Comparing the behaviors of some original short and long memory exponential volatility models

Volatility modeling is utilized across numerous fields including finance, environmental studies, and social sciences. It is particularly relevant in scenarios where understanding and predicting conditional variability is crucial, such as when dealing with incremental or time-dependent data. In this paper, novel short and long memory volatility models of the EGARCH family are introduced and analyzed, which are closely related to the well-established EGARCH model proposed by Nelson (1991) but share desirable theoretical properties in several dimensions. Recently developed members of the so-called EGARCH family, which introduces a modulus-log transformation proposed by John and Draper (1980) and a power transformation for the size and magnitude effect to tackle the problem with near-zero innovations and the asymmetric impact of positive and negative shocks on the volatility, are discussed. After a theoretical discussion of the proposed and related volatility models, the practical performance of the elaborated volatility models is compared to well-established and traditional GARCH approaches. A general QMLE algorithm is proposed to estimate the model parameters. The practical relevance of the advanced models is illustrated through a comparative study. By applying these volatility models to a variety of international stock index returns, this paper identifies market-specific characteristics as well as unique strengths and weaknesses of discussed volatility models. Although the practical performance of the recently introduced models is comparable to those obtained by the traditional EGARCH model, they generally outperform traditional non-exponential volatility models used as benchmarks and thus provide a useful alternative to existing short and long memory volatility models.