Stable non-Gaussian random processes , by G. Samorodnitsky and M. S. Taqqu. Pp. 632. £49.50. 1994. ISBN 0-412-05171-0 (Chapman and Hall).

Parametric statistics are based on the assumption of normality. Recent findings suggest that Type I error and power can be adversely affected when data are non-normal. This paper aims to assess the distributional shape of real data by examining the values of the third and fourth central moments as a measurement of skewness and kurtosis in small samples. The analysis concerned 693 distributions with a sample size ranging from 10 to 30. Measures of cognitive ability and of other psychological variables were included. The results showed that skewness ranged between −2.49 and 2.33. The values of kurtosis ranged between −1.92 and 7.41. Considering skewness and kurtosis together the results indicated that only 5.5% of distributions were close to expected values under normality. Although extreme contamination does not seem to be very frequent, the findings are consistent with previous research suggesting that normality is not the rule with real data.

http://diposit.ub.edu/dspace/bitstream/2445/153945/1/603461.pdf

Skewness and Kurtosis in Real Data Samples

Ensemble approach based on bagging, boosting and stacking for short-term prediction in agribusiness time series

This paper proposes a methodology for modelling time series of realized covariance matrices in order to forecast multivariate risks. The approach allows for flexible dynamic dependence patterns and guarantees positive definiteness of the resulting forecasts without imposing parameter restrictions. We provide an empirical application of the model, in which we show by means of stochastic dominance tests that the returns from an optimal portfolio based on the model’s forecasts second-order dominate returns of portfolios optimized on the basis of traditional MGARCH models. This result implies that any risk-averse investor, regardless of the type of utility function, would be better-off using our model.

Modelling and Forecasting Multivariate Realized Volatility

SUMMARY This paper proposes a methodology for dynamic modelling and forecasting of realized covariance matrices based on fractionally integrated processes. The approach allows for flexible dependence patterns and automatically guarantees positive definiteness of the forecast. We provide an empirical application of the model, which shows that it outperforms other approaches in the extant literature, both in terms of statistical precision as well as in terms of providing a superior mean-variance trade-off in a classical investment decision setting. Copyright © 2010 John Wiley & Sons, Ltd.

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Modelling and forecasting multivariate realized volatility

Moments-based spillovers across gold and oil markets

In this paper a new multivariate volatility model is proposed It combines the appealing properties of the stable Paretian distribution to model the heavy tails with the GARCH model to capture the volatility clustering Returns on assets are assumed to follow a sub-Gaussian distribution, which is a particular multivariate stable distribution In this way the characteristic function of the fitted returns has a tractable expression and the density function can be recovered by numerical methods A multivariate GARCH structure is then adopted to model the covariance matrix of the Gaussian vectors underlying the sub-Gaussian system The model is applied to a bivariate series of daily US stock returns Value-at-risk for long and short positions is computed and compared with the one obtained using the multivariate normal and the multivariate Student’s t distribution Finally, exploiting the recent developments in the vast dimensional time-varying covariances modeling, possible feasible extensions of our model to higher dimensions are suggested and an illustrative example using the Dow Jones index components is presented

Modeling fat tails in stock returns: a multivariate stable-GARCH approach

This paper studies the behavior of the conventional measures of skewness and kurtosis when the data generator process is a distribution which does not possess variance or third or fourth moment and assesses the robustness of the alternative measures for these particular cases. I first show that for symmetric fat tailed distribution skewness is far from being a valid indicator of the presence of asymmetry. Secondly, I study, via Monte Carlo simulations, the behavior of the alternative measures of skewness and kurtosis when applied to distributions that do not possess finite higher moments. Finally, I present an application to the series of daily returns on a large cap US stock and show why alternative measures are a better tool to describe the distribution of financial returns.

Robust Estimation of Skewness and Kurtosis in Distributions with Infinite Higher Moments

Robust estimation of skewness and kurtosis in distributions with infinite higher moments

We use the the heterogeneous autoregressive realized volatility (HAR-RV) model to analyze both in sample and out-of-sample whether a measure of investor happiness predicts the daily realized volatility of oil-price returns, where we use high-frequency intraday data to measure realized volatility. Full-sample estimates reveal that realized volatility is significantly negatively linked to investor happiness at a short forecast horizon. Similarly, out-of-sample results indicate that investor happiness significantly improves the accuracy of forecasts of realized volatility at a short forecast horizon. Results for a medium and a long forecast horizon are insignificant. We argue that our results shed light on the role played by speculation in oil products and the potential function of oil-related products as a hedge against risks in traditional financial assets.

Matteo Bonato

Papers

Moments-based spillovers across gold and oil markets

Modeling fat tails in stock returns: a multivariate stable-GARCH approach

Robust Estimation of Skewness and Kurtosis in Distributions with Infinite Higher Moments

Robust estimation of skewness and kurtosis in distributions with infinite higher moments

Investor Happiness and Predictability of the Realized Volatility of Oil Price