benchmarking: Restore temporal constraints

Description

Replication of the G-Series 2.0 SAS$^\circledR$ BENCHMARKING procedure (PROC BENCHMARKING). See the G-Series 2.0 documentation for details (Statistics Canada 2016).

This function ensures coherence between time series data of the same target variable measured at different frequencies (e.g., sub-annually and annually). Benchmarking consists of imposing the level of the benchmark series (e.g., annual data) while minimizing the revisions of the observed movement in the indicator series (e.g., sub-annual data) as much as possible. The function also allows nonbinding benchmarking where the benchmark series can also be revised.

The function may also be used for benchmarking-related topics such as temporal distribution (the reciprocal action of benchmarking: disaggregation of the benchmark series into more frequent observations), calendarization (a special case of temporal distribution) and linking (the connection of different time series segments into a single consistent time series).

Several series can be benchmarked in a single function call.

Usage

benchmarking(
  series_df,
  benchmarks_df,
  rho,
  lambda,
  biasOption,
  bias = NA,
  tolV = 0.001,
  tolP = NA,
  warnNegResult = TRUE,
  tolN = -0.001,
  var = "value",
  with = NULL,
  by = NULL,
  verbose = FALSE,
  # New in G-Series 3.0
  constant = 0,
  negInput_option = 0,
  allCols = FALSE,
  quiet = FALSE
)

Value

The function returns is a list of three data frames:

series: data frame containing the benchmarked data (primary function output). BY variables specified with argument by would be included in the data frame but not alterability coefficient variables specified with argument var.
benchmarks: copy of the input benchmarks data frame (excluding invalid benchmarks when applicable). BY variables specified with argument by would be included in the data frame but not alterability coefficient variables specified with argument with.
graphTable: data frame containing supplementary data useful for producing analytical tables and graphs (see function plot_graphTable()). It contains the following variables in addition to the BY variables specified with argument by:
- varSeries: Name of the indicator series variable
- varBenchmarks: Name of the benchmark variable
- altSeries: Name of the user-defined indicator series alterability coefficients variable
- altSeriesValue: Indicator series alterability coefficients
- altbenchmarks: Name of the user-defined benchmark alterability coefficients variable
- altBenchmarksValue: Benchmark alterability coefficients
- t: Indicator series period identifier (1 to $T$)
- m: Benchmark coverage periods identifier (1 to $M$)
- year: Data point calendar year
- period: Data point period (cycle) value (1 to periodicity)
- constant: Temporary additive constant (argument constant)
- rho: Autoregressive parameter $\rho$ (argument rho)
- lambda: Adjustment model parameter $\lambda$ (argument lambda)
- bias: Bias adjustment (default, user-defined or estimated bias according to arguments biasOption and bias)
- periodicity: The maximum number of periods in a year (e.g. 4 for a quarterly indicator series)
- date: Character string combining the values of variables year and period
- subAnnual: Indicator series values
- benchmarked: Benchmarked series values
- avgBenchmark: Benchmark values divided by the number of coverage periods
- avgSubAnnual: Indicator series values (variable subAnnual) averaged over the benchmark coverage period
- subAnnualCorrected: Bias corrected indicator series values
- benchmarkedSubAnnualRatio: Difference ($\lambda = 0$) or ratio ($\lambda \ne 0$) of the values of variables benchmarked and subAnnual
- avgBenchmarkSubAnnualRatio: Difference ($\lambda = 0$) or ratio ($\lambda \ne 0$) of the values of variables avgBenchmark and avgSubAnnual
- growthRateSubAnnual: Period to period difference ($\lambda = 0$) or relative difference ($\lambda \ne 0$) of the indicator series values (variable subAnnual)
- growthRateBenchmarked: Period to period difference ($\lambda = 0$) or relative difference ($\lambda \ne 0$) of the benchmarked series values (variable benchmarked)

Notes:

The output benchmarks data frame always contains the original benchmarks provided in the input benchmarks data frame. Modified nonbinding benchmarks, when applicable, can be recovered (calculated) from the output series data frame.
The function returns a NULL object if an error occurs before data processing could start. Otherwise, if execution gets far enough so that data processing could start, then an incomplete object would be returned in case of errors (e.g., output series data frame with NA values for the benchmarked data).
The function returns "data.frame" objects that can be explicitly coerced to other types of objects with the appropriate as*() function (e.g., tibble::as_tibble() would coerce any of them to a tibble).

