On the Use of Yeo-Johnson Transformation in the Functional Multivariate Time Series
Keywords:
Dependent data, Kernel regression estimator, Stationary, Time series prediction, Yeo-Johnson Transformation,
Abstract
Box-Cox and Yeo-Johnson transformation models were utilized in this paper to use density function to improve multivariate time series forecasting. The K-Nearest Neighbor function is used in our model, with automatic bandwidth selection using a cross-validation approach and semi-metrics used to measure the proximity of functional data. Then, to decorrelate multivariate response variables, we use principal component analysis. The methodology was applied on two time series data examples with multiple responses. The first example includes three time series datasets of the monthly average of Humidity (H), Rainfall (R) and Temperature (T). The simulation studies are provided in the second example. Mean square errors of predicted values were calculated to show forecast efficiency. The results have proved that applying multivariate nonparametric time series transformed stationary datasets using the Yeo-Johnson model more efficient than applying the univariate nonparametric analysis to each response independently.References
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28. R Core Team R: A Language and Environment for Statistical Computing, R Foundation,Vienna, Austria. (2020);
2. Masry, E. Nonparametric regression estimation for dependent functional data: Stoch Process Their Appl. 2005 Jan; 115(1),155–177.
3. Gannoun A, Saracco J, Yu K. Nonparametric prediction by conditional median and quantiles.J Stat Plan Infer, 2003 Dec; 117 (2), 207-223.
4. Aneiros-Perez G, Vieu P. Nonparametric time series prediction: A semi-functional partial linear modeling. J Multivar Anal. 2008; 99(5), 834 – 857.
5. Shang HL. Forecasting intraday S&P 500 index returns: A functional time series approach,” J. Forecast, 2017 Nov;36( 7). 741–755,
6. Shang, H. L. Dynamic principal component regression: Application to age-specific mortality forecasting.J IAA, 2019 Sep; 49(3): 619-645.
7. Shang H, Xu R. Functional time series forecasting of extreme values, Commun. Stat.: Case Stud. Data Anal. Appl., 2021 Jan; 7(2), 182-199
8. Chavez-Demoulin, V. & Davison, A. C. Modelling Time Series Extremes. REVSTAT–Statistical Journal, 2012 March; 10(1): 109–133.
9. Häardie W, Müller M. Multivariate and Semiparametric Kernel Regression. Smoothing and Regression: Approaches, Computation, and Application. 2000 Jul 24:357-91.
10. Ferraty F, Vieu P. Nonparametric models for functional data, with application in regression, time series prediction and curve discrimination. J Nonparametr Stat. 2004 Feb 1;16(1-2):111-25..
11. Box GE, Cox DR. An analysis of transformations. J R STAT SOC B 1964 Jul;26(2):211-43.
12. He Y, Zheng Y. Short-term power load probability density forecasting based on Yeo-Johnson transformation quantile regression and Gaussian kernel function. Energy. 2018 Jul 1(154):143-56.
13. Yeo IK, Johnson RA. A new family of power transformations to improve normality or symmetry. Biometrika. 2000 Dec 1;87(4):954-959.
14. Atkinson AC, Riani M, Corbellini A. The Box–Cox Transformation: Review and Extensions. Stat Sci. 2021 Apr;36(2):239-55.
15. Proietti T, Lütkepohl H. Does the Box–Cox transformation help in forecasting macroeconomic time series?. Int. J. Forecast. 2013 Jan 1;29(1):88-99.
16. Legendre P, Borcard D. Box–Cox‐chord transformations for community composition data prior to beta diversity analysis. Ecography. 2018 Nov;41(11):1820-4.
17. Soleymani S, “Exact Box-Cox analysis,” A Thesis Submitted in Partial Fulfillment of the Requirements for the Degree in Doctor of Philosophy in IJSAS, The University of Western Ontario, (2018).
18. Chen CW, Lee JC. On Selecting a Power Transformation in Time‐Series Analysis. J Forecast. 1997 Sep;16(5):343-54.
19. Xiao, Z. , Linton, O. , Carroll, R. , Mammen, E. More efficient local polynomial estimation in nonparametric regression with autocorrelated errors, J. Am. Stat. Assoc.. 2003 Dec 1;98(464):980-992.
20. Ferraty F, Vieu P. Nonparametric functional data analysis: theory and practice. SSBM; 2006 Nov 22.
21. Othman, S. A. and Mohammed Ali, H. T. Studying of Nonparametric Multivariate Time Series Analysis with Applications Methodology. J. Xi'an Univ. Archit. amp; Technol. 2020 Jun; 12(6): 1500-1514.
22. Pek J, Wong O, Wong AC. Data transformations for inference with linear regression: Clarifications and recommendations. Pract. Assess. Res. Evaluation. 2017;22(1):9.
23. Ruckstuhl AF, Welsh AH, Carroll RJ. Nonparametric function estimation of the relationship between two repeatedly measured variables. Statistica Sinica. 2000 Jan 1:51-71.
24. Othman SA, Ali HT. Improvement of the Nonparametric Estimation of Functional Stationary Time Series Using Yeo-Johnson Transformation with Application to Temperature Curves. Adv. Math. Phys.. 2021 Jan 30;2021:1-6.
25. Raymaekers J, Rousseeuw PJ. Transforming variables to central normality. Mach. Learn.. 2021 Mar 21:1-23.
26. Youngman BD. evgam: An R package for generalized additive extreme value models. arXiv preprint arXiv:2003.04067. 2020 Mar 9.URL: https://arxiv.org/abs/2003.04067
27. Tyralis H, Papacharalampous G, Tantanee S. How to explain and predict the shape parameter of the generalized extreme value distribution of streamflow extremes using a big dataset. J. Hydrol.. 2019 Jul 1;574:628-645.
28. R Core Team R: A Language and Environment for Statistical Computing, R Foundation,Vienna, Austria. (2020);
Published
2025-04-09
How to Cite
Sameera Abdulsalam Othman, & Haithem Taha Mohammed Ali. (2025). On the Use of Yeo-Johnson Transformation in the Functional Multivariate Time Series. Statistics, Optimization & Information Computing. https://doi.org/10.19139/soic-2310-5070-1569
Issue
Section
Research Articles
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