A Full Convex Combination Method for Linear Regression with Interval Data

Abstract

With the increasingly advanced data collection technologies in recent years, the massive streams of market data particularly prices of financial instruments in each trading day are collected and processed, and then normally recorded in the values of opening, closing, maximum, and minimum prices. Despite the present-day convenience in accessing the enormous market data for analysis and projection, it is not easy while costly for analysts and economist to incorporate all of this information in the financial modelling. Thus, in this paper, we extend the convex combination method for combining the plethoric price information on market data. The stock market and the Capital Asset Pricing Model (CAPM) are used as an example of market data and analytical model in this study. Our approach involving the use of opening, closing, maximum, and minimum prices is validated by comparing it with the conventional two-dimension convex combination method and center method which consider only the maximum and minimum values of the data. The results show that our proposed method outperforms the traditional methods in terms of Akaiki Information Criterion and Log-likelihood.