Cholette method is based on a benchmarking methodology developed at Statistics Canada. It is a generalized model relying on the principle of movement preservation that encompasses several other benchmarking methods. The Denton method (both the AFD and PFD variants), as well as the naive pro-rating method, emerge as particular cases of the Cholette method. This method has been widely used for the purpose of benchmarking seasonally adjusted series among others.
Arguments
- s
Preliminary series. Mandatory. 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.
- 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 = 1 for proportional benchmarking; lambda = 0 for additive benchmarking; and lambda = 0.5 with rho = 0 for the naive pro-rating method. See vignette for more information on the choice of the lambda parameter.
- bias
Character. Bias correction factor. No systematic bias is considered by default. See vignette for more details.
- conversion
Conversion rule. Usually "Sum" or "Average". Sum by default.
- obsposition
Position of the observation in the aggregated period (only used with "UserDefined" conversion).
Examples
ym_true <- rjd3toolkit::Retail$RetailSalesTotal
yq_true <- rjd3toolkit::aggregate(ym_true, 4)
Y_full <- rjd3toolkit::aggregate(ym_true, 1)
Y <- window(Y_full, end = c(2009,1)) # say no benchmark yet for the year 2010
xm <- ym_true + rnorm(n = length(ym_true), mean = -5000, sd = 10000)
xq <- rjd3toolkit::aggregate(xm, 4)
# Proportional benchmarking with a bias and some recommended value of rho for
# monthly and quarterly series respectively (see vignette)
cholette(s = xm, t = Y, rho = 0.9, lambda = 1, bias = "Multiplicative")
#> Jan Feb Mar Apr May Jun Jul Aug
#> 1992 117913.3 136339.9 120087.5 151122.0 163599.9 168712.9 137979.0 154591.6
#> 1993 161350.8 119378.4 160992.6 141634.0 160472.7 164390.9 171957.7 155879.7
#> 1994 163950.1 144410.1 163585.0 169913.9 166349.7 162235.5 181679.1 183271.3
#> 1995 136812.5 150573.0 177569.7 186297.0 190104.0 184270.6 181432.5 190137.8
#> 1996 167640.6 153737.3 200606.4 189471.8 204302.3 197601.7 198216.8 211157.0
#> 1997 194276.6 173744.8 218786.0 199971.6 203019.6 198657.7 223013.8 216022.9
#> 1998 198074.5 182062.4 215999.1 211376.8 220235.4 212287.9 211543.4 207677.8
#> 1999 185370.7 205264.8 199583.3 221773.4 238867.7 230763.5 239795.5 250585.4
#> 2000 212433.8 240449.8 272546.6 240901.3 259518.5 252860.1 238884.1 254988.0
#> 2001 230405.0 234372.3 251541.7 234191.0 270508.5 254501.9 255415.7 285868.8
#> 2002 247395.1 228876.9 267259.5 257670.7 269046.7 257114.7 269703.6 272333.1
#> 2003 242010.5 219465.0 255193.2 271328.5 274081.6 269566.5 289957.4 287451.4
#> 2004 261667.0 265476.1 275068.8 287596.9 279045.9 302979.1 297159.1 293517.5
#> 2005 264468.0 263062.5 317456.8 313734.0 295830.4 331459.3 318161.5 328601.4
#> 2006 283835.9 287385.2 324715.8 305439.8 348565.7 338250.6 330860.5 346498.7
#> 2007 281249.3 275077.1 315681.8 333700.5 355223.4 354582.0 328547.1 371020.7
