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 a preliminary 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
Preliminary 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 benchmarked series. Used if no preliminary 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$B1G_Y_data[,"B1G_FF"], frequency = 1, start = c(2009,1))
# cubic spline without preliminary series
y1 <- cubicspline(t = Y, nfreq = 4L)
# cubic spline with preliminary series
x1 <- y1 + rnorm(n = length(y1), mean = 0, sd = 10)
cubicspline(s = x1, t = Y)
#> Qtr1 Qtr2 Qtr3 Qtr4
#> 2009 4397.063 4389.525 4396.652 4371.160
#> 2010 4374.149 4379.796 4451.688 4514.467
#> 2011 4622.571 4712.685 4754.705 4766.039
#> 2012 4754.643 4723.967 4692.555 4678.535
#> 2013 4672.339 4660.743 4677.626 4702.792
#> 2014 4723.708 4747.876 4770.854 4765.563
#> 2015 4787.211 4811.529 4833.484 4861.776
#> 2016 4898.182 4902.189 4932.420 4945.610
#> 2017 4967.784 4965.589 5057.696 5158.831
#> 2018 5286.200 5394.973 5502.625 5583.602
#> 2019 5630.538 5662.939 5633.391 5587.333
#> 2020 5474.084 5410.108 5354.577 5327.731
# cubic splines used for temporal disaggregation
x2 <- ts(qna_data$TURN_Q_data[,"TURN_INDEX_FF"], frequency = 4, start = c(2009,1))
cubicspline(s = x2, t = Y)
#> Qtr1 Qtr2 Qtr3 Qtr4
#> 2009 3817.265 4655.940 4125.907 4955.289
#> 2010 3700.042 4651.986 4059.082 5308.990
#> 2011 3869.960 4971.484 4311.150 5703.406
#> 2012 4147.811 5013.761 4419.430 5268.698
#> 2013 4159.471 4867.414 4371.355 5315.259
#> 2014 4368.250 4889.973 4383.173 5366.604
#> 2015 4219.172 5090.938 4499.862 5484.029
#> 2016 4323.788 5190.106 4608.648 5555.858
#> 2017 4571.106 5296.208 4556.676 5725.911
#> 2018 4745.996 5623.545 5073.312 6324.547
#> 2019 5083.042 5847.280 5201.402 6382.476
#> 2020 5135.178 4920.197 5120.096 6391.030
#> 2021 5361.533 6291.365 5489.010 6962.494