rjd3filters allows to reproduce the entire X-11 process
library("rjd3filters")
library("rjd3x11plus")
b1 <- rjd3toolkit::ABS$X0.2.09.10.M
x11_step <- x11plus_trend(b1, trend.coefs = lp_filter(horizon = 6, ic = 3.5),
extreme.lsig = 300, extreme.usig = 400, mul = FALSE,
seas.s0 = "S3X3",
seas.s1 = "S3X5",
userdefined = sprintf("b%i", 1:11))
compare <- function(x, id, na.rm = TRUE){
if (na.rm)
x <- na.omit(x)
res <- cbind(x, x11_step$user_defined[[id]])
all.equal(res[,1], res[,2], check.attributes = FALSE)
}
compare(b1, "b1")
#> [1] TRUE
e1 <- simple_ma(12, - 6)
e2 <- simple_ma(12, - 5)
# used to have the 1rst estimate of the trend
tc_1 <- M2X12 <- (e1 + e2)/2
coef(M2X12) |> round(3)
#> t-6 t-5 t-4 t-3 t-2 t-1 t t+1 t+2 t+3 t+4 t+5 t+6
#> 0.042 0.083 0.083 0.083 0.083 0.083 0.083 0.083 0.083 0.083 0.083 0.083 0.042
M2X12 * b1 # b2
#> Jan Feb Mar Apr May Jun Jul
#> 1982 NA NA NA NA
#> 1983 494.8167 496.0250 497.5833 499.6750 502.9417 507.9500 512.5292
#> 1984 530.3292 535.3417 538.8958 543.5375 548.7792 554.2042 561.5917
#> 1985 596.9083 602.6792 607.6542 612.6875 619.1208 628.3708 636.8000
#> 1986 649.6417 652.1000 656.1583 661.4625 662.8083 670.4833 679.8083
#> 1987 704.5875 707.8458 709.1333 711.3792 714.9542 720.5583 725.1125
#> 1988 743.9333 744.4292 748.6083 751.5875 757.7375 767.6125 772.2125
#> 1989 782.8833 787.2375 791.7167 794.0792 797.2292 799.4333 801.3542
#> 1990 818.5417 819.8250 820.6083 821.3625 823.1375 823.1958 823.5917
#> 1991 822.9417 826.9083 827.3833 830.4000 833.9500 836.0500 839.5167
#> 1992 862.5208 860.3083 861.6208 866.7125 869.5375 872.6417 875.6708
#> 1993 886.5708 886.0875 887.3375 887.7250 887.1333 889.6750 891.4750
#> 1994 900.1583 903.5542 908.2375 911.9875 915.2417 920.9667 925.7042
#> 1995 938.0125 945.2125 947.0833 945.2417 947.4500 951.8958 956.9125
#> 1996 968.2500 970.0167 969.6792 969.2625 970.4000 970.1750 969.6833
#> 1997 967.9375 968.3625 970.5500 976.7417 979.7792 982.7458 987.6583
#> 1998 999.6000 1003.9792 1005.4042 1007.2667 1010.2167 1015.3417 1020.3958
#> 1999 1036.2333 1037.9750 1041.8292 1045.3833 1049.2125 1056.0208 1059.2208
#> 2000 1087.2250 1083.6625 1090.4125 1093.7042 1095.8708 1101.4208 1107.8750
#> 2001 1126.3208 1134.4583 1130.7958 1131.6250 1138.8708 1147.3833 1153.5500
#> 2002 1177.7375 1180.9792 1187.2333 1192.5083 1202.0792 1211.2208 1217.0750
#> 2003 1257.4875 1263.3875 1270.6125 1280.7292 1286.4708 1291.4167 1298.4667
#> 2004 1338.1208 1346.0167 1353.7375 1360.4833 1362.5958 1366.1417 1371.9750
#> 2005 1386.2500 1387.4208 1387.5792 1384.0792 1382.4042 1384.0250 1383.3000
#> 2006 1392.6208 1398.8875 1397.6292 1396.4417 1401.1542 1407.7375 1413.9333
#> 2007 1439.9625 1445.2375 1454.0083 1463.6000 1470.2917 1478.6458 1489.7458
#> 2008 1514.6583 1517.6958 1516.9833 1518.7250 1518.7167 1524.0125 1532.0250
#> 2009 1555.5083 1558.0708 1561.8083 1565.9125 1571.8542 1570.5917 1567.5542