Arguments

series_df

(mandatory)

Data frame (object of class "data.frame") that contains the indicator time series data to be benchmarked. In addition to the series data variable(s), specified with argument var, the data frame must also contain two numeric variables, year and period, identifying the periods of the indicator time series.

benchmarks_df

(mandatory)

Data frame (object of class "data.frame") that contains the benchmarks. In addition to the benchmarks data variable(s), specified with argument with, the data frame must also contain four numeric variables, startYear, startPeriod, endYear and endPeriod, identifying the indicator time series periods covered by each benchmark.

rho

(mandatory)

Real number in the $[0,1]$ interval that specifies the value of the autoregressive parameter $\rho$. See section Details for more information on the effect of parameter $\rho$.

lambda

(mandatory)

Real number, with suggested values in the $[-3,3]$ interval, that specifies the value of the adjustment model parameter $\lambda$. Typical values are lambda = 0.0 for an additive model and lambda = 1.0 for a proportional model.

biasOption

(mandatory)

Specification of the bias estimation option:

1: Do not estimate the bias. The bias used to correct the indicator series will be the value specified with argument bias.
2: Estimate the bias, display the result, but do not use it. The bias used to correct the indicator series will be the value specified with argument bias.
3: Estimate the bias, display the result and use the estimated bias to correct the indicator series. Any value specified with argument bias will be ignored.

Argument biasOption is ignored when rho = 1.0. See section Details for more information on the bias.

bias

(optional)

Real number, or NA, specifying the value of the user-defined bias to be used for the correction of the indicator series prior to benchmarking. The bias is added to the indicator series with an additive model (argument lambda = 0.0) while it is multiplied otherwise (argument lambda != 0.0). No bias correction is applied when bias = NA, which is equivalent to specifying bias = 0.0 when lambda = 0.0 and bias = 1.0 otherwise. Argument bias is ignored when biasOption = 3 or rho = 1.0. See section Details for more information on the bias.

Default value is bias = NA (no user-defined bias).

tolV, tolP

(optional)

Nonnegative real number, or NA, specifying the tolerance, in absolute value or percentage, to be used for the validation of the output binding benchmarks (alterability coefficient of $0.0$). This validation compares the input binding benchmark values with the equivalent values calculated from the benchmarked series (output) data. Arguments tolV and tolP cannot be both specified (one must be specified while the other must be NA).

Example: to set a tolerance of 10 units, specify tolV = 10, tolP = NA; to set a tolerance of 1%, specify tolV = NA, tolP = 0.01.

Default values are tolV = 0.001 and tolP = NA.

warnNegResult

(optional)

Logical argument specifying whether a warning message is generated when a negative value created by the function in the benchmarked (output) series is smaller than the threshold specified by argument tolN.

Default value is warnNegResult = TRUE.

tolN

(optional)

Negative real number specifying the threshold for the identification of negative values. A value is considered negative when it is smaller than this threshold.

Default value is tolN = -0.001.

var

(optional)

String vector (minimum length of 1) specifying the variable name(s) in the indicator series data frame (argument series_df) containing the values and (optionally) the user-defined alterability coefficients of the series to be benchmarked. These variables must be numeric.

The syntax is var = c("series1 </ alt_ser1>", "series2 </ alt_ser2>", ...). Default alterability coefficients of $1.0$ are used when a user-defined alterability coefficients variable is not specified alongside an indicator series variable. See section Details for more information on alterability coefficients.

Example: var = "value / alter" would benchmark indicator series data frame variable value with the alterability coefficients contained in variable alter while var = c("value / alter", "value2") would additionally benchmark variable value2 with default alterability coefficients of $1.0$.

