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Compound distributions for financial returns.

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This study introduces six new Student's t compound distributions for financial modeling. These novel distributions demonstrate superior performance compared to existing models in analyzing sample data.

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Area of Science:

  • Statistics
  • Econometrics
  • Probability Theory

Background:

  • Traditional statistical distributions often fail to capture the complex dynamics of financial data.
  • Generalized Autoregressive Conditional Heteroskedasticity (GARCH) models require robust innovation distributions for accurate modeling.
  • Existing compound distributions may not adequately represent the tail behavior and asymmetry common in financial time series.

Purpose of the Study:

  • To propose six novel Student's t based compound distributions by randomizing the scale parameter.
  • To derive the mathematical properties (PDF, CDF, moments, characteristic function) of these new distributions.
  • To evaluate the performance of these compound distributions as innovations in GARCH models.

Main Methods:

  • Development of six compound distributions using Student's t base with scale randomization from half-normal, Fréchet, Lomax, Burr III, inverse gamma, and generalized gamma distributions.
  • Derivation of key statistical properties for each proposed distribution.
  • Fitting GARCH models with the proposed compound distributions to sample data using the maximum likelihood method.

Main Results:

  • The proposed compound distributions provide a flexible framework for modeling financial data innovations.
  • Five of the six proposed distributions outperformed two commonly used distributions in GARCH model fitting for the sample data.
  • A simulation study confirmed the accuracy and reliability of the best-performing compound distribution model.

Conclusions:

  • The newly developed Student's t based compound distributions offer significant improvements for GARCH modeling.
  • These distributions provide a more accurate representation of financial data characteristics than traditional alternatives.
  • The findings suggest potential for enhanced risk management and forecasting in financial econometrics.