#> 2008 295106.2 298179.9 347920.9 328391.9 357521.5 347918.5 353987.2 346567.4
#> 2009 251067.5 267951.7 283160.8 290500.2 292491.9 340384.5 304301.6 318993.6
#> 2010 292549.5 287222.0 315401.6 336131.6 331003.3 327950.8 331009.1 333161.8
#> Sep Oct Nov Dec
#> 1992 149966.1 157743.1 153320.6 204340.0
#> 1993 165074.2 168519.0 157206.8 215391.0
#> 1994 176390.1 194010.2 184318.1 219907.9
#> 1995 186259.0 211681.0 193408.4 233958.3
#> 1996 167006.1 231364.6 202021.9 243538.5
#> 1997 208134.4 193828.1 192563.7 251983.8
#> 1998 219903.9 225355.2 218820.1 263768.4
#> 1999 241216.7 233455.1 247500.0 314380.0
#> 2000 230210.4 242400.4 250348.7 293214.2
#> 2001 237774.0 245538.0 261348.7 306259.4
#> 2002 238321.6 259708.9 250258.6 316632.5
#> 2003 264596.9 266179.2 291912.9 336410.9
#> 2004 269827.8 280681.5 304493.4 362916.9
#> 2005 285634.1 297340.4 302999.1 377943.4
#> 2006 302570.3 296564.0 316379.5 399070.1
#> 2007 323827.2 338444.8 348977.0 379467.1
#> 2008 307577.7 324679.3 298888.8 346193.5
#> 2009 303220.3 295028.3 317403.8 373966.8
#> 2010 305823.3 336810.7 341256.9 393591.2
cholette(s = xq, t = Y, rho = 0.729, lambda = 1, bias = "Multiplicative")
#> Qtr1 Qtr2 Qtr3 Qtr4
#> 1992 374268.3 483380.9 442461.7 515605.1
#> 1993 441437.9 466461.8 492965.7 541382.7
#> 1994 471955.4 498515.2 541347.5 598202.8
#> 1995 464948.9 560640.7 557814.6 639099.8
#> 1996 522116.3 591544.1 576445.6 676559.0
#> 1997 586664.0 601298.9 646980.7 639059.4
#> 1998 595756.3 643962.7 639419.0 707967.0
#> 1999 590843.2 691663.9 731480.0 794569.0
#> 2000 725293.9 753116.4 723980.5 786365.2
#> 2001 715929.0 759154.1 779173.5 813468.4
#> 2002 743823.0 784032.0 780372.7 826094.3
#> 2003 716631.5 814762.0 841860.1 894900.5
#> 2004 802118.3 869864.7 860761.4 947685.6
#> 2005 845174.0 940853.2 932117.9 978545.9
#> 2006 895589.6 992310.3 980091.5 1012144.6
#> 2007 872143.5 1043408.7 1023276.8 1066969.0
#> 2008 941231.0 1033998.2 1008298.4 969405.5
#> 2009 802423.8 923341.8 926367.8 986337.6
#> 2010 894520.6 994524.3 969583.0 1071368.1
# Proportional benchmarking with no bias
xm_no_bias <- ym_true + rnorm(n = length(ym_true), mean = 0, sd = 10000)
cholette(s = xm_no_bias, t = Y, rho = 0.9, lambda = 1)
#> Jan Feb Mar Apr May Jun Jul Aug
#> 1992 141379.4 119261.9 149114.4 138125.8 164717.7 140281.9 157659.3 149982.5
#> 1993 128835.7 147845.7 163487.3 169527.6 147922.4 174818.3 162655.7 161225.6
#> 1994 133137.1 139120.5 189096.6 163813.6 180340.7 175955.3 169636.8 200226.7
#> 1995 151884.1 136824.5 204682.9 170085.6 192580.3 197131.7 186132.9 173705.2
#> 1996 187611.3 179029.5 196561.1 185470.7 211552.2 183590.0 198114.7 202624.0
#> 1997 191959.2 172143.4 199567.9 195006.4 199723.0 208813.4 223558.4 195871.0
#> 1998 183221.9 172409.5 217654.1 222868.8 221906.5 215655.7 222583.2 234997.3
#> 1999 201794.5 180889.6 233716.7 227130.2 248762.8 233746.6 225779.7 241524.9
#> 2000 231858.0 209157.3 253448.3 248416.9 256317.4 256742.5 250341.1 233662.4
#> 2001 214645.2 212644.3 255221.9 258812.9 268215.6 283567.0 252731.7 254860.0
