Parameter regimes in partially functional linear regression for panel data

We introduce a novel semiparametric partially functional linear regression model for panel data. The parametric model part is completely time varying, whereas the functional non-parametric component is allowed to vary over a set of different (functional) parameter regimes. These parameter regimes are assumed latent and need to be estimated from the data additionally to the unknown model parameters. We develop asymptotic theory for the suggested estimators including rates of convergence as n, T -> infinity. Our statistical model is motivated from economic theory on asset pricing. It allows to identify different risk regimes, governing the pricing of idiosyncratic risk in stock markets. For our application we develop necessary theoretical ground and offer a vast empirical study based on high-frequency stock-level data for the S&P 500 Index.