Default value is var = "value" (benchmark variable value using default alterability coefficients of $1.0$).

with

(optional)

String vector (same length as argument var), or NULL, specifying the variable name(s) in the benchmarks data frame (argument benchmarks_df) containing the values and (optionally) the user-defined alterability coefficients of the benchmarks. These variables must be numeric. Specifying with = NULL results in using benchmark variable(s) with the same names(s) as those specified with argument var without user-defined benchmark alterability coefficients (i.e., default alterability coefficients of $0.0$ corresponding to binding benchmarks).

The syntax is with = NULL or with = c("bmk1 </ alt_bmk1>", "bmk2 </ alt_bmk2>", ...). Default alterability coefficients of $0.0$ (binding benchmarks) are used when a user-defined alterability coefficients variable is not specified alongside a benchmark variable. See section Details for more information on alterability coefficients.

Example: with = "val_bmk" would use benchmarks data frame variable val_bmk with default benchmark alterability coefficients of $0.0$ to benchmark the indicator series while with = c("val_bmk", "val_bmk2 / alt_bmk2") would additionally benchmark a second indicator series using benchmark variable val_bmk2 with the benchmark alterability coefficients contained in variable alt_bmk2.

Default value is with = NULL (same benchmark variable(s) as argument var using default benchmark alterability coefficients of $0.0$).

by

(optional)

String vector (minimum length of 1), or NULL, specifying the variable name(s) in the input data frames (arguments series_df and benchmarks_df) to be used to form groups (for BY-group processing) and allow the benchmarking of multiple series in a single function call. BY-group variables can be numeric or character (factors or not), must be present in both input data frames and will appear in all three output data frames (see section Value). BY-group processing is not implemented when by = NULL. See "Benchmarking Multiple Series" in section Details for more information.

Default value is by = NULL (no BY-group processing).

verbose

(optional)

Logical argument specifying whether information on intermediate steps with execution time (real time, not CPU time) should be displayed. Note that specifying argument quiet = TRUE would nullify argument verbose.

Default value is verbose = FALSE.

constant

(optional)

Real number that specifies a value to be temporarily added to both the indicator series and the benchmarks before solving proportional benchmarking problems (lambda != 0.0). The temporary constant is removed from the final output benchmarked series. E.g., specifying a (small) constant would allow proportional benchmarking with rho = 1 (e.g., proportional Denton benchmarking) on indicator series that include values of 0. Otherwise, proportional benchmarking with values of 0 in the indicator series is only possible when rho < 1. Specifying a constant with additive benchmarking (lambda = 0.0) has no impact on the resulting benchmarked data. The data variables in the graphTable output data frame include the constant, corresponding to the benchmarking problem that was actually solved.

Default value is constant = 0 (no temporary additive constant).

negInput_option

(optional)

Handling of negative values in the input data for proportional benchmarking (lambda != 0.0):

0: Do not allow negative values with proportional benchmarking. An error message is displayed in the presence of negative values in the input indicator series or benchmarks and missing (NA) values are returned for the benchmarked series. This corresponds to the G-Series 2.0 behaviour.
1: Allow negative values with proportional benchmarking but display a warning message.
2: Allow negative values with proportional benchmarking without displaying any message.

Default value is negInput_option = 0 (do not allow negative values with proportional benchmarking).

allCols

(optional)

Logical argument specifying whether all variables in the indicator series data frame (argument series_df), other than year and period, determine the set of series to benchmark. Values specified with arguments var and with are ignored when allCols = TRUE, which automatically implies default alterability coefficients, and variables with the same names as the indicator series must exist in the benchmarks data frame (argument benchmarks_df).

Default value is allCols = FALSE.

quiet

(optional)

Logical argument specifying whether or not to display only essential information such as warning messages, error messages and variable (series) or BY-group information when multiple series are benchmarked in a single call to the function. We advise against wrapping your benchmarking() call with suppressMessages() to further suppress the display of variable (series) or BY-group information when processing multiple series as this would make troubleshooting difficult in case of issues with individual series. Note that specifying quiet = TRUE would also nullify argument verbose.

