Return-Distributions-R

Fit a broad set of univariate return distributions to asset return series, compare models by logLik/AIC/BIC, and optionally plot fitted densities. Includes a simulation harness to validate fitting and model selection.

Requirements

• R (tested with R 4.4.x)
• Core packages: sn, tseries, fBasics, nortest
• Optional (only if plotting those overlays): logcondens, logspline

Files

• xreturns_dist.r: main fitting script
• xsim_dist.r: simulation-based model selection test harness
• return_utils.r: return computation + summary stats helpers
• dist_utils.r: distribution log-pdf/moments/metrics utilities
• plot_utils.r: density plot helpers

Input Format

CSV with a Date column and one or more asset price columns:

Date,SPY,VIX
1993-01-29,24.2414,12.42
1993-02-01,24.4138,12.33

Usage

Rscript xreturns_dist.r prices.csv

The script expects the first argument to be the CSV path unless you set infile in the script.

Simulation harness

Rscript xsim_dist.r
Rscript xsim_dist.r 50 5000   # 50 sims per model, 5000 observations

xsim_dist.r simulates returns from selected distributions, fits the chosen models directly, and reports selection counts and accuracy for logLik/AIC/BIC.

Key Options (xreturns_dist.r)

Edit at the top of xreturns_dist.r:

• return_type: "log" or "simple"
• ret_scale: multiply returns (e.g., 100 for percent)
• fixed_nu: set degrees of freedom for t-family models (NA to estimate)
• models_to_fit: vector of model names to fit
• max_models: optional cap on number of models fitted
• do_density_plots: generate per-asset density plots
• do_kde_plot, do_logcondens_plot, do_logspline_plot: add nonparametric overlays

Environment overrides (useful for automation):

• XRETURNS_MODELS: comma-separated list of models
• XRETURNS_MAX_MODELS: integer cap or NA
• XRETURNS_DENSITY_PLOTS: TRUE/FALSE

Example:

set XRETURNS_MODELS=Normal,Logistic,SkewNormal,SkewT
set XRETURNS_DENSITY_PLOTS=FALSE
Rscript xreturns_dist.r spy_vix.csv

Models Implemented

Symmetric / location-scale families

• Normal
• Logistic
• Laplace
• Cauchy
• Hyperbolic secant (Sech)
• Generalized secant hyperbolic (GSH)
• Generalized error distribution (GED)
• Student t (T)

Skewed or asymmetric families

• Asymmetric Laplace (ALaplace)
• Skewed GED (SGED; Fernandez-Steel skewing)
• Skewed GSH (SGSH)
• NEF-GHS (natural exponential family based on GSH)

Azzalini / t-family skewing

• Azzalini skew-normal (SkewNormal)
• Azzalini skew-t (SkewT)
• Fernandez-Steel skew-normal (FSSkewNormal)
• Fernandez-Steel skew-t (FSSkewT)
• Jones-Faddy skew-t (JFSkewT)
• Non-central t (NCT)

Other families

• EGB2 (McDonald)
• NIG (normal-inverse Gaussian)
• Variance-Gamma (VG)
• Hyperbolic (Hyperbolic)
• Generalized hyperbolic (GH)
• Champernowne (with lambda controlling sech/logistic limits)
• Normal-Laplace
• Generalized t (GT; McDonald–Newey)
• Skewed generalized t (SGT; Theodossiou)

Output

• Return summary table (excess kurtosis)
• Fit tables per model with parameters, moments (where defined), logLik/AIC/BIC
• AIC/BIC summary tables across assets and models
• Per-asset model ranking tables (logLik/AIC/BIC)
• Average model ranking table across assets (deltas + average moments)
• Optional density plots saved as <SYMBOL>.png

Notes

• All reported kurtosis values are excess kurtosis.
• For t-family models, moments require sufficiently large nu.
• Some moments are computed numerically and may emit warnings; likelihoods remain valid.
• Many fits use optim(..., method = "BFGS") with numerical gradients.

Example

Rscript xreturns_dist.r spy_vix.csv