Journal of Advanced Mathematical Modeling

Journal of Advanced Mathematical Modeling

Periodically correlated Interval valued Processes

Document Type : Original Paper

Authors
Department of Statistics, Shiraz University, Shiraz, Iran
Abstract
This paper introduces periodically correlated interval valued processes, by focusing on the estimation of their mean and autocovariance. The asymptotic behavior of these estimators is analyzed, Through simulation, the performance of estimators for the mean and autocovariance is studied, and the obtained results are critically evaluated to assess their effectiveness.
Keywords
Subjects

[1] Aumann, R. J., 1965. Integrals of set-valued functions. Journal of Mathematical Analysis and its Applications, 12, pp.1-12. https://doi.org/10.1016/0022-247X(65)90049-1
[2] Buansing, T., Golan. A. and Ullah, A., 2020, An information-theoretic approach for forecasting interval-valued SP500 daily returns. International Journal of Forecasting, 12(1), pp. 1-14.
https://doi.org/10.1016/j.ijforecast.2019.09.003
[3] Brito, P., 2014. Symbolic data analysis: Another look at the interaction of data mining and statistics. Wiley Interdisciplinary Reviews: Data Mining and Knowledge Discovery, 4, pp.281-295.
https://doi.org/10.1002/widm.1133.
[4] Beyaztas, U., Shang, H. L., and Abdel-Salam, A. S. G., 2020. Functional linear models for intervalvalued data. Communications in Statistics - Simulation and Computation, 51(7), pp. 3513–3532.
https://doi.org/10.1080/03610918.2020.1714662
[5] Gonzalez-Rivera, G. and Lin, W., 2013. Constrained Regression for Interval valued data. Journal of
Business and Economic Statistics, 21(4), pp. 473-490. https://doi.org/10.1080/07350015.2013.818004
[6] Hurd H. L. and Miamee A., 2007. Periodically correlated random sequences. Spectral theory and
practice. Wiley,Hoboken.
[7] Ji, A., Cao, Y., Zhang, J., and Li, Q. 2024. SVR-based method for fixed effects intervalvalued panel models. Communications in Statistics - Theory and Methods, 54(8), pp. 2393–2411.
https://doi.org/10.1080/03610926.2024.2369315
[8] Lin, W. and Gonzalez-Rivera, G., 2016. Interval-valued time series models: Estimation based on order statistics exploring the Agriculture Marketing Service data. Computational Statistics and Data
Analysis, 100, pp. 694-711. doi.org:10.1016/j.csda.2015.07.008
[9] Neto, E., Cordeiro, G., and Carvalho, F., 2011. Bivariate symbolic regression models for intervalvalued variables. Journal of Statistical Computation and Simulation, 81(11), pp. 1727-1744.
doi:10.1080/00949655.2010.500470
[10] Wang, X., Zhang, Z. and Li, S., 2016. Set-valued and interval-valued stationary time series. Journal
of Multivariate Analysis, 145, pp.208-223. https://doi.org/ 10.1016/j.jmva.2015.12.010
[11] Workman, A., and Song, J. J., 2023. Spatial analysis for interval-valued data. Journal of Applied
Statistics, 51(10), pp. 1946–1960. https://doi.org/10.1080/02664763.2023.2249636
[12] Yang, Z., Lin,D. and Zhang, A., 2019. Interval-valued data prediction via regularized artificial neural
network. Neurocomputing, 331, pp.336-345. https://doi.org/10.1016/j.neucom.2018.11.063
[13] Yang, X., and Li, S., 2005. The Dp-Metric space of set-valued random variables and its application
to covariances. International Journal of Innovative Computing, Information and Control, 1, pp.73-82.
https://doi.org/10.1007/11425-005-0007-4
[14] Zhang, J., and Ji, J., 2024. Locally linear method for fixed effects panel interval-valued data model,
Knowledge-Based Systems, 300, https://doi.org/10.1016/j.knosys.2024.112226.

  • Receive Date 24 November 2024
  • Revise Date 25 August 2025
  • Accept Date 15 November 2025