#> 2002 228541.4 234246.3 248563.3 252273.8 272565.9 273034.5 276364.5 287702.4
#> 2003 235607.9 241273.7 269974.5 281700.5 278614.7 279633.3 261242.1 276216.8
#> 2004 244014.0 244936.8 285880.7 297298.1 301798.5 286323.4 294763.3 307396.3
#> 2005 265833.5 263493.0 303528.6 307906.7 300803.4 316692.4 308712.4 326504.9
#> 2006 271089.6 292770.6 323351.2 312488.9 354930.9 322969.9 317160.0 350549.4
#> 2007 291170.7 275838.7 338247.3 317771.5 349123.4 336085.7 349781.0 358434.2
#> 2008 316896.8 310102.9 346106.8 325317.9 332582.7 351907.9 342322.2 328624.9
#> 2009 285290.1 281781.4 288592.5 293198.0 302262.8 308005.3 316783.8 303521.1
#> 2010 290718.8 279089.8 315896.8 314753.2 348313.5 330963.8 347252.8 334553.7
#> Sep Oct Nov Dec
#> 1992 143125.1 166180.5 169147.3 176740.1
#> 1993 161833.4 163576.8 160377.5 200142.0
#> 1994 179721.6 167409.4 187742.6 223820.3
#> 1995 183088.4 186551.0 193950.8 245886.7
#> 1996 188574.7 208392.1 190086.7 235057.9
#> 1997 186523.1 218124.6 213077.5 269635.2
#> 1998 226523.0 203638.3 212633.8 253013.0
#> 1999 235970.6 235077.9 253486.1 290676.5
#> 2000 251720.3 240203.3 252328.0 304560.5
#> 2001 226611.5 284006.8 262088.7 294319.4
#> 2002 238245.8 273426.0 253859.9 295498.0
#> 2003 275973.0 272023.5 274462.7 321431.5
#> 2004 286920.2 284222.3 293003.5 353872.8
#> 2005 314904.4 291839.8 308678.2 387793.8
#> 2006 297132.1 302648.7 331249.7 403795.1
#> 2007 325098.9 316417.4 354110.0 393719.3
#> 2008 319291.3 325779.3 309407.7 344592.7
#> 2009 280052.5 314201.3 297906.2 366875.8
#> 2010 305930.4 307278.8 335709.7 375194.5
# Additive benchmarking
cholette(s = xm, t = Y, rho = 0.9, lambda = 0, bias = "Additive")
#> Jan Feb Mar Apr May Jun Jul Aug
#> 1992 130292.9 144477.8 126272.5 153138.9 162857.7 166042.6 135929.2 150697.5
#> 1993 158362.9 119356.6 159705.6 141862.3 160410.6 164610.7 172235.5 157007.8
#> 1994 164660.2 145453.5 163989.1 170054.2 166483.1 162389.3 181387.0 182931.9
#> 1995 137524.1 151085.7 177620.1 186225.1 189998.0 184314.8 181565.4 190122.9
#> 1996 168205.9 154646.5 200464.4 189616.7 204109.4 197605.9 198239.7 210855.2
#> 1997 194798.6 175110.5 218409.5 200327.8 203225.8 198980.1 222370.8 215592.6
#> 1998 197666.1 181639.9 215608.0 211061.5 220114.8 212167.3 211496.9 207649.2
#> 1999 185467.0 205526.8 199887.8 222069.1 239058.2 231005.4 239929.7 250542.0
#> 2000 213614.2 240762.1 271683.2 241237.7 259125.4 252733.8 239317.5 254769.2
#> 2001 230790.2 234612.6 251415.2 234392.4 270176.9 254438.4 255375.2 285598.1
#> 2002 247419.1 228942.7 267206.5 257652.5 269000.6 257124.2 269674.1 272299.9
#> 2003 242547.4 220459.0 255600.8 271419.7 274097.1 269655.8 289584.2 287113.5
#> 2004 261687.0 265453.9 274983.7 287462.1 279053.2 302877.0 297169.7 293618.7
#> 2005 265453.0 264176.9 317323.5 313651.1 296196.2 330822.1 317868.4 328012.9
#> 2006 284180.9 287645.4 324519.5 305506.3 348326.7 338160.6 330851.0 346447.0
#> 2007 281162.1 274946.3 315449.7 333436.0 354948.3 354358.2 328431.6 370953.5
