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Interactive Gaussian-sum filtering for estimating systematic risk in financial econometrics

Motivated by application of signal processing techniques in financial econometrics, we propose a novel adaptive and robust non-linear filtering methodology to estimate the systematic risk of an investment arising from exposure to general market movements. There are extensive evidence that the asset returns exhibit non-normalities due to fat tails, excessive kurtosis, and asymmetry of the financial data. Gaussian sum filters (GSF) are attractive estimators for state-estimation in such non-Gaussian problems. However, due to the high computational cost of the GSF when applied to non-Gaussian risk estimation problems, no GSF has yet been investigated in the context of financial econometrics. The paper addresses this gap. To tackle this non-Gaussian problem, we introduce the interactive Gaussian sum filter (IGSF) by representing the non-systematic part of the risk in the Fama-French multi-factor model with the Gilbert-Elliott (GE) model. Due to incorporation of the GE-model, the proposed IGSF is a computationally attractive adaptive filter with an interactive multiple model (IMM) collapsing style. In other words, the number of Gaussian components is controlled utilizing a modified Bayesian learning technique, which is used to collapse the Gaussian mixture representation of the non-systematic risk into an equivalent Gaussian term at each filtering cycle.