Swap Regression Methodology for Predicting Relationship with Historical Bivariate Data

TL;DR

This paper introduces a novel regression approach inspired by SWAP that dynamically determines the directional relationship between variables using GMM and beta distribution, applied to US macroeconomic data.

Contribution

It develops a new method combining GMM and beta distribution to identify variable roles and causality in time series data, extending SWAP regression concepts.

Findings

Successfully applied to US GDP and Public Debt data from 1966-2023.

Demonstrates the method's ability to detect bi-directional causality.

Provides a flexible framework for role-switching in regression analysis.

Abstract

This study revisits regression for samples with alternating predictors (SWAP) proposed in Chow et al.[2015] with the purpose of finding the best fit model when the role of the response and the explanatory variables was established. In the current work, we explore the directional relationship between the two variables at a given point of time, by a novel approach which draws direct inspiration from the concept of SWAP regression. Our method, based on the Gaussian Mixture Model (GMM) and the beta distribution, while estimating the probability of a latent variable, predicts the suitable model, i.e., earmarks if a variable can take the role of an explanatory or response, at any point of time. To make this switch-over role between variables, a valid consideration, we have established the existence of a bi-directional (Granger) causality between the two variables. A detailed real data analysis of the methodology is carried out using the historical quarterly data on probably the two most intertwined macroeconomic indicators explaining the health of an economy, viz., the Gross Domestic Product (GDP) and Public Debt, thereby making the application, in real data, more challenging. In particular, we use data of the US economy during the sample period 1966-2023.