Cholette method is based on a benchmarking methodology developed at Statistics Canada. It is a generalized method relying on the principle of movement preservation that encompasses 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 129476.7 136648.0 153798.2 128168.5 149945.8 149472.7 149966.0 147154.3
#> 1993 118020.0 129407.5 153633.1 165769.0 155842.0 169681.3 170375.9 152449.4
#> 1994 146559.3 139242.4 160567.4 183125.2 180109.3 183750.0 192356.8 185963.3
#> 1995 168026.2 154400.0 174018.3 174208.7 185658.3 193739.9 208033.8 191101.5
#> 1996 162077.2 169321.0 189949.7 190290.1 209911.8 172315.0 223221.7 199740.3
#> 1997 178407.9 166368.5 194661.6 211168.9 214353.3 211887.5 192828.3 198328.2
#> 1998 192373.0 188988.4 205934.8 212688.5 218588.5 238188.1 228130.9 220973.0
#> 1999 189464.9 197564.3 219738.3 224492.1 241137.5 240667.3 230517.9 239912.6
#> 2000 211721.8 226155.6 251018.2 233883.7 256733.7 244434.3 244521.9 259355.6
#> 2001 212618.4 225048.9 246313.9 250789.0 285228.4 259372.2 229365.1 263538.2
#> 2002 233256.4 228672.4 258283.0 265195.1 271823.2 258052.0 272455.7 270059.7
#> 2003 247050.8 223976.0 260606.8 273415.2 280184.6 267081.4 268199.8 301069.9
#> 2004 255135.4 235891.2 301436.7 286960.0 296236.9 277132.2 288578.9 304494.1
#> 2005 272752.9 247398.5 318870.3 301975.6 317625.4 303019.7 312937.7 314184.6
#> 2006 279289.3 298280.5 339735.9 327479.6 351140.4 328406.1 314512.0 337114.9
#> 2007 305920.3 290012.6 348811.2 312898.7 370067.4 340137.8 336472.8 351583.8
#> 2008 304973.1 309272.6 344529.3 343162.1 364451.8 336798.2 360204.1 344387.4
#> 2009 270136.1 245900.9 320382.2 283379.8 307724.1 318024.6 299791.2 324293.8
#> 2010 293445.2 276841.6 326776.5 324356.5 333414.3 316459.3 341257.4 333610.3
#> Sep Oct Nov Dec
#> 1992 155051.8 178175.0 138725.9 199133.0
#> 1993 168943.6 185889.4 171506.9 200729.8
#> 1994 175437.6 160318.1 182532.3 220059.2
#> 1995 185453.5 182533.0 171299.7 234031.1
#> 1996 190654.3 212495.5 196704.3 249984.2
#> 1997 205429.8 225088.4 210845.4 264635.3
#> 1998 210789.3 210844.7 225354.1 234251.7
#> 1999 242913.1 226281.0 248558.1 307308.8
#> 2000 244470.9 253159.1 266928.1 296373.1
#> 2001 241756.2 280943.9 262574.8 310175.9
#> 2002 258019.5 263857.4 252735.7 301911.9
#> 2003 269775.2 280398.1 282511.8 313884.6
#> 2004 289701.7 288167.2 291494.5 365201.3
#> 2005 308033.9 303191.3 321199.4 375501.9
#> 2006 332923.8 301267.4 309445.3 360541.0
#> 2007 305348.7 315480.5 329485.7 399578.4
#> 2008 313089.9 289414.9 302889.3 339760.2
#> 2009 292279.6 310125.5 312314.6 354118.6
#> 2010 309711.9 329990.6 320849.7 399381.2
cholette(s = xq, t = Y, rho = 0.729, lambda = 1, bias = "Multiplicative")
