  This paper develops a point impact linear regression model in which the
trajectory of a continuous stochastic process, when evaluated at a sensitive
time point, is associated with a scalar response. The proposed model
complements and is more interpretable than the functional linear regression
approach that has become popular in recent years. The trajectories are assumed
to have fractal (self-similar) properties in common with a fractional Brownian
motion with an unknown Hurst exponent. Bootstrap confidence intervals based on
the least-squares estimator of the sensitive time point are developed.
Misspecification of the point impact model by a functional linear model is also
investigated. Non-Gaussian limit distributions and rates of convergence
determined by the Hurst exponent play an important role.
