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If the frequency distribution of a data set is more inclined towards smaller or larger values, the distribution is said to be skewed. If data values are skewed to the right, then the distribution is called positively skewed. Conversely, if the plot is skewed to the left, the distribution is called negatively skewed.
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The measures of central tendency calculated from a data set may not reveal much about its intrinsic distribution. If a plot is made of the data set’s values, the mean and the median may not only differ, but also the plot may have more values on one side of the central tendencies. Such a data set is said to be skewed towards that side.
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The accurate values of population parameters such as population proportion, population mean, and population standard deviation (or variance) are usually unknown. These are fixed values that can only be estimated from the data collected from the samples. The estimates of each of these parameters are sample proportion, the sample mean, and sample standard deviation (or variance). To obtain the values of these sample statistics, data are required that have particular distribution and central...
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A random variable is a single numerical value that indicates the outcome of a procedure. The concept of random variables is fundamental to the probability theory and was introduced by a Russian mathematician, Pafnuty Chebyshev, in the mid-nineteenth century.
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Skew selection for factor stochastic volatility models.

Jouchi Nakajima1

  • 1Bank for International Settlements, Basel, Switzerland.

Journal of Applied Statistics
|June 16, 2022
PubMed
Summary

This study introduces factor stochastic volatility models incorporating skew error distributions. Empirical analysis reveals skewness is crucial for common factors, enhancing prediction and portfolio performance.

Keywords:
37M1062M1091B84Factor stochastic volatilitygeneralized hyperbolic skew t-distributionportfolio allocationskew selectionstock returns

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Area of Science:

  • Quantitative Finance
  • Econometrics
  • Statistical Modeling

Background:

  • Stochastic volatility models are essential for financial market analysis.
  • Existing models often assume symmetric error distributions, which may not capture market dynamics.
  • Factor models are widely used to explain asset returns.

Purpose of the Study:

  • To propose and analyze factor stochastic volatility models incorporating skew error distributions.
  • To investigate the role and importance of skewness in financial factor models.
  • To develop a parsimonious approach for high-dimensional skew stochastic volatility models.

Main Methods:

  • Utilizing the generalized hyperbolic skew t-distribution for error terms.
  • Employing a Bayesian sparsity modeling strategy for the skewness parameter.
  • Analyzing daily stock return data to assess model performance.

Main Results:

  • Skewness is found to be significant for common-factor processes.
  • The impact of skewness on idiosyncratic shocks is less pronounced.
  • A parsimonious sparse skew structure improves model predictability.

Conclusions:

  • Skew error distributions are important in factor stochastic volatility models.
  • Bayesian sparsity offers an effective method for parsimonious skew modeling.
  • The proposed models enhance financial forecasting and portfolio optimization.