This function is a close imitation of the way FAME handles time scale
conversions. See the chapter on "Time Scale Conversion" in the Users
Guide to Fame if the explanation given here is not detailed enough. Start with some definitions. Combining values of a higher frequency
input series to create a lower frequency output series is known as
aggregation. Doing the opposite is known as disaggregation.
Disaggration for "discrete" series: (i) for observed == "beginning"
("end"), the first (last) output period that begins (ends) in a
particular input period is assigned the value of that input period.
All other output periods that begin (end) in that input period are NA.
(ii) for observed == "summed" or "averaged", all output periods that
end in a particular input period are assigned the same value. For
"summed", that value is the input period value divided by the number
of output periods that end in the input period, while for an
"averaged" series, the output period values are the same as the
corresponding input period values.
Aggregation for "discrete" series: (i) for observed == "beginning"
("end"), the output period is assigned the value of the first (last)
input period that begins (ends) in the output period. (ii) for
observed == "summed" ("averaged"), the output value is the sum
(average) of all the input values for periods that end in the output
period.
Methods "constant", "linear", and "cubic" all work by constructing a
continuous function F(t) and then reading off the appropriate
point-in-time values if observed == "beginning" or "end", or by
integrating F(t) over the output intervals when observed == "summed",
or by integrating F(t) over the output intervals and dividing by the
lengths of those intervals when observed == "averaged". The unit of
time itself is given by the basis argument.
The form of F(t) is determined by the conversion method. For
"constant" conversions, F(t) is a step function with jumps at the
boundaries of the input periods. If the first and/or last input
periods only partly cover an output period, F is linearly extended to
cover the first and last output periods as well. The heights of the
steps are set such that F(t) aggregates over the input periods to the
original input series.
For "linear" ("cubic") conversions, F(t) is a linear (cubic) spline.
The x-coordinates of the spline knots are the beginnings or ends of
the input periods if observed == "beginning" or "end", else they are
the centers of the input periods. The y-coordinates of the splines are
chosen such that aggregating the resulting F(t) over the input periods
yields the original input series.
For "constant" conversions, if ignore == F, the first (last)
output period is the first (last) one for which complete input data is
available. For observed == "beginning", for example, this means that
data for the first input period that begins in the first output period
is available, while for observed == "summed", this means that the
first output period is completely contained within the available input
periods. If ignore == T, data for only a single input period
is sufficient to create an output period value. For example, if
converting weekly data to monthly data, and the last observation is
June 14, the output series will end in June if ignore == T, or
May if it is F.
Unlike the "constant" method, the domain of F(t) for "linear" and
"cubic" conversions is NOT extended beyond the input periods, even if
the ignore option is T. The first (last) output period is therefore
the first (last) one that is completely covered by input periods.
Series with observed == "annualized" are handled the same as observed
== "averaged".