Reconciliation by means of the Multivariate Cholette method
Source:R/benchmark.R
multivariatecholette.RdThis is a multivariate extension of the Cholette benchmarking method which can be used for the purpose of reconciliation. While standard benchmarking methods consider one target series at a time, reconciliation techniques aim to restore consistency in a system of time series with regards to both contemporaneous and temporal constraints. Reconciliation techniques are typically needed when the total and its components are estimated independently (the so-called direct approach). The multivariate Cholette method relies on the principle of movement preservation and encompasses other reconciliation methods such as the multivariate Denton method.
Arguments
- xlist
a named list of ts objects including all input. Each element of the list should correspond to one input series (a preliminary series, a low-frequency series corresponding to one of the temporal aggregation constraints or a high-frequency series corresponding to one of the contemporaneous constraints).
- tcvector
a character vector defining each temporal constraints. Each element of the vector must be written as "Y = sum(x)" where "Y" is the name of a low frequency temporal constraint and "x" is the name of a high-frequency preliminary series. The names are the one given in the 'xlist' argument. Default is NULL, which means that no temporal constraint is considered.
- ccvector
a character vector defining each contemporaneous constraints. Each element of the vector must be written in the form "z=[w1*]x1+...+[wn*]xn" or "c=[w1*]x1+...+[wn*]xn" where "z" is the name of a high frequency contemporaneous constraint, wj are optional numeric weights, "x1,...,xn" are the names of the high-frequency preliminary series and c is a constant. The "+" operator can be replaced by "-". The names of the contemporaneous constraint(s) and the preliminary series are the one given in the 'xlist' argument. Note that any series put on the left hand side cannot appear on the right hand side of any other constraint. This is because left hand side quantities are fixed while right hand side quantities are adjusted so the equality holds. Default is NULL, which means that no contemporaneous constraint is considered. This is equivalent to applying the univariate Cholette method to each of the preliminary series separately.
- rho
Numeric. Smoothing parameter whose value should be between 0 and 1. See vignette for more information on the choice of the rho parameter.
- lambda
Numeric. Adjustment model parameter. Typically, lambda = 0 for additive benchmarking and lambda close to 1 to approach proportional benchmarking. Setting lambda = 1 is also an option but it should be used with caution as, in the case of a multivariate model, it may sometimes result in benchmarked series whose level differs strongly from the preliminary series. See vignette for more information on the choice of the lambda parameter.
Examples
# Example 1: one "standard" contemporaneous constraint: x1+x2+x3 = z
x1 <- ts(c(7, 7.2, 8.1, 7.5, 8.5, 7.8, 8.1, 8.4), frequency = 4, start = c(2010, 1))
x2 <- ts(c(18, 19.5, 19.0, 19.7, 18.5, 19.0, 20.3, 20.0), frequency = 4, start = c(2010, 1))
x3 <- ts(c(1.5, 1.8, 2, 2.5, 2.0, 1.5, 1.7, 2.0), frequency = 4, start = c(2010, 1))
z <- ts(c(27.1, 29.8, 29.9, 31.2, 29.3, 27.9, 30.9, 31.8), frequency = 4, start = c(2010, 1))
Y1 <- ts(c(30.0, 30.6), frequency = 1, start = c(2010, 1))
Y2 <- ts(c(80.0, 81.2), frequency = 1, start = c(2010, 1))
Y3 <- ts(c(8.0, 8.1), frequency = 1, start = c(2010, 1))
### check consistency between temporal and contemporaneous constraints
lfs <- cbind(Y1,Y2,Y3)
rowSums(lfs) - stats::aggregate.ts(z) # should all be 0
