1. Arellano-Valle R. B., Castro L. M., Genton M. G., & Gómez H. W. (2008). Bayesian Inference for Shape Mixtures of Skewed Distributions, With Application to Regression Analysis. Bayesian Analysis, 3(3), 513-539. [ DOI:10.1214/08-BA320] 2. Basawa, I. V., & Lund, R. B. (2001). Large Sample Properties of Parameter Estimates for Periodic ARMA Models. Journal of Time Series Analysis, 22, 651-663. [ DOI:10.1111/1467-9892.00246] 3. Basso, R. M., Lachos, V. H., Cabral, C. R. B., & Ghosh, P. (2010). Robust Mixture Modeling Based on the Scale Mixtures of Skew-Normal Distributions. Computational Statistics and Data Analysis, 54, 2926-2941. [ DOI:10.1016/j.csda.2009.09.031] 4. Broszkiewicz‐Suwaj, E., Makagon, A., Weron, R., & Wylomanska, A. (2004). On Detecting and Modeling Periodic Correlation in Financial Data. Physica A: Statistical Mechanics and Its Applications, 336(1-2), 196-205. [ DOI:10.1016/j.physa.2004.01.025] 5. Chaari, F., Leskow, J., Napolitano, A., Zimroz, R., & Wylomanska, A. (2017). Cyclostationarity: Theory and Methods III, Applied Condition Monitoring. Springer. [ DOI:10.1007/978-3-319-51445-1] 6. Ferreira, C. S., & Dias, R. (2024). Semiparametric Regression Models Under Skew Scale Mixtures of Normal Distributions. Communications in Statistics: Simulation and Computation, 1-23. [ DOI:10.1080/03610918.2024.2372667] 7. Franses, P. H., & Paap, R. (1994). Model Selection in Periodic Autoregressive. Oxford Bulletin of Economics and Statistics, 56(4), 421-439. [ DOI:10.1111/j.1468-0084.1994.tb00018.x] 8. Giri, P., Grzesiek, A., Żuławiński, W., & Sundar, S. (2022). The Modified Yule-Walker Method for Multidimensional Infinite-Variance Periodic Autoregressive Model of Order 1. Journal of the Korean Statistical Society, 51(4), 1130-1142. [ DOI:10.1007/s42952-022-00191-3] 9. Gladyshev, E. G. (1961). Periodically Correlated Random Sequences. Soviet Mathematics, 2, 385-388. 10. Hashemi, F., & Goodarzi, F. (2024). Linear Mixed Model Based on Mean Mixture of Multivariate Normal Distributions: A Flexible Estimate Based on Missing Value. Journal of Statistical Modelling: Theory and Applications, 5(2), 97-119. 11. Hipel, K. W., & McLeod, A. I. (1994). Time Series Modelling of Water Resources and Environmental Systems. Elsevier. 12. Hurd, H. L., & Miamee, A. (2007). Periodically Correlated Random Sequences: Spectral Theory and Practice. John Wiley & Sons. [ DOI:10.1002/9780470182833] 13. Kermarrec, G., Maddanu, F., Klos, A., Proietti, T., & Bogusz, J. (2024). Modeling Trends and Periodic Components in Geodetic Time Series: A Unified Approach. Journal of Geodesy, 98, Article 3. [ DOI:10.1007/s00190-024-01826-5] 14. Lachos V. H., Ghosh P., & Arellano-Valle R. B. (2010). Likelihood Based Inference for Skew Normal/Independent Linear Mixed Models. Statistica Sinica, 20, 303-322. 15. Liu, C., & Rubin, D. B. (1994). The ECME Algorithm: A Simple Extension of EM and ECM With Faster Monotone Convergence. Biometrika, 81, 633-648. [ DOI:10.1093/biomet/81.4.633] 16. Lund, R. B., & Basawa, I. V. (2000). Recursive Prediction and Likelihood Evaluation for Periodic ARMA Models. Journal of Time Series Analysis, 21, 75-93. [ DOI:10.1111/1467-9892.00174] 17. Maleki, M., & Arellano-Valle, R. B. (2016). Maximum A-Posteriori Estimation of Autoregressive Processes Based on Finite Mixtures of Scale-Mixtures of Skew-Normal Distributions. Journal of Statistical Computation and Simulation, 87(6), 1061-1083. [ DOI:10.1080/00949655.2016.1245305] 18. Maleki, M., Arellano-Valle, R. B., Dey, D. K., Mahmoudi, M. R., & Jalili, S. M. J. (2018). A Bayesian Approach to Robust Skewed Autoregressive Processes. Calcutta Statistical Association Bulletin, 69(2), 165-182. [ DOI:10.1177/0008068317732196] 19. Maleki, M., Wraith, D., Mahmoudi, M. R., & Contreras-Reyes, J. E. (2020). Asymmetric Heavy-Tailed Vector Auto-Regressive Processes With Application to Financial Data. Journal of Statistical Computation and Simulation, 90(2), 324-340. [ DOI:10.1080/00949655.2019.1680675] 20. Mahmoudi, M. R., Maleki, M., Baleanu, D., Nguyen, V.