mclustAddons (version 0.10)

GMMlogreturn: Modeling log-returns distribution via Gaussian Mixture Models

Description

Gaussian mixtures for modeling the distribution of financial log-returns.

Usage

GMMlogreturn(y, ...)
# S3 method for GMMlogreturn
summary(object, ...)

Value

Returns an object of class 'GMMlogreturn'.

Arguments

y

A numeric vector providing the log-returns of a financial stock.

...

Further arguments passed to mclust::densityMclust(). For a full description of available arguments see the corresponding help page.

object

An object of class 'GMMlogreturn'.

Author

Luca Scrucca

Details

Let \(P_t\) be the price of a financial stock for the current time frame (day for instance), and \(P_{t-1}\) the price of the previous time frame. The log-return at time \(t\) is defined as: $$ y_t = \log( \frac{P_t}{P_{t-1}} ) $$ By default, a univariate heteroscedastic GMM using Bayesian regularization (as described in mclust::priorControl()) is fitted to the observed log-returns. The number of mixture components is automatically selected by BIC, unless specified with the optional G argument.

References

Scrucca L. (2024) Entropy-based volatility analysis of financial log-returns using Gaussian mixture models. Entropy, 26(11), 907. tools:::Rd_expr_doi("10.3390/e26110907")

See Also

VaR.GMMlogreturn(), ES.GMMlogreturn().

Examples

data(gold)
head(gold)
mod = GMMlogreturn(gold$log.returns)
summary(mod)
plot(mod, what = "density", data = gold$log.returns,
     xlab = "log-returns", col = 4, lwd = 2)