#> Qtr1 Qtr2 Qtr3 Qtr4
#> 1992 419922.5 427571.6 452171.5 516050.4
#> 1993 401071.9 491346.5 491779.3 558050.4
#> 1994 446249.3 546841.9 553681.0 563248.7
#> 1995 496256.2 553656.2 584677.7 587914.0
#> 1996 521541.3 572617.0 613590.3 658916.4
#> 1997 539447.6 637402.9 596531.7 700620.8
#> 1998 586936.4 669247.4 659893.4 671027.8
#> 1999 607169.0 706856.4 713573.3 780957.3
#> 2000 689086.9 734592.6 747887.5 817189.0
#> 2001 683526.2 795636.6 735198.0 853364.2
#> 2002 720763.4 794924.3 800115.2 818519.1
#> 2003 731115.4 820654.4 839337.8 877046.4
#> 2004 792786.5 860452.3 882681.4 944509.7
#> 2005 839099.7 922693.7 935140.2 999757.4
#> 2006 916979.4 1006663.3 984530.6 971962.7
#> 2007 944660.1 1023404.0 993693.6 1044040.4
#> 2008 959253.8 1044433.7 1017472.2 931773.2
#> 2009 836211.4 909092.3 916442.5 976724.8
#> 2010 897068.5 974223.5 984570.2 1050228.0
# 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 119121.9 140636.2 128740.8 150099.9 148247.9 145534.7 161629.8 166241.0
#> 1993 149904.9 120705.2 167194.6 158848.1 162866.4 167408.6 165965.9 155897.2
#> 1994 138568.1 151359.4 171559.4 167696.7 193743.5 183507.3 161958.2 185693.5
#> 1995 148940.5 154180.2 183716.4 176169.5 167115.2 188427.0 181804.2 190899.1
#> 1996 162317.3 182060.7 180887.0 195746.7 207305.4 199006.0 206977.3 193632.5
#> 1997 178028.1 167633.3 207674.8 214410.3 195695.6 190759.6 217009.5 217664.0
#> 1998 199148.9 185647.4 203818.0 218169.2 240506.6 239223.1 201336.9 210538.1
#> 1999 195572.2 209239.9 225295.8 214145.8 236625.4 240381.7 237454.4 252075.6
#> 2000 225549.7 228830.7 258370.9 247954.3 236478.1 265835.3 241754.4 259520.4
#> 2001 235229.8 221680.2 274386.2 247973.5 254866.8 248999.9 268458.5 265290.6
#> 2002 225729.1 229206.8 268687.7 265534.9 280053.9 250566.3 278611.8 266473.5
#> 2003 258892.2 232202.6 275076.8 250314.2 275423.6 285051.9 280666.3 290311.0
#> 2004 265567.4 258313.8 283259.6 282465.4 307370.2 291475.0 289492.2 290878.8
#> 2005 269678.9 255526.4 306153.7 294504.0 317050.5 332214.7 306830.4 318737.2
#> 2006 282723.0 300777.3 319382.4 308967.9 350245.9 318557.2 316775.1 348378.9
#> 2007 289701.7 283956.4 331158.9 334769.1 358831.8 342583.4 315591.3 357262.1
#> 2008 299270.6 281070.9 344901.8 327810.1 342959.2 345583.0 358716.5 353129.8
#> 2009 275977.1 259670.3 293091.0 301154.1 298003.0 300484.1 324880.5 310834.5
#> 2010 276945.6 298910.6 333661.7 344259.9 338012.8 319123.4 314217.2 330575.8
#> Sep Oct Nov Dec
#> 1992 133039.6 148719.1 169639.3 204065.8
#> 1993 154673.5 152685.7 163459.1 222638.7
#> 1994 175934.0 172131.1 165290.4 242579.4
#> 1995 198515.0 202920.9 197686.2 232129.9
#> 1996 190460.1 214878.6 198757.4 234635.8
