Cubic splines are piecewise cubic functions that are linked together in a way to guarantee smoothness at data points. Additivity constraints are added for benchmarking purpose and sub-period estimates are derived from each spline. When a sub-period indicator (or disaggregated series) is used, cubic splines are no longer drawn based on the low frequency data but the Benchmark-to-Indicator (BI ratio) is the one being smoothed. Sub- period estimates are then simply the product between the smoothed high frequency BI ratio and the indicator.
Usage
cubicspline(
s = NULL,
t,
nfreq = 4L,
conversion = c("Sum", "Average", "Last", "First", "UserDefined"),
obsposition = 1L
)Arguments
- s
Disaggregated series. If not NULL, it must be the same class as t.
- t
Aggregation constraint. Mandatory. it must be either an object of class ts or a numeric vector.
- nfreq
Integer. Annual frequency of the disaggregated variable. Used if no disaggregated series is provided.
- conversion
Conversion rule. Usually "Sum" or "Average". Sum by default.
- obsposition
Integer. Postion of the observation in the aggregated period (only used with "UserDefined" conversion)
Examples
data("qna_data")
Y <- ts(qna_data$B1G_Y_data[,"B1G_FF"], frequency = 1, start = c(2009,1))
# cubic spline without disaggregated series
y1 <- rjd3bench::cubicspline(t = Y, nfreq = 4L)
# cubic spline with disaggregated series
x1 <- y1+rnorm(n = length(y1), mean = 0, sd = 10)
y2 <- rjd3bench::cubicspline(s = x1, t = Y)
# cubic splines used for temporal disaggregation
x2 <- ts(qna_data$TURN_Q_data[,"TURN_INDEX_FF"], frequency = 4, start = c(2009,1))
y3 <- rjd3bench::cubicspline(s = x2, t = Y)