Statistical Modelling of Global ETF Returns: Evidence from the Indian Financial Market

Abstract

Prokarsha Kumar Ghosh

In modern economy, Exchange Traded Funds have emerged as one of the most important instruments for portfolio diversification and global market exposure, underlying the statistical behavior, interdependence, and predictive dynamics of ETF returns is considered essential for investors and financial researchers. In this study, the statistical structure and predictive relationships among selected international ETFs have been studied with the combination of statistical techniques, stochastic modelling, probability distribution fitting, and machine learning methods. This study consists of daily return observations for six ETFs representing major global markets, which are iShares MSCI India ETF, INDA, iShares MSCI United Kingdom ETF, EWU, iShares MSCI Japan ETF, EWJ, iShares MSCI Germany ETF, EWG, iShares MSCI China ETF, MCHI, and iShares USA. ETF, IYY during the tenure of 5 years. The behavior of INDA relative to other global ETFs have been primarily analyzed, where market interdependencies are explored through correlation analysis and pairwise visualizations. The influence of global ETF returns on INDA returns have been estimated using linear regression and Bayesian linear regression models. The distributional characteristics of ETF returns are evaluated using the Kolmogorov–Smirnov test and by fitting Weibull, and Laplace distributions, while stochastic modelling based on Brownian motion is applied to observe random walk behavior. Nonlinear predictive relationships are further analyzed using artificial neural networks and deep neural networks, and concepts from quantum statistical mechanics are incorporated by fitting Bose–Einstein and Fermi–Dirac distributions to evaluate alternative probabilistic frameworks for modelling ETF return dynamics.

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