Default value is quiet = FALSE.

Details

When $\rho < 1$, this function returns the generalized least squared solution of a special case of the general regression-based benchmarking model proposed by Dagum and Cholette (2006). The model, in matrix form, is: $$\displaystyle \begin{bmatrix} s^\dagger \\ a \end{bmatrix} = \begin{bmatrix} I \\ J \end{bmatrix} \theta + \begin{bmatrix} e \\ \varepsilon \end{bmatrix} $$ where

$a$ is the vector of length $M$ of the benchmarks.
$s^\dagger = \left\{ \begin{array}{cl} s + b & \text{if } \lambda = 0 \\ s \cdot b & \text{otherwise} \end{array} \right. $ is the vector of length $T$ of the bias corrected indicator series values, with $s$ denoting the initial (input) indicator series.
$b$ is the bias, which is specified with argument bias when argument bias_option != 3 or, when bias_option = 3, is estimated as $\hat{b} = \left\{ \begin{array}{cl} \frac{{1_M}^\mathrm{T} (a - Js)}{{1_M}^\mathrm{T} J 1_T} & \text{if } \lambda = 0 \\ \frac{{1_M}^\mathrm{T} a}{{1_M}^\mathrm{T} Js} & \text{otherwise} \end{array} \right. $, where $1_X = (1, ..., 1)^\mathrm{T}$ is a vector of $1$ of length $X$.
$J$ is the $M \times T$ matrix of temporal aggregation constraints with elements $j_{m, t} = \left\{ \begin{array}{cl} 1 & \text{if benchmark } m \text{ covers period } t \\ 0 & \text{otherwise} \end{array} \right. $.
$\theta$ is the vector of the final (benchmarked) series values.
$e \sim \left( 0, V_e \right)$ is the vector of the measurement errors of $s^\dagger$ with covariance matrix $V_e = C \Omega_e C$.
$C = \mathrm{diag} \left( \sqrt{c_{s^\dagger}} \left| s^\dagger \right|^\lambda \right)$ where $c_{s^\dagger}$ is the vector of the alterability coefficients of $s^\dagger$, assuming $0^0 = 1$.
$\Omega_e$ is a $T \times T$ matrix with elements $\omega_{e_{i,j}} = \rho^{|i-j|}$ representing the autocorrelation of an AR(1) process, again assuming $0^0 = 1$.
$\varepsilon \sim (0, V_\varepsilon)$ is the vector of the measurement errors of the benchmarks $a$ with covariance matrix $V_\varepsilon = \mathrm{diag} \left( c_a a \right)$ where $c_a$ is the vector of the alterability coefficients of the benchmarks $a$.

The generalized least squared solution is: $$\displaystyle \hat{\theta} = s^\dagger + V_e J^{\mathrm{T}} \left( J V_e J^{\mathrm{T}} + V_\varepsilon \right)^+ \left( a - J s^\dagger \right) $$ where $A^{+}$ designates the Moore-Penrose inverse of matrix $A$.

When $\rho = 1$, the function returns the solution of the (modified) Denton method: $$\displaystyle \hat{\theta} = s + W \left( a - J s \right) $$ where

$W$ is the upper-right corner matrix from the following matrix product $$ \left[\begin{array}{cc} D^{+} \Delta^{\mathrm{T}} \Delta D^{+} & J^{\mathrm{T}} \\ J & 0 \end{array} \right]^{+} \left[\begin{array}{cc} D^{+} \Delta^{\mathrm{T}} \Delta D^{+} & 0 \\ J & I_M \end{array} \right] = \left[\begin{array}{cc} I_T & W \\ 0 & W_\nu \end{array} \right] $$
$D = \mathrm{diag} \left( \left| s \right|^\lambda \right)$, assuming $0^0 = 1$. Note that $D$ corresponds to $C$ with $c_{s^\dagger} = 1.0$ and without bias correction (arguments bias_option = 1 and bias = NA).
$\Delta$ is a $T-1 \times T$ matrix with elements $\delta_{i,j} = \left\{ \begin{array}{cl} -1 & \text{if } i=j \\ 1 & \text{if } j=i+1 \\ 0 & \text{otherwise} \end{array} \right. $.
$W_\nu$ is a $M \times M$ matrix associated with the Lagrange multipliers of the corresponding minimization problem, expressed as: $$\displaystyle \begin{aligned} & \underset{\theta}{\text{minimize}} & & \sum_{t \ge 2} \left[ \frac{\left( s_t - \theta_t \right)}{\left| s_t\right|^\lambda} - \frac{\left( s_{t-1} - \theta_{t-1} \right)}{\left| s_{t-1}\right|^\lambda} \right]^2 \\ & \text{subject to} & & a = J \theta \end{aligned} $$

