Biology Reference
In-Depth Information
2.2.3 adding effects of Holidays, Seasonality, and DOW
The inclusion of the three types of patterns to the initial data is done sequen-
tially. We describe a certain order, but if all components are entered either
multiplicatively or additively (rather than a mix), then the order of pattern
inclusion does not matter.
2.2.3.1 Holidays
Holiday effects are added either in multiplicative form (the new point is a
fraction of the original) or in additive form (the new point is the original,
with some amount subtracted). Holidays can be specified at any point in the
series; the default is to use multiplicative holiday effects on all federal holi-
days (derived from the office of personnel management site, www.opm.gov/
fedhol: New Year's Day, birthday of Martin Luther King, Jr., Washington's
Birthday, Memorial Day, Independence Day, Labor Day, Columbus Day,
Veterans Day, Thanksgiving Day, and Christmas Day).
2.2.3.2 Seasonality
Seasonality is added in either additive or multiplicative form. It can be a sca-
lar (in which case, it modifies a shifted sine wave function with a period of
365.25 days,
f
=
sin
(2
π
*
x
/(365.25) + 2)) or a fully specified vector. The default
is to add no seasonality; a multiplicative one-half-scale sine wave appears to
be a good approximation for respiratory seasonality.
2.2.3.3 Day-of-Week (DOW)
The DOW pattern can be multiplicative or additive, and must be fully speci-
fied as a vector containing an index for each day. By default, it is set to multi-
plicative, with weekends set to one-third of weekday values.
In each of these steps, the dataset is normalized to maintain the same
means (by dividing by or adding the appropriate amount to the series over-
all). However, the covariance does increase as the effects are applied uni-
formly to each series.
Finally, after all patterns of interest are added, the series are rounded to
integers and bounded to be nonnegative in order to yield valid count data.
2.3 Mimicking Existing Dataset Qualities
In addition to generating a general type of multivariate time series with spe-
cific temporal and dependence patterns, our data simulator can also be used
