Signal Regression Models for Location, Scale and Shape with an Application to Stock Returns

TL;DR

This paper introduces a flexible scalar-on-function regression framework that models all distribution parameters of responses, like stock returns, using covariates, combining GAMLSS with advanced estimation techniques for improved inference and variable selection.

Contribution

It develops a novel approach integrating signal regression with GAMLSS, compares gradient boosting and penalized likelihood estimation, and addresses practical issues like identifiability and model selection.

Findings

Gradient boosting enables high-dimensional variable selection.

Penalized likelihood provides direct statistical inference.

Application to stock returns models both mean and variance effectively.

Abstract

We discuss scalar-on-function regression models where all parameters of the assumed response distribution can be modeled depending on covariates. We thus combine signal regression models with generalized additive models for location, scale and shape (GAMLSS). We compare two fundamentally different methods for estimation, a gradient boosting and a penalized likelihood based approach, and address practically important points like identifiability and model choice. Estimation by a component-wise gradient boosting algorithm allows for high dimensional data settings and variable selection. Estimation by a penalized likelihood based approach has the advantage of directly provided statistical inference. The motivating application is a time series of stock returns where it is of interest to model both the expectation and the variance depending on lagged response values and functional liquidity curves.