#> 2010 1559.3708 1559.0708 1559.2625 1557.2917 1553.1042 1550.0292 1545.8958
#> 2011 1535.8875 1532.5958 1528.1458 1522.4583 1518.0542 1515.2458 1512.2417
#> 2012 1518.3458 1516.5292 1520.1792 1522.6792 1524.7958 1526.2833 1528.6917
#> 2013 1519.1083 1516.8333 1515.5750 1516.0875 1516.7833 1515.4583 1516.5333
#> 2014 1510.4833 1511.6500 1508.0667 1508.5833 1510.0083 1512.1000 1514.2500
#> 2015 1524.9292 1529.8042 1534.8625 1540.3333 1545.7667 1554.0792 1562.6083
#> 2016 1589.1917 1584.5833 1582.7250 1579.5792 1574.7833 1570.2250 1563.8125
#> 2017 1549.9833 1549.4167 NA NA NA NA NA
#> Aug Sep Oct Nov Dec
#> 1982 NA NA 490.4125 492.5500 493.6583
#> 1983 515.5292 517.5750 517.4292 520.3958 525.6167
#> 1984 567.4083 570.7042 576.6000 585.0500 591.8750
#> 1985 640.1292 642.1000 643.2750 645.6875 647.4750
#> 1986 683.0750 686.7208 692.2333 693.9917 697.3042
#> 1987 727.4042 732.2417 737.2333 740.0833 743.3458
#> 1988 772.2708 774.0125 774.9625 775.2083 778.8875
#> 1989 804.7250 806.4750 808.7375 812.7875 816.8208
#> 1990 825.0208 825.4750 825.3292 826.0292 822.9958
#> 1991 843.9833 845.7958 848.5250 854.0917 859.4875
#> 1992 875.6375 876.8750 879.4542 881.0083 884.7208
#> 1993 891.6833 895.3833 897.8167 897.5000 898.6208
#> 1994 926.7375 927.0625 929.7292 933.6250 934.1833
#> 1995 962.5500 964.8583 964.4417 965.4750 967.0333
#> 1996 969.6042 971.1125 971.1000 970.5083 968.5750
#> 1997 990.3750 988.4500 992.0375 996.0583 995.8333
#> 1998 1022.3500 1026.6208 1029.2625 1030.2667 1033.8500
#> 1999 1061.0000 1063.4375 1066.3625 1071.0542 1084.0625
#> 2000 1110.5167 1116.0167 1121.4375 1125.0083 1122.1167
#> 2001 1157.0000 1159.2167 1161.8208 1166.1333 1173.8625
#> 2002 1222.5125 1227.0083 1235.1708 1243.2250 1249.1042
#> 2003 1305.6708 1311.0042 1314.8958 1318.9750 1326.8667
#> 2004 1376.5958 1385.6333 1387.5500 1381.7375 1383.9875
#> 2005 1381.1250 1377.1292 1381.2375 1389.5000 1388.5917
#> 2006 1417.3875 1423.0708 1426.4500 1428.5958 1435.2625
#> 2007 1499.0792 1503.8125 1508.5667 1514.8167 1513.4042
#> 2008 1530.7458 1528.7167 1534.8708 1543.6542 1551.8708
#> 2009 1570.6125 1572.6250 1567.3583 1558.5417 1556.8208
#> 2010 1543.7750 1541.5792 1542.6042 1545.2958 1541.2208
#> 2011 1510.7417 1512.4833 1510.2417 1508.8500 1516.8708
#> 2012 1529.3958 1530.6458 1530.4792 1527.6833 1523.7667
#> 2013 1516.7375 1510.3708 1510.3583 1513.4292 1509.0167
#> 2014 1514.6292 1517.2500 1520.3042 1520.9792 1522.4875
#> 2015 1568.8583 1576.6208 1580.5000 1581.7417 1587.4167
#> 2016 1557.3917 1551.3667 1550.9667 1554.0625 1552.5542
#> 2017 NA
compare(M2X12 * b1 , "b2")
#> [1] TRUE
si_1 <- 1 - tc_1
si_1 * b1 # b3
#> Jan Feb Mar Apr May
#> 1982 NA NA
#> 1983 -115.6166667 -118.0250000 -25.4833333 3.7250000 7.6583333
#> 1984 -115.6291667 -120.8416667 -54.1958333 -56.2375000 49.1208333
#> 1985 -80.6083333 -150.1791667 -81.8541667 -24.9875000 81.1791667
#> 1986 -79.1416667 -173.9000000 -108.7583333 -67.1625000 88.7916667
