The series is differenced till its variance is decreasing.
Arguments
- data
Series being differenced.
- period
Period considered in the automatic differencing.
- mad
Use of MAD in the computation of the variance (true by default).
- centile
Percentage of the data used for computing the variance (90 by default).
- k
tolerance in the decrease of the variance. The algorithm stops if the new variance is higher than k*the old variance. k should be equal or slightly higher than 1 (1.2 by default)
Value
Stationary transformation
ddata: data after differencingmean: mean correctiondifferences:lag: \(ddata(t)=data(t)-data(t-lag)\)order: order of the differencing
Examples
differencing_fast(log(ABS$X0.2.09.10.M), 12)
#> $ddata
#> Jan Feb Mar Apr May
#> 1983 -0.0741493458
#> 1984 0.0091461904 0.0026871821 -0.0658394637 -0.0588444482 0.1903421439
#> 1985 0.1435137649 -0.1314178361 -0.0063240191 0.1059458943 -0.0292513650
#> 1986 -0.0333814559 -0.0445838855 -0.0149824076 -0.0290912556 0.0595278241
#> 1987 -0.0681075811 -0.0026823014 0.0209466003 0.0344110474 -0.1773155307
#> 1988 -0.0377543953 0.0437768340 0.0512811469 -0.0626491781 -0.0230348959
#> 1989 -0.0717786136 0.0008396861 0.0569348226 -0.0841818002 0.0574988906
#> 1990 0.0717265265 -0.0112313059 -0.0493230032 0.0537395830 -0.0003425015
#> 1991 0.0270520826 0.0080417082 -0.0415832924 0.0160067409 0.0099583615
#> 1992 0.0406581429 0.0322288161 -0.1213256255 0.1303592885 -0.0463656445
#> 1993 -0.0017018876 -0.0644223794 0.1072988705 -0.0611802343 0.0202477556
#> 1994 -0.0572195378 0.0544940596 0.0528672988 -0.0963700315 0.0123061194
#> 1995 -0.0517314821 0.0179334264 -0.0394954540 0.0981848118 -0.0646425937
#> 1996 0.0802775388 -0.0249245444 -0.0759753338 -0.0129778564 0.0496685629
#> 1997 0.0199286686 -0.0225660995 0.0682342381 -0.1079751731 0.0856839767
#> 1998 0.0646292593 -0.1024789007 -0.0261357810 0.1749928286 -0.1583794488
#> 1999 -0.0235591251 0.0039555236 0.0625831006 -0.1106837400 0.0589652013
#> 2000 -0.0647522370 0.0961931604 -0.0793138731 0.0737707842 -0.0324899202
#> 2001 -0.0012547829 -0.0292292923 0.1002622655 -0.1065489686 0.0514192683
#> 2002 0.0146381333 -0.0236502706 -0.0067549148 0.0085334449 0.0241120051
#> 2003 0.0371628108 0.0007272659 -0.0221949953 0.0825284489 -0.0901558399
#> 2004 0.0373463236 0.0212573009 -0.0597486316 0.0089716368 -0.0094512485
#> 2005 0.0211010036 -0.0053365514 0.0926500960 -0.2411413695 0.0889627992
#> 2006 -0.0570987906 0.0435069769 -0.0773004589 0.2330077651 -0.1534070106
#> 2007 0.0306473741 -0.0509087197 0.0913944774 -0.1350214338 0.1088070874
#> 2008 0.0472731003 -0.0124730881 -0.0705559981 0.0546966115 -0.0294749107
#> 2009 -0.0120433008 -0.1137639588 0.1021185382 0.0517647540 -0.0105884347
#> 2010 0.0444352201 0.0386170635 -0.0560740659 -0.0773655422 0.0198245129
#> 2011 -0.0238233646 0.0442417742 -0.0481916928 0.1011095584 -0.0708468742
#> 2012 -0.0281956119 0.0488110071 0.0080418209 -0.0775315623 0.0903644945
#> 2013 0.0170500671 -0.0414884332 0.0511528953 -0.0731989164 0.0278197352
#> 2014 0.0477879015 -0.0823567193 -0.0327049237 0.1520792670 -0.0957534332
#> 2015 0.0023704579 -0.0243036397 0.0661233052 -0.0561303378 0.0123847057
#> 2016 -0.0231770837 0.0602845799 -0.0325574144 -0.0537494033 0.0085084502
#> 2017 -0.0396288431 0.0051433035 -0.0011521762 0.1057342365 -0.0463057039
#> Jun Jul Aug Sep Oct
#> 1983 0.0252644272 -0.0212152419 0.0243329695 -0.0070311279 0.0323946955
#> 1984 -0.0788595498 0.0697591196 -0.0546572681 -0.0142756736 0.0572759536
#> 1985 -0.0423471627 -0.0119983663 0.0422043330 -0.0716858522 0.0608215295
#> 1986 -0.0857603002 0.1105559844 -0.0978974634 0.1640635812 -0.1178949945