See Quenneville et al. (2006) and Dagum and Cholette (2006) for details.

Autoregressive Parameter $\rho$ and bias

Parameter $\rho$ (argument rho) is associated to the change between the (input) indicator and the (output) benchmarked series for two consecutive periods and is often called the movement preservation parameter. The larger the value of $\rho$, the more the indicator series period to period movements are preserved in the benchmarked series. With $\rho = 0$, period to period movement preservation is not enforced and the resulting benchmarking adjustments are not smooth, as in the case of prorating ($\rho = 0$ and $\lambda = 0.5$) where the adjustments take the shape of a step function. At the other end of the spectrum is $\rho = 1$, referred to as Denton benchmarking, where period to period movement preservation is maximized, which results in the smoothest possible set of benchmarking adjustments available with the function.

The bias represents the expected discrepancies between the benchmarks and the indicator series. It can be used to pre-adjust the indicator series in order to reduce, on average, the discrepancies between the two sources of data. Bias correction, which is specified with arguments biasOption and bias, can be particularly useful for periods not covered by benchmarks when $\rho < 1$. In this context, parameter $\rho$ dictates the speed at which the projected benchmarking adjustments converge to the bias (or converge to no adjustment without bias correction) for periods not covered by a benchmark. The smaller the value of $\rho$, the faster the convergence to the bias, with immediate convergence when $\rho = 0$ and no convergence at all (the adjustment of the last period covered by a benchmark is repeated) when $\rho = 1$ (Denton benchmarking). Arguments biasOption and bias are actually ignored when $\rho = 1$ since correcting for the bias has no impact on Denton benchmarking solutions. The suggested value for $\rho$ is $0.9$ for monthly indicators and $0.9^3 = 0.729$ for quarterly indicators, representing a reasonable compromise between maximizing movement preservation and reducing revisions as new benchmarks become available in the future (benchmarking timeliness issue). In practice, note that Denton benchmarking could be approximated with the regression-based model by using a $\rho$ value that is smaller than, but very close to, $1.0$ (e.g., $\rho = 0.999$). See Dagum and Cholette (2006) for a complete discussion on this topic.

Alterability Coefficients

Alterability coefficients $c_{s^\dagger}$ and $c_a$ conceptually represent the measurement errors associated with the (bias corrected) indicator time series values $s^\dagger$ and benchmarks $a$ respectively. They are nonnegative real numbers which, in practice, specify the extent to which an initial value can be modified in relation to other values. Alterability coefficients of $0.0$ define fixed (binding) values while alterability coefficients greater than $0.0$ define free (nonbinding) values. Increasing the alterability coefficient of an intial value results in more changes for that value in the benchmarking solution and, conversely, less changes when decreasing the alterability coefficient. The default alterability coefficients are $0.0$ for the benchmarks (binding benchmarks) and $1.0$ for the indicator series values (nonbinding indicator series). Important notes:

With a value of $\rho = 1$ (argument rho = 1, associated to Denton Benchmarking), only the default alterability coefficients ($0.0$ for a benchmark and $1.0$ for a an indicator series value) are valid. The specification of user-defined alterability coefficients variables is therefore not allowed. If such variables are specified (see arguments var and with), the function ignores them and displays a warning message in the console.
Alterability coefficients $c_{s^\dagger}$ come into play after the indicator series has been corrected for the bias, when applicable ($c_{s^\dagger}$ is associated to $s^\dagger$, not $s$). This means that specifying an alterability coefficient of $0.0$ for a given indicator series value will not result in an unchanged value after benchmarking with bias correction (see arguments biasOption and bias).