#> 1987 -90.6875000 -194.6458333 -109.2333333 -37.2791667 -0.9541667
#> 1988 -112.9333333 -193.3291667 -70.5083333 -35.8875000 -16.9375000
#> 1989 -151.3833333 -235.2375000 -72.7166667 -96.4791667 -32.4291667
#> 1990 -140.3416667 -233.6250000 -93.8083333 -77.2625000 -7.6375000
#> 1991 -128.9416667 -222.2083333 -108.1833333 -82.2000000 -5.7500000
#> 1992 -122.5208333 -194.4083333 -160.1208333 -35.3125000 9.0625000
#> 1993 -124.4708333 -243.0875000 -133.2375000 -47.0250000 19.4666667
#> 1994 -154.4583333 -239.1541667 -86.7375000 -80.2875000 -7.2416667
#> 1995 -185.6125000 -262.7125000 -135.8833333 -39.2416667 -20.2500000
#> 1996 -135.1500000 -232.9166667 -157.6791667 -74.0625000 -7.6000000
#> 1997 -127.0375000 -240.9625000 -112.6500000 -127.7416667 15.0208333
#> 1998 -82.3000000 -287.7791667 -182.5041667 -37.1666667 -40.0166667
#> 1999 -94.2333333 -299.5750000 -138.6291667 -92.1833333 -38.0125000
#> 2000 -162.3250000 -285.4625000 -188.5125000 -69.0041667 -43.5708333
#> 2001 -154.4208333 -319.8583333 -113.2958333 -92.4250000 -15.3708333
#> 2002 -149.8375000 -339.5791667 -143.3333333 -117.2083333 -11.1791667
#> 2003 -158.1875000 -362.8875000 -177.9125000 -58.3291667 -49.3708333
#> 2004 -155.2208333 -356.2166667 -222.3375000 -83.3833333 -82.2958333
#> 2005 -139.9500000 -350.1208333 -86.7791667 -230.3791667 -118.2041667
#> 2006 -198.9208333 -361.1875000 -193.1291667 -47.8416667 -133.5541667
#> 2007 -172.6625000 -398.2375000 -122.4083333 -161.0000000 -105.1916667
#> 2008 -116.8583333 -377.1958333 -165.2833333 -122.1250000 -97.6166667
#> 2009 -104.5083333 -501.4708333 -174.9083333 -56.8125000 -52.4541667
#> 2010 -90.2708333 -447.1708333 -179.3625000 -167.5916667 -125.9041667
#> 2011 -123.2875000 -415.0958333 -206.5458333 -49.8583333 -109.1541667
#> 2012 -155.9458333 -384.8291667 -170.9791667 -131.4791667 -67.8958333
#> 2013 -121.7083333 -403.2333333 -118.2750000 -176.9875000 -74.8833333
#> 2014 -59.4833333 -446.7500000 -214.8666667 -65.6833333 -98.2083333
#> 2015 -53.7291667 -476.0041667 -167.6625000 -98.1333333 -117.0666667
#> 2016 -69.9916667 -428.7833333 -131.2250000 -128.5791667 -125.0833333
#> 2017 -121.4833333 -457.0166667 NA NA NA
#> Jun Jul Aug Sep Oct
#> 1982 NA NA NA NA -37.7125000
#> 1983 -45.5500000 -44.2291667 -57.3291667 -34.8750000 -32.1291667
#> 1984 -53.8041667 -18.1916667 -64.0083333 -47.9041667 -20.0000000
#> 1985 -66.5708333 -34.0000000 -57.6291667 -79.0000000 -6.1750000
#> 1986 -117.0833333 -16.6083333 -101.9750000 -24.8208333 -26.6333333
#> 1987 -50.0583333 -4.2125000 -125.8041667 -59.9416667 -28.1333333
#> 1988 -45.6125000 -88.7125000 -121.3708333 -50.7125000 -45.3625000
#> 1989 -13.1333333 -86.2541667 -80.9250000 -48.5750000 -57.0375000
#> 1990 9.2041667 -113.2916667 -65.6208333 -84.3750000 -38.7291667
#> 1991 -89.1500000 -45.0166667 -73.5833333 -104.2958333 10.0750000
#> 1992 -46.6416667 -87.4708333 -152.0375000 -57.0750000 23.0458333
#> 1993 -2.5750000 -119.9750000 -162.9833333 -50.6833333 -10.9166667
