GROUPING ROA (RETURN ON ASSETS) OF FINANCE AND INVESTMENT COMPANIES IN INDONESIA WITH THE FINITE MIXTURE SKEW-T MODEL Angga Setiyowati (1*), Irwan Susanto (2), & Sri Subanti (3)
1) Program Studi Statistika, Fakultas Matematika dan Ilmu Pengetahuan Alam, Universitas Sebelas Maret
Jl. Ir Sutami No.36 A, Surakarta, Jawa Tengah, 57126, Indonesia
Email : angga.setiyowati[at]gmail.com
2) Program Studi Statistika, Fakultas Matematika dan Ilmu Pengetahuan Alam, Universitas Sebelas Maret
Jl. Ir Sutami No.36 A, Surakarta, Jawa Tengah, 57126, Indonesia
Email : irwansusanto[at]staff.uns.ac.id
3) Program Studi Statistika, Fakultas Matematika dan Ilmu Pengetahuan Alam, Universitas Sebelas Maret
Jl. Ir Sutami No.36 A, Surakarta, Jawa Tengah, 57126, Indonesia
Email : sri_subanti[at]yahoo.co.id
Abstract
At the end of 2019, economic development in Indonesia experienced a slowdown from the previous year. One of the causes is the decline in investment and weakening financial conditions. Financial data is not always normally distributed. Often some financial data are skewed and heavy-tailed, such as ROA (Return On Assets) data on investment and finance companies. The ROA value can be positive or negative. It makes ROA had a multimodal data pattern, indicated by histogram ROA data which has several peaks and non-fulfillment of the unimodal pattern significance test. One of the data grouping methods for multimodal data patterns is finite mixture modeling. Grouping with the finite mixture model is base on the representation of the probability distribution function applicable to continuous or discrete data. In this paper, the finite mixture model is used to model the ROA (Return On Assets) value data of finance and investment companies in Indonesia in the 4th quarter of 2019. Estimation parameters of the finite mixture model using calculations with the EM (Expectation-Maximization) algorithm. Ensured that the finite mixture model is suitable, performed a significance test using bootstrap likelihood ratio statistics. The best number of clusters is determined based on the minimum Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) values. Based on the analysis, the suitable model for modeling the ROA (Return on Assets) value data of financial and investment companies in Indonesia in the 4th quarter of 2019 is the Skew-t finite mix model with two components.
Keywords: Mixture Model, EM Algorithm, Skew T, ROA, Finance, Investment
