BIRESPONSE SPLINE TRUNCATED NONPARAMETRIC REGRESSION MODELING FOR LONGITUDINAL DATA ON MONTHLY STOCK PRICES OF THREE PRIVATE BANKS IN INDONESIA

Abstract

This study investigates the application of a truncated spline nonparametric regression model for biresponse analysis of longitudinal data, focusing on modeling monthly stock prices specifically opening and closing prices of three private banks in Indonesia: Bank Mayapada, Bank Mega, and Bank Sinar Mas. The data used in this research are secondary data sourced from the website Id.Investing.com and monthly financial statement publications of three private banks in Indonesia. Longitudinal data, combining cross-sectional and time-series dimensions, are utilized to capture trends and patterns not detectable in traditional cross-sectional analysis. The truncated spline method is selected for its adaptability to nonlinear relationships and abrupt data behavior changes. The model incorporates three predictor variables traded stock volume, total assets, and total liabilities and evaluates their influence on stock prices. Assumptions of longitudinal data are validated using the Ljung-Box autocorrelation test, Bartlett’s sphericity test, and Pearson correlation. Results confirm significant within-subject correlations, independence between subjects, and strong interdependence between response variables. The optimal configuration is determined using Generalized Cross Validation (GCV), with up to three knots considered for segmentation. Weighted Least Squares (WLS) is employed for parameter estimation, accounting for within-subject correlations. Model evaluation based on Mean Absolute Percentage Error (MAPE) indicates high accuracy, with all MAPE values below 5%. The highest MAPE value is 4.41% for the closing price of Bank Mayapada, while the lowest is 2.65% for the opening price of the same bank. The segmentation analysis reveals that traded stock volume and total assets positively influence stock prices, while total liabilities exhibit a predominantly negative impact. The model is limited to internal financial indicators and does not include external macroeconomic factors such as interest rates or inflation. This study is the first to apply a biresponse truncated spline nonparametric regression approach to analyze stock prices of private banks in Indonesia by simultaneously modeling both opening and closing prices, providing a flexible and effective method for capturing complex patterns in longitudinal financial data.