#> 1987 0.2432639406 -0.1085188078 -0.0487539140 -0.0190797312 0.0477174885
#> 1988 0.0371537152 -0.1272752114 0.1320370232 -0.0056438436 -0.0446195259
#> 1989 0.0534295817 -0.0401175232 0.0609633537 -0.0594317136 -0.0168865075
#> 1990 -0.0072123648 -0.0637096726 0.0547485137 -0.0704294185 0.0677984337
#> 1991 -0.1238350362 0.2204073571 -0.0976443573 -0.0138416201 0.0870437032
#> 1992 0.0415884057 -0.1086245874 -0.0547099857 0.1630563535 -0.0505197121
#> 1993 0.0399913350 -0.0927781350 0.0284385641 0.0228977555 -0.0473575805
#> 1994 0.0267969129 -0.0136716509 0.0771801748 -0.0429850293 0.0035229463
#> 1995 -0.0273006633 0.1239742693 -0.0277431683 -0.1244958143 0.0195474643
#> 1996 -0.0356933792 0.0286578506 -0.0136220947 -0.0443496843 0.0414604498
#> 1997 -0.1229343237 0.1574233887 -0.1285412012 0.1804044746 -0.0738192392
#> 1998 0.0479030584 0.0478920569 -0.0310059897 -0.0394302456 0.0441279081
#> 1999 0.0102320969 -0.0399859733 0.0218238797 0.0313504736 -0.0431154982
#> 2000 0.2249118557 -0.4694562517 0.3197780590 -0.0642099743 -0.0256038705
#> 2001 -0.1940257005 0.3762294955 -0.2945341678 0.0065157606 0.0962976138
#> 2002 0.0508008268 -0.1321269137 0.1245869556 -0.0559756403 0.0222449962
#> 2003 0.0416994036 0.0144762958 -0.0616553250 0.0898762058 -0.0395610851
#> 2004 0.0773092188 -0.0119491741 -0.0418200745 0.0373546653 -0.0636580300
#> 2005 0.0620607267 -0.0615785358 0.0491064692 -0.0678334572 -0.0019539186
#> 2006 -0.0201668601 0.1077684266 -0.0670200989 -0.0702942730 0.0697432509
#> 2007 -0.0312949112 -0.0078040265 0.0247474118 0.0446823611 -0.0354700501
#> 2008 -0.1023714174 0.1410368299 -0.1153295039 0.0583864526 -0.0137682277
#> 2009 0.0012996442 -0.0755420496 0.0633902321 -0.0441032706 0.0429280338
#> 2010 0.0959604004 -0.0268231848 -0.0196671117 0.0287944593 -0.0619507961
#> 2011 -0.0396984411 0.0214464965 0.0078514345 -0.0318442727 0.0131867837
#> 2012 0.0601457384 -0.1674993840 0.1232494255 -0.0331081266 0.0103339983
#> 2013 -0.0397595739 0.0267957091 0.0071418076 0.0100110759 0.0204073018
#> 2014 -0.0294647495 0.1273568495 -0.1408758540 0.0618706618 0.0126784589
#> 2015 0.0012188311 0.0127171700 0.0342731201 -0.0283990437 0.0258432953
#> 2016 0.0603214441 -0.1231745350 0.0193158114 0.0242204862 -0.0402607846
#> 2017 -0.0265345390 0.0090238304 0.0227351143
#> Nov Dec
#> 1983 0.0144252111 -0.0036174067
#> 1984 -0.0455651524 -0.0158955805
#> 1985 -0.0230184021 0.0211452554
#> 1986 -0.0383259094 0.1359901092
#> 1987 -0.0047077068 0.0066282454
#> 1988 0.1293729138 -0.0853020995
#> 1989 0.0298167488 -0.0600398569
#> 1990 -0.0370819598 -0.0123229438
#> 1991 -0.0735120691 0.0094488560
#> 1992 -0.0248812212 0.0061451689
#> 1993 0.0188807954 0.0340207902
#> 1994 -0.0215272664 0.0298170775
#> 1995 0.0799188638 -0.0432178182
#> 1996 -0.0009139147 -0.0238252462
#> 1997 -0.0181400303 -0.0047565085
#> 1998 -0.0209691326 0.0266516478
#> 1999 0.0375991817 -0.0128623620
#> 2000 -0.0045193201 0.0300810794
#> 2001 0.0312471068 -0.0458185630
#> 2002 0.0381570553 -0.0759548743
#> 2003 -0.0609986243 0.0140516353
#> 2004 -0.0260144121 0.0255624198
#> 2005 0.0352584930 0.0115724930
#> 2006 0.0297027081 -0.0232354395
#> 2007 -0.0299390840 0.0117137802
#> 2008 -0.0152924854 0.0565315210
#> 2009 -0.0192780462 -0.0676170699
#> 2010 0.0282164144 0.0026762300
#> 2011 0.0149225034 0.0190522048
#> 2012 -0.0188822392 0.0005744047
#> 2013 -0.0166410386 -0.0077543741
#> 2014 0.0007327642 0.0002530341
#> 2015 -0.0325090979 0.0302388411
#> 2016 0.0179255424 0.0051302422
#> 2017
#>
#> $mean
#> [1] FALSE
#>
#> $differences
#> [,1] [,2]
#> lag 1 12
#> order 1 1
#>