#> 1997 222067.7 206303.2 196732.4 260024.6
#> 1998 196455.1 224981.8 199614.5 267665.2
#> 1999 228596.2 251443.7 223647.5 294077.7
#> 2000 255553.9 233331.7 240487.7 295088.8
#> 2001 231111.2 262632.1 267591.8 289504.6
#> 2002 233135.7 252239.7 270430.5 313652.0
#> 2003 261313.5 267023.4 265122.8 326755.7
#> 2004 280833.4 288518.4 291437.6 350818.3
#> 2005 318435.3 287225.1 322116.1 368218.8
#> 2006 334432.4 309084.6 308714.8 382096.4
#> 2007 318913.1 336661.4 340368.1 396000.6
#> 2008 310801.2 323780.2 317770.7 347138.9
#> 2009 292401.1 313564.0 308950.1 359461.2
#> 2010 294817.5 323822.7 333537.6 408230.0
# Additive benchmarking
cholette(s = xm, t = Y, rho = 0.9, lambda = 0, bias = "Additive")
#> Jan Feb Mar Apr May Jun Jul Aug
#> 1992 140343.1 144085.5 157969.5 130765.6 149960.3 147963.6 147277.1 143755.5
#> 1993 116944.4 128760.1 152796.1 165069.9 156028.9 169737.2 170727.0 153765.2
#> 1994 148230.6 141099.9 161398.4 182890.0 179900.6 183312.0 191522.6 185346.7
#> 1995 167978.1 154665.4 173936.6 174185.9 185545.4 193610.5 207831.1 191128.7
#> 1996 162516.4 169696.0 190077.6 190417.2 209752.7 172750.4 222822.0 199753.2
#> 1997 179079.3 167408.9 194963.3 211006.9 214095.6 211702.9 193200.3 198539.9
#> 1998 192729.1 189413.6 206054.3 212714.9 218548.7 237942.9 228014.5 220911.3
#> 1999 188996.1 197086.1 219481.7 224352.7 241251.4 240844.5 230681.5 240198.7
#> 2000 213115.4 227297.7 251283.5 234824.2 256613.2 244803.3 244790.1 258808.4
#> 2001 212753.0 224800.8 245857.4 250445.4 285047.8 259319.0 229298.0 263727.1
#> 2002 233929.5 229507.5 258551.8 265244.0 271632.1 258203.3 272135.7 269772.8
#> 2003 247145.1 224420.1 260476.7 273185.9 279966.4 267038.5 268204.7 300954.8
#> 2004 255402.4 236323.1 301362.0 287011.5 296199.5 277319.3 288652.2 304372.4
#> 2005 273395.5 248675.2 318545.8 302070.8 317345.3 303141.3 312826.8 314074.2
#> 2006 280391.8 298932.5 339387.7 327452.4 350602.4 328360.0 314698.7 336876.1
#> 2007 305439.8 289343.4 348574.1 312376.7 370336.3 340115.7 336487.0 351889.8
#> 2008 305844.6 310336.7 345441.6 344004.4 364874.4 337356.5 360082.5 344134.8
#> 2009 267910.3 243600.9 316192.5 280059.0 304260.5 315063.9 298309.4 323710.8
#> 2010 306800.3 293733.9 345551.9 345782.4 357007.4 342486.3 368711.7 362918.4
#> Sep Oct Nov Dec
#> 1992 150937.7 173158.8 135324.6 194174.8
#> 1993 169756.5 186091.3 172314.4 200257.0
#> 1994 175185.4 160552.2 182032.5 218550.0
#> 1995 185572.1 182706.9 171601.2 233742.1
#> 1996 190858.7 212278.0 196842.7 248900.1
#> 1997 205438.6 224571.9 210726.6 263268.9
#> 1998 210752.7 210751.3 225196.0 234075.8
#> 1999 243255.6 226751.8 248953.2 306702.7
#> 2000 244474.7 252641.1 265776.9 294327.6
