Sains Malaysiana 50(9)(2021): 2755-2764

http://doi.org/10.17576/jsm-2021-5009-21

Adaptive Elastic Net with Distance Correlation on the Grouping Effect and Robust of High Dimensional Stock Market Price

(Jaring Elastik Mudah Suai dengan Korelasi Jarak ke atas Kesan Pengelompokan dan Keteguhan Dimensi Tinggi Harga Pasaran Saham)

YUSRINA ANDU^1,2, MUHAMMAD HISYAM LEE²* & ZAKARIYA YAHYA ALGAMAL³

¹Faculty of Computer and Mathematical Sciences, Universiti Teknologi MARA, Kuala Pilah Campus, 72000 Kuala Pilah, Negeri Sembilan Darul Khusus, Malaysia

²Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 Johor Bahru, Johor Darul Takzim, Malaysia

³Department of Statistics and Informatics, University of Mosul, Mosul, Iraq

Diserahkan: 26 Julai 2020/Diterima: 18 Januari 2021

ABSTRACT

Stock market is found in many financial studies. Nonetheless, many of these literatures do not consider on the highly correlated stock market price. In particular, the studies on variable selection, grouping effects and robust dedicated to high dimension stock market price can be considered as scarce. Penalized linear regression using elastic net is one of the recognized methods to perform variable selection. However, the lack of consistency in variable selection may reduce the model performance. Hence, adaptive elastic net with distance correlation (AEDC) is proposed in this study and compared against elastic net, adaptive elastic net with elastic weight and adaptive elastic net with ridge weight. AEDC had lower mean squared error when the alpha increases from 0.05 to 0.95. Thus, the proposed method has successfully contributed to encouraging grouping effects between the highly correlated variables and also has an improved model performance in the presence of robustness.

Keywords: Adaptive elastic net; high dimensional data; penalized linear regression; robust; stock market price

ABSTRAK

Pasaran saham sering ditemui dalam banyak kajian kewangan. Namun begitu, kebanyakan literatur tidak mengambil kira mengenai harga pasaran saham yang berkorelasi tinggi. Secara terperincinya, kajian mengenai pemilihan pemboleh ubah, penggalakan kesan pengelompokan dan keteguhan yang didedikasikan terhadap harga pasaran saham berdimensi tinggi adalah kurang. Kaedah regresi linear terhukum merupakan salah satu kaedah yang diperakui untuk melakukan pemilihan pemboleh ubah. Namun demikian, pemilihan pemboleh ubah yang kurang tekal boleh menjejaskan keberhasilan model. Maka, jaring elastik mudah suai dengan korelasi jarak (EJMSKJ) diusulkan dalam kajian ini dan dibandingkan dengan jaring elastik, jaring elastik mudah suai dengan pemberat elastik dan jaring elastikmudah suai dengan pemberat batas. EJMSKJ mempunyai min ralat kuasa dua yang rendah apabila nilai alfa meningkat daripada 0.05 ke 0.95. Maka, kaedah yang diusulkan telah menyumbang kepada penggalakan kesan pengelompokan antara pemboleh ubah berkorelasi tinggi dan juga keberhasilan model yang lebih baik apabila keteguhan wujud.

Kata kunci: Data dimensi tinggi; harga pasaran saham; jaring elastik mudah suai; regresi linear terhukum; teguh

RUJUKAN

Alhamzawi, R. 2015. Model selection in quantile regression models. Journal of Applied Statistics 42(2): 445-458.

Andu, Y., Lee, M.H. & Algamal, Z.Y. 2020. Variable selection of yearly high dimension stock market price using ordered homogenous pursuit lasso. AIP Conference Proceedings 2266(1): 090012.

Arashi, M. & Roozbeh, M. 2019. Some improved estimation strategies in high-dimensional semiparametric regression models with application to riboflavin production data. Statistical Papers 60(3): 317-336.

Dong, Y., Song, L. & Amin, M. 2018. SCAD-ridge penalized likelihood estimators for ultra-high dimensional models. Hacettepe Journal of Mathematics and Statistics 47(2): 423-436.

Gharleghi, B., Shaari, A.H. & Sarmidi, T. 2014. Application of the threshold model for modelling and forecasting of exchange rate in selected ASEAN countries. Sains Malaysiana 43(10): 1609-1622.

Hastie, T., Tibshirani, R. & Wainwright, M. 2015. Statistical Learning with Sparsity: The Lasso and Generalizations. Boca Raton: Chapman and Hall/CRC.

Hoerl, E. & Kennard, R.W. 1970. Ridge regression: Biased estimation for nonorthogonal problems. Technometrics 12(1): 55-67.

Jafry, N.H.A., Ab Razak, R. & Ismail, N. 2020. Ukuran kebersandaran bagi pulangan lima-minit berbanding pulangan harian menggunakan kopula statik dan dinamik. Sains Malaysiana 49(8): 2023-2034.

Kurnaz, F.S., Hoffmann, I. & Filzmoser, P. 2018. Robust and sparse estimation methods for high-dimensional linear and logistic regression. Chemometrics and Intelligent Laboratory Systems 172: 211-222.

Rish, I. & Grabarnik, G. 2014. Sparse Modeling:Theory, Algorithms, and Applications. Boca Raton: CRC Press.

Shen, C., Priebe, C.E. & Vogelstein, J.T. 2020. From distance correlation to multiscale graph correlation. Journal of the American Statistical Association115(529): 280-291.

Székely, G.J., Rizzo, M.L. & Bakirov, N.K. 2007. Measuring and testing dependence by correlation of distances. Annals of Statistics 35(6): 2769-2794.

Tibshirani, R. 1996. Regression shrinkage and selection via the lasso. Journal of the Royal Statistical Society: Series B (Methodological) 58(1): 267-288.

Zhou, D.X. 2013. On grouping effect of elastic net. Statistics and Probability Letters 83(9): 2108-2112.

Zou, H. & Zhang, H.H. 2009. On the adaptive elastic-net with a diverging number of parameters. Annals of Statistics 37(4): 1733-1751.

Zou, H. & Hastie, T. 2005. Regularization and variable selection via the elastic net. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 67(2): 301-320.

*Pengarang untuk surat-menyurat; email: mhl@utm.my