Canonical correlation analysis on joint production: empirical study for the desirability of linear and log linear estimation in terms of crude oil and petroleum products

Abstract

Canonical correlation analysis seeks to identify and quantify the associations between two sets of variables. Harold Hotelling, who initially developed the technique, provided the example of relating arithmetic speed and arithmetic power to reading speed and reading power. Relating governmental policy variables with economic goal variables and relating college performance variables with precollege variables are other examples of this type. Canonical correlation analysis focuses on the correlation between a linear combination of the variables in one set and a linear combination of the variables in another set. The idea is first to determine the pair of linear combinations having the largest correlation. Next, we determine the pair of linear combinations having the largest correlation among all pairs uncorrelated with the initially selected pair. The process continues. The pairs of linear combinations are called the canonical variables, and their correlations are called canonical correlations. The canonical correlations measure the strength of association between the two sets of variables. The maximization aspect of the technique represents an attempt to concentrate a high-dimensional relationship between two sets of variables into a few pairs of canonical variables. An attempt has been made here to analyse the jointly produced goods crude oil and petroleum products using linear and log-linear estimation based on Harold Hotelling canonical correlation approach and to compare these two estimation procedures among themselves. The analysis suggests that log-linear estimation is superior to the linear estimation for such type of study.