#> 2001 241954.0 281317.6 262949.1 310255.7
#> 2002 258060.9 263689.3 252826.5 300768.6
#> 2003 269865.2 280474.5 282603.9 313818.2
#> 2004 289812.0 288337.3 291650.0 363988.2
#> 2005 308132.3 303469.5 321044.4 373969.8
#> 2006 332716.5 301337.7 309294.1 360086.1
#> 2007 305172.9 315596.6 329930.1 400535.5
#> 2008 312951.7 289190.7 301718.0 336997.0
#> 2009 294207.5 313871.7 318640.4 362644.2
#> 2010 341001.0 362288.2 354559.6 432789.9
# Denton PFD
cholette(s = xm, t = Y, rho = 1, lambda = 1)
#> Jan Feb Mar Apr May Jun Jul Aug
#> 1992 129880.4 136947.1 154010.9 128260.9 149967.6 149425.7 149865.8 147018.4
#> 1993 117923.0 129325.2 153558.6 165712.9 155812.8 169672.7 170390.2 152481.9
#> 1994 146643.5 139322.0 160645.3 183188.9 180144.5 183755.4 192331.1 185913.5
#> 1995 168030.8 154432.3 174068.6 174259.2 185702.9 193770.3 208045.5 191091.3
#> 1996 162007.0 169247.2 189876.1 190232.7 209872.0 172304.2 223236.7 199777.7
#> 1997 178437.0 166379.2 194657.7 211151.8 214328.5 211860.5 192805.3 198307.4
#> 1998 192484.1 189127.0 206093.6 212838.5 218710.0 238269.3 228147.7 220925.1
#> 1999 189261.6 197361.0 219536.8 224324.7 241013.6 240608.8 230530.5 240000.7
#> 2000 211816.2 226203.1 251041.6 233897.9 256744.5 244441.9 244520.4 259336.5
#> 2001 212674.3 225142.9 246419.2 250874.6 285288.0 259384.0 229341.8 263487.1
#> 2002 233124.7 228537.6 258150.1 265095.5 271767.0 258043.2 272487.5 270125.0
#> 2003 247209.9 224120.7 260755.4 273534.2 280258.9 267102.7 268173.8 300994.3
#> 2004 254989.9 235768.1 301309.5 286874.8 296190.9 277129.4 288616.7 304571.4
#> 2005 272771.9 247382.7 318820.5 301917.3 317564.0 302970.9 312903.5 314171.8
#> 2006 279433.0 298454.5 339929.3 327638.0 351259.4 328456.1 314493.8 337023.6
#> 2007 305828.6 289972.4 348805.1 312910.1 370099.0 340167.7 336501.4 351612.6
#> 2008 304873.6 309143.0 344393.2 343060.5 364395.8 336798.7 360257.9 344479.4
#> 2009 270138.6 245865.6 320297.3 283285.8 307614.0 317917.7 299712.5 324247.3
#> 2010 293816.5 277293.7 327418.4 325090.5 334258.4 317337.0 342278.1 334673.6
#> Sep Oct Nov Dec
#> 1992 154882.0 177965.2 138568.2 198923.7
#> 1993 168995.1 185959.7 171584.7 200831.3
#> 1994 175373.9 160251.9 182457.1 219994.0
#> 1995 185424.4 182488.3 171245.5 233944.8
#> 1996 190708.5 212568.9 196774.4 250059.6
#> 1997 205414.6 225085.2 210866.8 264709.0
#> 1998 210683.1 210685.0 225139.6 234002.1
#> 1999 243071.2 226475.6 248796.7 307574.8
#> 2000 244435.9 253106.1 266869.2 296342.8
#> 2001 241694.7 280866.4 262493.3 310058.5
#> 2002 258106.5 263963.9 252851.7 302069.2
#> 2003 269671.6 280264.0 282360.2 313708.4
#> 2004 289800.4 288277.5 291600.9 365300.6
#> 2005 308046.8 303232.1 321274.9 375634.5
