaces, J. Time Ser. Anal., 44(3), 2023.
  • [26] G.M. Ljung and G.E.P. Box, On a measure of lack of fit in time series models, Biometrika, 65, 297303, 1978.
  • [27] Z. Liu, X. Zhang, and P. Chen, Kernel-based joint independence tests for multivariate time series, J. Multivar. Anal., 153, 2023.
  • [28] F. López, M. Matilla-García, J. Mur, and M.R. Marín, A non-parametric spatial independence test using symbolic entropy, Reg. Sci. Urban Econ., 40, 106115, 2010.
  • [29] M. Matilla-García and M.R. Marín, A non-parametric independence test using permutation entropy, J. Econom., 144, 139155, 2008.
  • [30] M. Mohammadi, D. Li, and J. Kim, Model-free prediction approach for time series using nonparametric methods, J. Forecast., 44, 2024.
  • [31] L. Pardo, Statistical Inference Based on Divergence Measures, Chapman and Hall/CRC, Taylor & Francis Group, 2006.
  • [32] Y. Polyanskiy and Y. Wu, Information Theory: From Coding to Learning, Cambridge University Press, 2023.
  • [33] J.S. Racine and E. Maasoumi, A versatile and robust metric entropy test of timereversibility, and other hypotheses, J. Econom., 138, 547567, 2007.
  • [34] P.M. Robinson, Consistent nonparametric entropy-based testing, Rev. Econ. Stud., 58, 437453, 1991.
  • [35] A.L. Rukhin, Optimal estimator for the mixture parameter by the method of moments and information affinity, In Trans., 12th Prague Conference on Information Theory, 214219, 1994.
  • [36] H.J. Skaug and D. Tjøstheim, A nonparametric test of serial independence based on the empirical distribution function, Biometrika, 80, 591602, 1993.
  • [37] A. Wald and J. Wolfowitz, On a test whether two samples are from the same population, Ann. Math. Stat., 11, 147162, 1940.
  • [38] J. Wang, H. Xie, and L. Zhang, Foundation model with series-symbol data generation for sparse time series analysis, J. Comput. Stat., 39, 2025.
  • [39] J. Wang, L. Li, and Y. Chen, Detecting state correlations in heterogeneous time series using advanced methods, J. Time Ser. Econom., 16, 2024.
  • [40] L. Weiß and M. Schnurr, Generalized ordinal patterns for discrete-valued time series, Chaos, 34, 053109, 2024.
  • [41] J. Yu, S. Li, and H. Zhou, Semiparametric latent ANOVA model for event-related potentials analysis in time series, J. Neurosci. Methods, 223, 2024.
  • [42] Y. Zhou and P. Müller, Testing independence between random objects in metric spaces using profile association measures, Ann. Stat., 53, 2025.
There are 42 citations in total.

Details

Primary Language English
Subjects Computational Statistics, Applied Statistics
Journal Section Statistics
Authors

Emad Ashtari Nezhad 0009-0009-6779-4742

Early Pub Date June 7, 2025
Publication Date June 24, 2025
Submission Date November 18, 2024
Acceptance Date May 26, 2025
Published in Issue Year 2025 Volume: 54 Issue: 3

Cite

APA Ashtari Nezhad, E. (2025). Utilizing symmetric Phi-divergence in serial independence testing. Hacettepe Journal of Mathematics and Statistics, 54(3), 1206-1235. https://doi.org/10.15672/hujms.1586978
AMA Ashtari Nezhad E. Utilizing symmetric Phi-divergence in serial independence testing. Hacettepe Journal of Mathematics and Statistics. June 2025;54(3):1206-1235. doi:10.15672/hujms.1586978
Chicago Ashtari Nezhad, Emad. “Utilizing Symmetric Phi-Divergence in Serial Independence Testing”. Hacettepe Journal of Mathematics and Statistics 54, no. 3 (June 2025): 1206-35. https://doi.org/10.15672/hujms.1586978.
EndNote Ashtari Nezhad E (June 1, 2025) Utilizing symmetric Phi-divergence in serial independence testing. Hacettepe Journal of Mathematics and Statistics 54 3 1206–1235.
IEEE E. Ashtari Nezhad, “Utilizing symmetric Phi-divergence in serial independence testing”, Hacettepe Journal of Mathematics and Statistics, vol. 54, no. 3, pp. 1206–1235, 2025, doi: 10.15672/hujms.1586978.
ISNAD Ashtari Nezhad, Emad. “Utilizing Symmetric Phi-Divergence in Serial Independence Testing”. Hacettepe Journal of Mathematics and Statistics 54/3 (June 2025), 1206-1235. https://doi.org/10.15672/hujms.1586978.
JAMA Ashtari Nezhad E. Utilizing symmetric Phi-divergence in serial independence testing. Hacettepe Journal of Mathematics and Statistics. 2025;54:1206–1235.
MLA Ashtari Nezhad, Emad. “Utilizing Symmetric Phi-Divergence in Serial Independence Testing”. Hacettepe Journal of Mathematics and Statistics, vol. 54, no. 3, 2025, pp. 1206-35, doi:10.15672/hujms.1586978.
Vancouver Ashtari Nezhad E. Utilizing symmetric Phi-divergence in serial independence testing. Hacettepe Journal of Mathematics and Statistics. 2025;54(3):1206-35.

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