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Pareto Hybrids with Asymmetric Tails

• Introduction
  • P.H.A.T. - Pareto Hybrids with Asymmetric Tails
    • Installation
    • Quickstart
    • Dependencies
    • Enhancements
• Demo
  • Download Data
  • Fit GARCH and Estimate \(\alpha\) in Both Tails
  • Fit \(\mu\) and \(\sigma\) with Machine Learning
  • Compare Fit with Gaussian and T
  • Generate Garch Forecasts

Define

• What Are Fat Tails?
  • Thin vs. Fat
  • The Borderline Sigmoid
  • The Devil is in the Tails
  • Scale Invariance
  • Six Sigma is Not Six Sigma
• the Phat Distribution
  • In Search of Two Tails
  • the Double Pareto
  • the CarBen Hybrid
  • Pareto Hybrids with Asymmetric Tails: a Mixture Model
  • Pitfalls
• Characteristics
  • Density
    • Phat
    • Right CarBen
    • Left CarBen
  • Cumulative Distribution Function
    • Phat
    • Right CarBen
    • Left CarBen
  • Quantile Function
    • Phat
    • Right CarBen
    • Left CarBen
  • Moments
    • Carben Right
    • Carben Left
    • Mean
    • Variance

Fit

• Peak-Over Threshold
• Estimating the Tail - PoT
• Estimating the Tail - Double Bootstrap
  • Tail Quest
  • the Hill Double Bootstrap
    • Testing
    • Caveats
• Maximum Likelihood
• Neural Networks
  • Fitting a Standard Gaussian
  • Fitting S&P 500 Daily Returns
• Fitting the Phat
  • Failure of a Standard Loss Function
  • PhatLoss: A Custom Loss Function
  • PhatNet
  • Caution on Scaling

Forecast

• ARMA-GARCH for Time Series
  • Non-Stationarity
  • ARMA
    • Importance of Scale
  • GARCH Forecasting
    • Projection with Expanding Window
    • Feed Forward for Out-of-Sample Projections
    • Fixed Windows
    • Fixed Window Across Entire Time Series
  • Garchcaster
    • Garchcaster Tests
• Phat-GARCH
  • Approach
  • A Note on Scaling
  • Forecasting Time Series with Pareto Hybrids
    • Generate ARMA-GARCH Residuals
    • Fit Residuals to the Phat Distribution
    • Some More Notes on Scaling
    • Comparing Fit
    • Phatcast
    • 1-Year Price Forecast
  • Phat-ARGARCH
  • T v Phat-ARGARCH
  • Skew T v Phat-ARGARCH
  • CAVEATS

Misc

• References
• API

Introduction