-T., & Pho, K.-H. (2020). A Bayesian Approach to Heavy-Tailed Finite Mixture Autoregressive Models. Symmetry, 12(6), Article 929. [ DOI:10.3390/sym12060929] 21. Manouchehri, T., & Nematollahi, A. R. (2019a). On the Estimation Problem of Periodic Autoregressive Time Series: Symmetric and Asymmetric Innovations. Journal of Statistical Computation and Simulation, 89(1), 71-97. [ DOI:10.1080/00949655.2018.1535599] 22. Manouchehri, T., & Nematollahi, A. R. (2019b). Periodic Autoregressive Models With Closed Skew-Normal Innovations. Computational Statistics, 34(3), 1183-1213. [ DOI:10.1007/s00180-019-00893-z] 23. Manouchehri, T., & Nematollahi, A. R. (2022). A Comparison of the Bayesian and Non-Bayesian Approaches for the Periodic AR Models Based on the SMSN Innovations. Iranian Journal of Science and Technology: Transactions A, 46(2), 615-630. [ DOI:10.1007/s40995-022-01266-w] 24. Meng, X. L., & Rubin, D. B. (1993). Maximum Likelihood Estimation Via the ECM Algorithm: A General Framework. Biometrika, 80, 267-278. [ DOI:10.1093/biomet/80.2.267] 25. Nematollahi, A. R., Soltani, A. R., & Mahmoudi, M. R. (2017). Periodically Correlated Modeling by Means of the Periodograms Asymptotic Distributions. Statistical Papers, 1(1), 1-12. [ DOI:10.1007/s00362-016-0748-9] 26. Pagano, M. (1978). On Periodic and Multiple Autoregressions. The Annals of Statistics, 6, 1310-1317. [ DOI:10.1214/aos/1176344376] 27. Shao, Q. (2006). Mixture Periodic Autoregressive Time Series Models. Statistics & Probability Letters, 76(6), 609-618. [ DOI:10.1016/j.spl.2005.09.015] 28. Shao, Q. (2007). Robust Estimation for Periodic Autoregressive Time Series. Journal of Time Series Analysis, 29, 251-263. [ DOI:10.1111/j.1467-9892.2007.00555.x] 29. Thomas, H. A., & Fiering, M. B. (1962). Mathematical Synthesis of Streamflow Sequences for the Analysis of River Basins by Simulation. Design of Water Resource Systems, 459-493. [ DOI:10.4159/harvard.9780674421042.c15] 30. Troutman, B. M. (1979). Some Results in Periodic Autoregression. Biometrika, 66, 219-228. [ DOI:10.1093/biomet/66.2.219] 31. Ursu, E., & Turkman, K. F. (2012). Periodic Autoregressive Model Identification Using Genetic Algorithm. Journal of Time Series Analysis, 33, 398-405. [ DOI:10.1111/j.1467-9892.2011.00772.x] 32. Vecchia, A. V. (1985a). Periodic Autoregressive-Moving Average (PARMA) Modeling With Applications to Water Resources. Water Resources Bulletin, 21, 721-730. [ DOI:10.1111/j.1752-1688.1985.tb00167.x] 33. Vecchia, A. V. (1985b). Maximum Likelihood Estimation for Periodic Autoregressive Moving Average Models. Technometrics, 27, 375-384. [ DOI:10.1080/00401706.1985.10488076] 34. Yaghoubi, S., & Farnoosh, R. (2025). Static Finite Mixture Model of Multivariate Skew-Normal Distributions to Cluster Multivariate Time Series Based on Generalized Autoregressive Score Approach. International Journal of Nonlinear Analysis and Applications, 16(4), 27-39. 35. Zeller, C. B., Cabral, C. R. B., & Lachos, V. H. (2016). Robust Mixture Regression Modeling Based on Scale Mixtures of Skew-Normal Distributions. TEST, 25(2), 375-396. [ DOI:10.1007/s11749-015-0460-4] 36. Żuławiński, W., & Wyłomańska, A. (2023). Estimation of Coefficients for Periodic Autoregressive Model With Additive Noise-A Finite-Variance Case. arXiv Preprint, arXiv:2302.07070. [ DOI:10.1016/j.cam.2023.115131] 37. Żuławiński, W., Antoni, J., Zimroz, R., & Wyłomańska, A. (2024). Robust Coherent and Incoherent Statistics for Detection of Hidden Periodicity in Models With Non-Gaussian Additive Noise. EURASIP Journal on Advances in Signal Processing, 2024(1). [ DOI:10.1186/s13634-024-01168-6]
|