Nonbinding benchmarks, when applicable, can be recovered (calculated) from the benchmarked series (see output data frame series in section Value). The output benchmarks data frame always contains the original benchmarks provided in the input benchmarks data frame (argument benchmarks_df).

Benchmarking Multiple Series

Multiple series can be benchmarked in a single benchmarking() call, by specifying allCols = TRUE, by (manually) specifying multiple variables with argument var (and argument with) or with BY-group processing (argument by != NULL). An important distinction is that all indicator series specified with allCols = TRUE or with argument var (and benchmarks with argument with) are expected to be of the same length, i.e., same set of periods and same set (number) of benchmarks. Benchmarking series of different lengths (different sets of periods) or with different sets (number) of benchmarks must be done with BY-group processing on stacked indicator series and benchmarks input data frames (see utility functions stack_tsDF() and stack_bmkDF()). Arguments by and var can be combined in order to implement BY-group processing for multiple series as illustrated by Example 2 in the Examples section. While multiple variables with argument var (or allCols = TRUE) without BY-group processing (argument by = NULL) is slightly more efficient (faster), a BY-group approach with a single series variable is usually recommended as it is more general (works in all contexts). The latter is illustrated by Example 3 in the Examples section. The BY variables specified with argument by appear in all three output data frames.

Arguments `constant` and `negInput_option`

These arguments extend the usage of proportional benchmarking to a larger set of problems. Their default values correspond to the G-Series 2.0 behaviour (SAS$^\circledR$ PROC BENCHMARKING) for which equivalent options are not defined. Although proportional benchmarking may not necessarily be the most appropriate approach (additive benchmarking may be more appropriate) when the values of the indicator series approach 0 (unstable period-to-period ratios) or "cross the 0 line" and can therefore go from positive to negative and vice versa (confusing, difficult to interpret period-to-period ratios), these cases are not invalid mathematically speaking (i.e., the associated proportional benchmarking problem can be solved). It is strongly recommended, however, to carefully analyze and validate the resulting benchmarked data in these situations and make sure they correspond to reasonable, interpretable solutions.

Treatment of Missing (`NA`) Values

If a missing value appears in one of the variables of the benchmarks input data frame (other than the BY variables), the observations with the missing values are dropped, a warning message is displayed and the function executes.
If a missing value appears in the year and/or period variables of the indicator series input data frame and BY variables are specified, the corresponding BY-group is skipped, a warning message is displayed and the function moves on to the next BY-group. If no BY variables are specified, a warning message is displayed and no processing is done.
If a missing value appears in one of the indicator series variables in the indicator series input data frame and BY variables are specified, the corresponding BY-group is skipped, a warning message is displayed and the function moves on to the next BY-group. If no BY variables are specified, the affected indicator series is not processed, a warning message is displayed and the function moves on to the next indicator series (when applicable).

References

Dagum, E. B. and P. Cholette (2006). Benchmarking, Temporal Distribution and Reconciliation Methods of Time Series. Springer-Verlag, New York, Lecture Notes in Statistics, Vol. 186

Fortier, S. and B. Quenneville (2007). "Theory and Application of Benchmarking in Business Surveys". Proceedings of the Third International Conference on Establishment Surveys (ICES-III). Montréal, June 2007.

Latendresse, E., M. Djona and S. Fortier (2007). "Benchmarking Sub-Annual Series to Annual Totals – From Concepts to SAS$^\circledR$ Procedure and Enterprise Guide$^\circledR$ Custom Task". Proceedings of the SAS$^\circledR$ Global Forum 2007 Conference. Cary, NC: SAS Institute Inc.

