  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.