#> 2008 295932.0 299158.7 349037.8 329468.6 358490.0 348650.4 354357.7 346497.0
#> 2009 248911.5 265055.4 279766.4 287062.8 289461.6 336634.2 302827.5 318526.1
#> 2010 306577.4 304693.3 335031.5 357887.0 355332.6 354549.1 359503.1 363380.5
#> Sep Oct Nov Dec
#> 1992 145862.2 153056.3 149128.0 197960.2
#> 1993 166026.8 169425.5 158447.0 214796.7
#> 1994 176186.0 193487.1 184014.3 218985.3
#> 1995 186346.7 211257.2 193381.8 233062.2
#> 1996 168038.7 230497.8 202123.0 242261.7
#> 1997 207909.2 193914.6 192526.9 250836.5
#> 1998 220159.2 225757.7 219160.4 264623.9
#> 1999 241326.4 233753.0 247498.1 312492.6
#> 2000 230926.3 242608.2 250231.4 291747.0
#> 2001 237899.6 245608.8 261342.0 306075.7
#> 2002 238538.2 259813.6 250511.1 316139.4
#> 2003 264716.8 266233.2 291464.4 335262.1
#> 2004 270218.7 281056.9 304654.5 362194.6
#> 2005 286188.7 297554.2 303038.6 376405.5
#> 2006 302649.0 296620.8 316360.0 398868.8
#> 2007 323927.3 338682.6 349393.2 380109.2
#> 2008 307189.5 323564.5 297369.7 343216.9
#> 2009 305156.3 299509.7 323828.3 381731.2
#> 2010 338277.1 369987.1 375633.1 428002.8
# Denton PFD
cholette(s = xm, t = Y, rho = 1, lambda = 1)
#> Jan Feb Mar Apr May Jun Jul Aug
#> 1992 119207.4 137418.8 120713.4 151537.7 163708.8 168544.6 137671.5 154097.2
#> 1993 160972.1 119210.8 160879.7 141609.3 160502.5 164459.9 172053.0 155976.3
#> 1994 164036.2 144480.9 163651.1 169962.7 166375.7 162239.2 181660.1 183232.8
#> 1995 136783.3 150552.7 177558.3 186296.4 190112.9 184286.1 181451.8 190158.7
#> 1996 167598.2 153685.7 200530.1 189402.5 204239.6 197561.3 198202.2 211172.4
#> 1997 194382.3 173838.7 218890.9 200050.4 203073.1 198676.6 222990.6 215960.5
#> 1998 198103.4 182134.1 216109.2 211480.8 220322.3 212338.9 211558.4 207658.3
#> 1999 185176.7 205029.8 199369.2 221580.8 238730.0 230708.6 239823.1 250697.0
#> 2000 212549.2 240521.8 272579.9 240906.1 259502.5 252831.1 238848.0 254941.2
#> 2001 230492.7 234499.7 251686.2 234309.0 270608.1 254549.2 255412.2 285809.3
#> 2002 247256.8 228763.8 267153.2 257595.7 269001.1 257103.7 269727.6 272390.6
#> 2003 242071.2 219501.1 255222.0 271350.7 274097.6 269575.4 289957.2 287439.3
#> 2004 261640.8 265455.4 275048.4 287575.4 279026.4 302964.0 297153.3 293523.7
#> 2005 264459.0 263038.2 317422.1 313705.2 295812.6 331448.3 318159.4 328605.9
#> 2006 283936.4 287506.7 324849.8 305542.6 348644.9 338280.6 330841.6 346432.4
#> 2007 281158.1 275006.3 315628.3 333672.6 355220.3 354597.5 328571.9 371059.3
#> 2008 295143.1 298222.1 347984.2 328462.4 357610.0 348007.1 354068.9 346621.6
#> 2009 250681.9 267442.4 282582.0 289923.2 291980.4 339923.6 304066.7 318977.2
#> 2010 294210.6 289238.9 317998.8 339267.2 334417.6 331625.3 334983.4 337402.8
#> Sep Oct Nov Dec
#> 1992 149393.7 157095.7 152706.6 203620.6
#> 1993 165176.6 168617.9 157292.0 215497.8
#> 1994 176339.3 193945.6 184255.9 219841.6
#> 1995 186276.2 211691.8 193405.0 233930.7
#> 1996 167044.4 231446.1 202115.7 243666.9
#> 1997 208043.3 193727.3 192467.1 251902.0
#> 1998 219851.8 225269.6 218701.8 263576.4