Quenneville, B., S. Fortier, Z.-G. Chen and E. Latendresse (2006). "Recent Developments in Benchmarking to Annual Totals in X-12-ARIMA and at Statistics Canada". Proceedings of the Eurostat Conference on Seasonality, Seasonal Adjustment and Their Implications for Short-Term Analysis and Forecasting. Luxembourg, May 2006.

Quenneville, B., P. Cholette, S. Fortier and J. Bérubé (2010). "Benchmarking Sub-Annual Indicator Series to Annual Control Totals (Forillon v1.04.001)". Internal document. Statistics Canada, Ottawa, Canada.

Quenneville, B. and S. Fortier (2012). "Restoring Accounting Constraints in Time Series – Methods and Software for a Statistical Agency". Economic Time Series: Modeling and Seasonality. Chapman & Hall, New York.

Statistics Canada (2012). Theory and Application of Benchmarking (Course code 0436). Statistics Canada, Ottawa, Canada.

Statistics Canada (2016). "The BENCHMARKING Procedure". G-Series 2.0 User Guide. Statistics Canada, Ottawa, Canada.

Examples

Run this code

# Set the working directory (for the PDF files)
iniwd <- getwd() 
setwd(tempdir())


###########
# Example 1: Simple case with a single quarterly series to benchmark to annual values

# Quarterly indicator series
my_series1 <- ts_to_tsDF(ts(c(1.9, 2.4, 3.1, 2.2, 2.0, 2.6, 3.4, 2.4, 2.3),
                            start = c(2015, 1),
                            frequency = 4))
my_series1

# Annual benchmarks for quarterly data
my_benchmarks1 <- ts_to_bmkDF(ts(c(10.3, 10.2),
                                 start = 2015,
                                 frequency = 1),
                              ind_frequency = 4)
my_benchmarks1

# Benchmarking using...
#   - recommended `rho` value for quarterly series (`rho = 0.729`)
#   - proportional model (`lambda = 1`)
#   - bias-corrected indicator series with the estimated bias (`biasOption = 3`)
out_bench1 <- benchmarking(my_series1,
                           my_benchmarks1,
                           rho = 0.729,
                           lambda = 0,
                           biasOption = 3)

# Generate the benchmarking graphs
plot_graphTable(out_bench1$graphTable, "Ex1_graphs.pdf")


###########
# Example 2: Two quarterly series to benchmark to annual values,
#            with BY-groups and user-defined alterability coefficients

# Sales data (same sales for groups A and B; only alter coefs for van sales differ)
qtr_sales <- ts(matrix(c(# Car sales
                         1851, 2436, 3115, 2205, 1987, 2635, 3435, 2361, 2183, 2822,
                         3664, 2550, 2342, 3001, 3779, 2538, 2363, 3090, 3807, 2631,
                         2601, 3063, 3961, 2774, 2476, 3083, 3864, 2773, 2489, 3082,
                         # Van sales
                         1900, 2200, 3000, 2000, 1900, 2500, 3800, 2500, 2100, 3100,
                         3650, 2950, 3300, 4000, 3290, 2600, 2010, 3600, 3500, 2100,
                         2050, 3500, 4290, 2800, 2770, 3080, 3100, 2800, 3100, 2860),
                       ncol = 2),
                start = c(2011, 1),
                frequency = 4,
                names = c("car_sales", "van_sales"))

ann_sales <- ts(matrix(c(# Car sales
                         10324, 10200, 10582, 11097, 11582, 11092,
                         # Van sales
                         12000, 10400, 11550, 11400, 14500, 16000),
                       ncol = 2),
                start = 2011,
                frequency = 1,
                names = c("car_sales", "van_sales"))

# Quarterly indicator series (with default alter coefs for now)
my_series2 <- rbind(cbind(data.frame(group = rep("A", nrow(qtr_sales)),
                                     alt_van = rep(1, nrow(qtr_sales))),
                          ts_to_tsDF(qtr_sales)),
                    cbind(data.frame(group = rep("B", nrow(qtr_sales)),
                                     alt_van = rep(1, nrow(qtr_sales))),
                          ts_to_tsDF(qtr_sales)))

