In studies, we will often find it useful to construct functions that
output the value of some exogenous variable over time. This package —
ramp.func — has utilities to construct and
modify composed time series functions. Each
function is the product of four components:
\[ x(t) = \bar x \times F_S(t) \times F_T(t) \times F_K(t) \]
where
\(\bar x\) is a scaling parameter. It is close to the mean value of an unperturbed system. It is the mean over an interval \((t_0, t_1)\) only if \(F_K(t)=1\) and \[\int_{t_0}^{t_1} F_S(t)\; F_T(t)\; dt = t_1-t_0\]
\(F_S(t)>0\) is a seasonal pattern function, normalized over the interval such that \[\int_{t_0}^{t_1} F_S(t) \;dt = t_1 - t_0\]
\(F_T(t)>0\) is a trend pattern function, normalized over the interval such that \[\int_{t_0}^{t_1} F_T(t) \; dt = t_1 - t_0\]
\(F_K(t)>0\) is a shock function