Essays on the estimation of distribution moments - Serrasqueiro, Pedro Nogueira (2022)
The set of four articles herein compiled focuses on specific aspects of the first four moments of probability distributions: mean, variance, skewness and kurtosis. The structure of the first three articles is similar, where hypotheses are formulated and/or theoretical properties are studied and later tested with simulation and applied to real life cases. The fourth article is of empirical nature, contextualized by the current SARS-CoV-2 pandemic. The first article (Chapter 2) analyzes the relationship between the geometric and harmonic means with respect to the aggregation of financial ratios. In the second article (Chapter 3), regarding the estimation of linear regression models, a new measure is proposed to rank independent variables according to their relative importance to explain the variability around the mean of the dependent variable. The third article (Chapter 4) approaches known diculties with the estimation of skewness and kurtosis. Applying the Generalized Method of Moments, confidence intervals and hypothesis tests are derived, taking into account the heteroskedasticity and autocorrelation typically present in financial time series. In the last article (Chapter 5), models of the GARCH family are estimated with the introduction of dummy variables to investigate and quantify the impact of SARS-CoV-2 in the volatility (standard deviation) of returns of a set of US-listed stocks and indices