# Set binding van sales (alter coef = 0) for 2012 Q1 and Q2 in group A (rows 5 and 6)
my_series2$alt_van[c(5,6)] <- 0
head(my_series2, n = 10)
tail(my_series2)


# Annual benchmarks for quarterly data (without alter coefs)
my_benchmarks2 <- rbind(cbind(data.frame(group = rep("A", nrow(ann_sales))),
                              ts_to_bmkDF(ann_sales, ind_frequency = 4)),
                        cbind(data.frame(group = rep("B", nrow(ann_sales))),
                              ts_to_bmkDF(ann_sales, ind_frequency = 4)))
my_benchmarks2

# Benchmarking using...
#   - recommended `rho` value for quarterly series (`rho = 0.729`)
#   - proportional model (`lambda = 1`)
#   - without bias correction (`biasOption = 1` and `bias` not specified)
#   - `quiet = TRUE` to avoid generating the function header
out_bench2 <- benchmarking(my_series2,
                           my_benchmarks2,
                           rho = 0.729,
                           lambda = 1,
                           biasOption = 1,
                           var = c("car_sales", "van_sales / alt_van"),
                           with = c("car_sales", "van_sales"),
                           by = "group",
                           quiet = TRUE)

# Generate the benchmarking graphs
plot_graphTable(out_bench2$graphTable, "Ex2_graphs.pdf")

# Check the value of van sales for 2012 Q1 and Q2 in group A (fixed values)
all.equal(my_series2$van_sales[c(5,6)], out_bench2$series$van_sales[c(5,6)])


###########
# Example 3: same as example 2, but benchmarking all 4 series as BY-groups
#            (4 BY-groups of 1 series instead of 2 BY-groups of 2 series)

qtr_sales2 <- ts.union(A = qtr_sales, B = qtr_sales)
my_series3 <- stack_tsDF(ts_to_tsDF(qtr_sales2))
my_series3$alter <- 1
my_series3$alter[my_series3$series == "A.van_sales"
                & my_series3$year == 2012 & my_series3$period <= 2] <- 0
head(my_series3)
tail(my_series3)


ann_sales2 <- ts.union(A = ann_sales, B = ann_sales)
my_benchmarks3 <- stack_bmkDF(ts_to_bmkDF(ann_sales2, ind_frequency = 4))
head(my_benchmarks3)
tail(my_benchmarks3)

out_bench3 <- benchmarking(my_series3,
                           my_benchmarks3,
                           rho = 0.729,
                           lambda = 1,
                           biasOption = 1,
                           var = "value / alter",
                           with = "value",
                           by = "series",
                           quiet = TRUE)

# Generate the benchmarking graphs
plot_graphTable(out_bench3$graphTable, "Ex3_graphs.pdf")

# Convert data frame `out_bench3$series` to a "mts" object
qtr_sales2_bmked <- tsDF_to_ts(unstack_tsDF(out_bench3$series), frequency = 4)

# Print the first 10 observations
ts(qtr_sales2_bmked[1:10, ], start = start(qtr_sales2), deltat = deltat(qtr_sales2))

# Check the value of van sales for 2012 Q1 and Q2 in group A (fixed values)
all.equal(window(qtr_sales2[, "A.van_sales"], start = c(2012, 1), end = c(2012, 2)),
          window(qtr_sales2_bmked[, "A.van_sales"], start = c(2012, 1), end = c(2012, 2)))


# Reset the working directory to its initial location
setwd(iniwd)

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benchmarking: Restore temporal constraints

Description

Usage

Value

Arguments

Details

Autoregressive Parameter \(\rho\) and bias

Alterability Coefficients

Benchmarking Multiple Series

Arguments `constant` and `negInput_option`

Treatment of Missing (`NA`) Values

References

See Also

Examples

Description

Usage

Value

Arguments

Details

Autoregressive Parameter \(\rho\) and bias

Alterability Coefficients

Benchmarking Multiple Series

Arguments constant and negInput_option

Treatment of Missing (NA) Values

References

See Also

Examples

Arguments `constant` and `negInput_option`

Treatment of Missing (`NA`) Values