Parameter Regimes in Partial Functional Panel Regression

TL;DR

This paper introduces a novel partial functional linear regression model for panel data with time-varying parameters and unknown regimes, providing consistency and convergence rates, motivated by financial data analysis.

Contribution

It develops a new model allowing for time-varying parameters and unknown regimes, with proven consistency and convergence rates, applicable to high-frequency financial data.

Findings

Consistent estimators for the model parameters and regimes.

Derived convergence rates under different asymptotic scenarios.

Application to S&P 500 data addressing the idiosyncratic volatility puzzle.

Abstract

A new partial functional linear regression model for panel data with time varying parameters is introduced. The parameter vector of the multivariate model component is allowed to be completely time varying while the function-valued parameter of the functional model component is assumed to change over K unknown parameter regimes. Consistency is derived for the suggested estimators and for the classification procedure used to detect the K unknown parameter regimes. Additionally, the convergence rates of the estimators are derived under a double asymptotic differentiating between asymptotic scenarios depending on the relative order of the panel dimensions n and T. The statistical model is motivated by a real data application considering the so-called idiosyncratic volatility puzzle using high frequency data from the S&P500.