#> 1999 241389.6 233664.7 247737.0 314649.6
#> 2000 230167.3 242358.3 250321.9 293228.7
#> 2001 237682.0 245410.3 261193.0 306073.4
#> 2002 238395.4 259810.4 250365.0 316758.6
#> 2003 264573.8 266144.1 291865.2 336356.4
#> 2004 269845.5 280712.0 304532.8 362952.3
#> 2005 285644.5 297357.4 303028.2 378010.2
#> 2006 302476.9 296450.7 316252.2 398921.4
#> 2007 323862.0 338484.1 349020.4 379517.1
#> 2008 307582.7 324617.8 298740.0 345873.0
#> 2009 303467.3 295561.7 318331.4 375533.3
#> 2010 309915.4 341515.2 346203.9 399484.4
# Pro-rating
cholette(s = xm, t = Y, rho = 0, lambda = 0.5)
#> Jan Feb Mar Apr May Jun Jul Aug
#> 1992 118765.9 136926.5 120312.8 151093.3 163317.5 168261.6 137562.4 154133.9
#> 1993 159233.3 118145.9 159743.3 140873.7 159968.7 164220.1 172123.3 156330.8
#> 1994 162951.3 143766.8 163093.9 169619.3 166243.3 162282.9 181874.3 183583.4
#> 1995 136983.3 150741.2 177741.6 186445.6 190219.0 184341.9 181458.3 190112.7
#> 1996 168565.0 154498.2 201468.6 190143.3 204850.0 197937.2 198332.9 211016.1
#> 1997 193432.4 172724.0 217287.2 198555.2 201667.1 197551.9 222166.6 215759.5
#> 1998 194488.8 179887.9 214581.6 210927.4 220546.0 213139.4 212756.3 209046.4
#> 1999 189002.7 208514.5 202036.2 223753.0 240227.9 231353.0 239668.9 249685.8
#> 2000 213461.4 240897.1 272416.2 240393.8 258699.0 251953.6 238067.6 254299.5
#> 2001 227082.7 231839.3 249643.1 233105.4 269961.8 254570.4 255997.2 287017.7
#> 2002 247994.9 229504.1 268029.1 258388.4 269711.7 257608.1 270010.8 272362.1
#> 2003 243037.2 219941.8 255312.3 271100.3 273603.7 268960.1 289269.5 286852.8
#> 2004 260901.9 265246.3 275275.8 288150.6 279781.7 303860.7 297961.2 294108.8
#> 2005 265941.7 263803.4 317633.1 313378.2 295154.4 330481.4 317185.2 327724.5
#> 2006 280817.5 285152.7 323026.8 304536.8 348220.8 338475.1 331532.2 347584.1
#> 2007 281057.0 274873.5 315451.9 333478.7 355026.3 354437.9 328475.5 371029.5
#> 2008 296531.2 299692.3 349675.9 329923.5 358937.3 348920.1 354492.5 346423.2
#> 2009 253809.7 269951.5 284432.9 291080.1 292478.2 339818.8 303455.3 317880.6
#> 2010 283582.1 278790.1 306511.0 327011.1 322336.6 319645.3 322882.0 325214.0
#> Sep Oct Nov Dec
#> 1992 149607.4 157532.6 153363.2 204839.0
#> 1993 165859.8 169629.3 158528.0 217591.8
#> 1994 176774.8 194499.0 184817.4 220514.6
#> 1995 186177.1 211515.3 193182.7 233585.2
#> 1996 166659.3 230520.8 200929.6 241744.1
#> 1997 208589.0 195075.0 194784.7 256410.4
#> 1998 221357.0 226643.0 219668.0 264063.4
#> 1999 239608.4 231169.2 244284.0 309252.3
#> 2000 229895.7 242526.0 251106.5 295039.5
#> 2001 239074.6 247185.4 263371.2 308876.3
#> 2002 238037.5 259002.9 249127.9 314544.5
#> 2003 264232.0 266102.4 292265.1 337476.8
#> 2004 270059.4 280475.9 303643.4 360964.3
#> 2005 285141.9 297249.9 303493.8 379503.4
#> 2006 303768.4 297920.9 317959.0 401141.5
#> 2007 323925.6 338663.1 349341.5 380037.5
#> 2008 306761.1 322976.0 296426.8 342173.1
#> 2009 302077.6 293950.7 316402.1 373133.5
#> 2010 298719.7 329177.9 333697.2 385053.0