#> 1994 -8.3666667 -142.8041667 -127.9375000 -40.0625000 4.8708333
#> 1995 -45.0958333 -76.3125000 -88.6500000 -108.0583333 -43.8416667
#> 1996 -61.5750000 -61.6833333 -80.7041667 -137.4125000 -37.4000000
#> 1997 -152.5458333 -16.5583333 -154.3750000 -49.3500000 -15.1375000
#> 1998 -165.9416667 21.9041667 -152.4500000 -87.2208333 -7.9625000
#> 1999 -161.6208333 -4.7208333 -161.5000000 -61.1375000 -22.6625000
#> 2000 64.0791667 -248.5750000 -101.3166667 -61.4166667 -51.0375000
#> 2001 -122.4833333 -52.7500000 -194.0000000 -146.3166667 -29.8208333
#> 2002 -68.2208333 -141.3750000 -156.6125000 -166.9083333 -23.7708333
#> 2003 -53.5166667 -116.4666667 -204.4708333 -112.8041667 1.2041667
#> 2004 17.9583333 -66.0750000 -209.7958333 -67.7333333 -29.2500000
#> 2005 70.1750000 -93.2000000 -170.4250000 -99.3291667 -66.8375000
#> 2006 21.2625000 -1.9333333 -178.1875000 -203.9708333 -81.8500000
#> 2007 12.8541667 -27.4458333 -183.5791667 -150.5125000 -67.9666667
#> 2008 -122.4125000 50.2750000 -262.3458333 -145.4166667 -82.4708333
#> 2009 -70.0916667 3.1458333 -229.1125000 -172.7250000 -33.0583333
#> 2010 1.3708333 35.1041667 -219.7750000 -119.5791667 -77.7041667
#> 2011 -43.3458333 20.2583333 -217.2416667 -166.7833333 -105.5416667
#> 2012 90.1166667 -105.2916667 -170.3958333 -162.8458333 -87.8791667
#> 2013 21.9416667 -125.9333333 -179.5375000 -150.9708333 -47.0583333
#> 2014 -50.5000000 -12.6500000 -260.4291667 -160.8500000 -41.6041667
#> 2015 -73.1791667 -21.7083333 -236.9583333 -176.5208333 -14.2000000
#> 2016 25.8750000 -95.5125000 -263.4916667 -157.8666667 -53.5666667
#> 2017 NA NA NA
#> Nov Dec
#> 1982 30.3500000 395.6416667
#> 1983 48.3041667 438.0833333
#> 1984 38.1500000 447.5250000
#> 1985 51.4125000 540.0250000
#> 1986 6.9083333 670.5958333
#> 1987 3.1166667 716.7541667
#> 1988 95.0916667 791.1125000
#> 1989 111.0125000 752.5791667
#> 1990 105.4708333 740.1041667
#> 1991 90.6083333 740.8125000
#> 1992 87.5916667 766.1791667
#> 1993 72.5000000 811.8791667
#> 1994 66.7750000 883.3166667
#> 1995 101.9250000 890.1666667
#> 1996 111.0916667 869.0250000
#> 1997 115.2416667 883.2666667
#> 1998 107.4333333 941.8500000
#> 1999 136.1458333 985.5375000
#> 2000 107.4916667 1055.3833333
#> 2001 178.6666667 1095.6375000
#> 2002 251.8750000 1089.4958333
#> 2003 209.2250000 1097.3333333
#> 2004 154.9625000 1116.8125000
#> 2005 150.9000000 1147.4083333
#> 2006 194.7041667 1175.8375000
#> 2007 173.0833333 1233.5958333
#> 2008 132.2458333 1334.2291667
#> 2009 178.0583333 1238.2791667
#> 2010 160.2041667 1211.1791667
#> 2011 151.1500000 1213.6291667
#> 2012 145.2166667 1229.5333333
#> 2013 155.4708333 1216.4833333
#> 2014 166.7208333 1234.4125000
#> 2015 148.7583333 1326.1833333
#> 2016 130.2375000 1297.8458333
#> 2017
compare(si_1 * b1 , "b3")
#> [1] TRUE
M3X3 <- macurves("S3x3")
M3X3_s <- to_seasonal(M3X3, 12)
s_1 <- M3X3_s * si_1
s_1_norm <- M2X12 * s_1
