Parameter regimes in partial functional panel regression

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.

A Literature Review of Semi-functional Partial Linear Regression Models

“… Time Series and Panel Data: The extensions that are related to the time series and forecasting are: the Semi-functional partial linear time series modeling for prediction [31], with autoregressive errors [32,33], with timevarying parameters for latent parameter regimes [34], regularized forecasting via smooth-rough partitioning of the regression coefficients [35].  Bayesian: The Bayesian estimation methods are present in some papers ,but we only mention these two papers in this part: the Bayesian bandwidth estimation and semi-metric selection for a functional partial linear model with unknown error density [36,37].…”