#> 2006 332771.1 301088.9 309247.9 360340.4
#> 2007 305366.2 315494.9 329490.9 399549.2
#> 2008 313196.7 289519.3 302985.5 339829.4
#> 2009 292288.6 310203.2 312478.4 354422.1
#> 2010 310753.7 331153.2 322026.0 400896.8
# Pro-rating
cholette(s = xm, t = Y, rho = 0, lambda = 0.5)
#> Jan Feb Mar Apr May Jun Jul Aug
#> 1992 130111.6 137182.1 154255.0 128437.6 150133.7 149540.0 149918.0 146997.6
#> 1993 118411.7 129750.6 153938.2 165994.5 155964.7 169722.7 170332.8 152341.6
#> 1994 145860.1 138566.6 159800.6 182307.0 179414.9 183210.0 192030.9 185949.1
#> 1995 166171.0 153200.4 173168.3 173789.0 185598.4 194004.3 208584.4 191770.4
#> 1996 163108.6 170222.3 190766.0 190912.3 210379.5 172514.4 223233.7 199519.4
#> 1997 178761.7 166473.9 194570.8 210900.7 213977.2 211481.1 192487.3 198061.6
#> 1998 190028.4 187092.4 204302.5 211444.5 217762.5 237784.4 228227.5 221548.1
#> 1999 190262.1 198824.8 221460.2 226393.5 243129.1 242380.4 231680.9 240412.0
#> 2000 214740.9 227775.7 251390.1 233242.5 255269.1 242644.5 242637.6 257575.6
#> 2001 208625.7 222431.7 244952.6 250648.1 286156.8 260863.1 230984.8 265478.7
#> 2002 236359.4 230540.7 259286.0 265320.4 271253.5 257060.3 271135.5 268690.3
#> 2003 244283.0 222206.3 259310.5 272741.9 280081.2 267431.5 268901.2 302139.3
#> 2004 256733.0 237127.5 302715.2 287886.4 296887.0 277444.4 288584.6 304146.4
#> 2005 274049.4 248208.8 319498.9 302244.6 317627.0 302812.7 312563.6 313704.1
#> 2006 276755.6 295799.1 337231.5 325456.4 349477.9 327421.0 314206.2 337573.5
#> 2007 303556.4 288849.6 348497.4 313350.5 371231.1 341510.2 337890.3 352881.4
#> 2008 309147.3 312330.8 346783.7 344409.9 364862.0 336460.0 359193.4 342912.3
#> 2009 270206.6 245912.2 320339.4 283308.4 307624.1 317915.2 299699.5 324223.7
#> 2010 287409.1 271246.6 320278.3 318001.0 326969.0 310416.7 334813.9 327375.2
#> Sep Oct Nov Dec
#> 1992 154773.2 177727.1 138282.9 198357.3
#> 1993 168748.3 185596.6 171174.2 200272.1
#> 1994 175773.7 161003.8 183808.2 222296.2
#> 1995 186190.1 183277.8 171956.4 234793.3
#> 1996 190210.2 211724.8 195717.4 248356.4
#> 1997 205300.8 225179.4 211226.9 265581.6
#> 1998 211815.4 212372.8 227555.7 237170.9
#> 1999 242468.0 224758.7 245440.7 301345.6
#> 2000 243326.7 252852.8 267909.9 299390.5
#> 2001 243319.9 282205.9 262894.3 309163.3
#> 2002 256850.5 262997.9 252429.9 302397.5
#> 2003 270873.1 281584.0 283645.5 314956.5
#> 2004 289013.0 287102.9 290006.9 362782.6
#> 2005 307514.0 302682.4 320715.8 375069.8
#> 2006 334272.9 303417.1 312732.1 365792.7
#> 2007 306087.2 315648.4 328823.0 397472.5
#> 2008 311377.3 287560.3 300729.5 337166.4
#> 2009 292260.5 310167.7 312438.9 354374.9
#> 2010 303977.0 323931.5 315003.4 392154.3