Functional descriptive statistics for generated functional data objects
A related sanity check for the functional data objects generated for each model component (before they are used in the functional linear regression analysis) is the plotting of functional descriptive statistics (see section 6.1.1 of \cite{Ramsay_2009}). The functional mean and standard deviation of the functional data objects for the number of non-corporates and the number of cited references by priority year are shown in Fig. \ref{413726} and Fig. \ref{437199} respectively, and show that for both model components variability increases as time progresses (as would be expected with most forecasts). In addition the mean functional data object values show that there is a notable early surge in non-corporates by priority year during the emergence phase before a technology achieves mainstream adoption. This corresponds well to the hype cycle associated with new technologies during early development when significant levels of R&D are first launched in a race to achieve commercialisation, which can often prove premature or short-lived. By contrast, the mean cited references by priority year measure shows that a steadily accelerating growth is observed during the emergence phase, without significant undulation, potentially implying that scientific development efforts are less phased by disturbances as they begin to accumulate.