#> Time Series:
#> Start = 2010
#> End = 2011
#> Frequency = 1
#> [1] 0 0
data_list <- list(x1 = x1, x2 = x2, x3 = x3, z = z, Y1 = Y1, Y2 = Y2, Y3 = Y3)
tc <- c("Y1 = sum(x1)", "Y2 = sum(x2)", "Y3 = sum(x3)") # temporal constraints
cc <- c("z = x1+x2+x3") # contemporaneous constraints
multivariatecholette(xlist = data_list, tcvector = tc, ccvector = cc, rho = 1, lambda = .5) # Denton
#> $x1
#> Qtr1 Qtr2 Qtr3 Qtr4
#> 2010 7.045542 7.376876 8.064691 7.512891
#> 2011 8.023645 7.033308 7.564454 7.978594
#>
#> $x2
#> Qtr1 Qtr2 Qtr3 Qtr4
#> 2010 18.58604 20.59697 19.79830 21.01869
#> 2011 19.12180 19.22024 21.37601 21.48195
#>
#> $x3
#> Qtr1 Qtr2 Qtr3 Qtr4
#> 2010 1.468420 1.826157 2.037007 2.668416
#> 2011 2.154551 1.646451 1.959538 2.339460
#>
multivariatecholette(xlist = data_list, tcvector = tc, ccvector = cc, rho = 0.729, lambda = .5) # Cholette
#> $x1
#> Qtr1 Qtr2 Qtr3 Qtr4
#> 2010 7.070672 7.385807 8.059196 7.484325
#> 2011 7.945589 6.975158 7.571946 8.107307
#>
#> $x2
#> Qtr1 Qtr2 Qtr3 Qtr4
#> 2010 18.55121 20.58910 19.81051 21.04918
#> 2011 19.17769 19.26249 21.36970 21.39013
#>
#> $x3
#> Qtr1 Qtr2 Qtr3 Qtr4
#> 2010 1.478117 1.825096 2.030295 2.666492
#> 2011 2.176725 1.662357 1.958353 2.302565
#>
multivariatecholette(xlist = data_list, tcvector = NULL, ccvector = cc, rho = 1, lambda = .5) # no temporal constraints
#> $x1
#> Qtr1 Qtr2 Qtr3 Qtr4
#> 2010 0.09471188 0.24191380 0.61537179 0.19776270
#> 2011 0.75425553 0.33620487 0.74406548 0.97135123
#>
#> $x2
#> Qtr1 Qtr2 Qtr3 Qtr4
#> 2010 19.70581 21.39462 20.60378 21.06272
#> 2011 19.88066 20.29720 22.26361 22.09731
#>
#> $x3
#> Qtr1 Qtr2 Qtr3 Qtr4
#> 2010 7.299482 8.163465 8.680845 9.939513
#> 2011 8.665084 7.266593 7.892321 8.731341
#>
# Example 2: two contemporaneous constraints: x1+3*x2+0.5*x3+x4+x5 = z1 and x1+x2 = x4
x1 <- ts(c(7.0,7.3,8.1,7.5,8.5,7.8,8.1,8.4), frequency=4, start=c(2010,1))
x2 <- ts(c(1.5,1.8,2.0,2.5,2.0,1.5,1.7,2.0), frequency=4, start=c(2010,1))
x3 <- ts(c(18.0,19.5,19.0,19.7,18.5,19.0,20.3,20.0), frequency=4, start=c(2010,1))
x4 <- ts(c(8,9.5,9.0,10.7,8.5,10.0,10.3,9.0), frequency=4, start=c(2010,1))
x5 <- ts(c(5,9.6,7.2,7.1,4.3,4.6,5.3,5.9), frequency=4, start=c(2010,1))
z1 <- ts(c(38.1,41.8,41.9,43.2,38.8,39.1,41.9,43.7), frequency=4, start=c(2010,1))
Y1 <- ts(c(30.0,30.5), frequency=1, start=c(2010,1))
Y2 <- ts(c(10.0,10.5), frequency=1, start=c(2010,1))
Y3 <- ts(c(80.0,81.0), frequency=1, start=c(2010,1))
Y4 <- ts(c(40.0,41.0), frequency=1, start=c(2010,1))
Y5 <- ts(c(25.0,20.0), frequency=1, start=c(2010,1))
### check consistency between temporal and contemporaneous constraints
lfs <- cbind(Y1,3*Y2,0.5*Y3,Y4,Y5)
rowSums(lfs) - stats::aggregate.ts(z1) # should all be 0
#> Time Series:
#> Start = 2010
#> End = 2011
#> Frequency = 1
#> [1] 0 0
data.list <- list(x1=x1,x2=x2,x3=x3,x4=x4,x5=x5,z1=z1,Y1=Y1,Y2=Y2,Y3=Y3,Y4=Y4,Y5=Y5)
tc <- c("Y1=sum(x1)", "Y2=sum(x2)", "Y3=sum(x3)", "Y4=sum(x4)", "Y5=sum(x5)")
cc <- c("z1=x1+3*x2+0.5*x3+x4+x5", "0=x1+x2-x4")
multivariatecholette(xlist = data.list, tcvector = tc, ccvector = cc, rho = 1, lambda = .5)
#> $x1
#> Qtr1 Qtr2 Qtr3 Qtr4
#> 2010 7.461426 7.453406 7.724638 7.360531
#> 2011 7.347524 7.756222 7.876066 7.520188
#>
#> $x2
#> Qtr1 Qtr2 Qtr3 Qtr4
#> 2010 2.230614 2.193747 2.520035 3.055604
#> 2011 2.602163 2.310811 2.591295 2.995731
#>
#> $x3
#> Qtr1 Qtr2 Qtr3 Qtr4
#> 2010 19.66444 20.17525 19.99352 20.16679
#> 2011 19.33101 19.71956 20.96161 20.98781
#>
#> $x4
#> Qtr1 Qtr2 Qtr3 Qtr4
#> 2010 9.692039 9.647153 10.244673 10.416135
#> 2011 9.949687 10.067033 10.467361 10.515919
#>
#> $x5
#> Qtr1 Qtr2 Qtr3 Qtr4
#> 2010 4.422475 8.030573 6.373824 6.173128
#> 2011 4.030796 4.484531 5.301882 6.182792
#>