s_1_norm <- impute_last_obs(s_1_norm, n = 6, nperiod = 1)
s_1_demean <- s_1 - s_1_norm
s_1_f <- impute_last_obs(s_1_demean, n = 6, nperiod = 12)
s_1_f * b1 # b5
#> Jan Feb Mar Apr May Jun
#> 1982 -23.443152 40.457639 -51.370306
#> 1983 -106.560590 -122.548862 -45.041917 -23.443152 40.457639 -51.370306
#> 1984 -100.417618 -131.460095 -57.565471 -31.532112 53.242445 -61.594991
#> 1985 -91.950714 -148.875829 -76.433365 -37.456250 60.597762 -71.377508
#> 1986 -89.219039 -168.030633 -90.434896 -44.251003 53.555826 -76.770467
#> 1987 -98.483353 -188.111748 -91.703453 -46.708873 23.017863 -63.055517
#> 1988 -115.586593 -204.015085 -85.194213 -56.021123 -3.121354 -43.115606
#> 1989 -130.666377 -219.099209 -84.528144 -69.792342 -17.230363 -29.340586
#> 1990 -135.009722 -222.247029 -96.500463 -72.955131 -12.411497 -30.701312
#> 1991 -132.037674 -221.934934 -114.283179 -67.895872 -3.048920 -39.670679
#> 1992 -130.621701 -219.923939 -125.656790 -57.455941 4.848843 -36.087982
#> 1993 -138.252874 -230.676755 -125.617091 -54.098399 5.165258 -28.207407
#> 1994 -148.660590 -239.527141 -124.039333 -57.300193 -1.318326 -25.932350
#> 1995 -152.968808 -246.511979 -127.054707 -65.718229 -5.079861 -47.981597
#> 1996 -139.313831 -247.866590 -137.071971 -73.815066 -8.295409 -84.094232
#> 1997 -119.851157 -257.107600 -141.862654 -80.664198 -11.319001 -124.791570
#> 1998 -108.633623 -271.840220 -153.306925 -75.785918 -22.936053 -125.333854
#> 1999 -116.871412 -287.908005 -151.815066 -76.660860 -29.372049 -107.613966
#> 2000 -136.012731 -301.390837 -153.160108 -78.221682 -29.675598 -68.212982
#> 2001 -149.057176 -318.277932 -144.185012 -85.551775 -25.110899 -66.487712
#> 2002 -154.576678 -335.480691 -156.517554 -87.754726 -31.487423 -53.795486
#> 2003 -153.380401 -350.336863 -162.929977 -100.505073 -52.628684 -35.832350
#> 2004 -157.686535 -356.666898 -172.175559 -111.822068 -81.057948 4.079591
#> 2005 -162.826408 -362.527913 -156.136343 -130.583546 -103.587191 27.822415
#> 2006 -165.870351 -369.241725 -153.784066 -123.952411 -111.643808 14.741127
#> 2007 -154.324961 -391.214564 -148.296740 -121.639892 -103.584626 -17.986323
#> 2008 -132.788484 -415.742940 -162.056597 -112.734896 -95.972126 -51.408083
#> 2009 -114.862944 -441.814313 -172.530035 -108.099460 -92.348823 -54.604398
#> 2010 -112.467496 -438.813889 -183.726717 -109.240220 -97.234915 -28.476678
#> 2011 -122.041898 -424.153318 -180.123129 -109.485050 -93.722473 1.070177
#> 2012 -123.208063 -408.453356 -172.166262 -119.455536 -87.812288 20.463465
#> 2013 -106.881501 -416.155228 -164.181867 -117.285706 -85.886825 3.657542
#> 2014 -83.100405 -433.365181 -166.438600 -110.163465 -95.648129 -15.037828
#> 2015 -72.797518 -447.629231 -163.001080 -104.630022 -107.973900 -30.333963
#> 2016 -77.856713 -449.882774 -160.691371 -103.602392 -115.707748 -27.906584
#> 2017 -87.078292 -448.150514 -160.691371 -103.602392 -115.707748 -27.906584
#> Jul Aug Sep Oct Nov Dec
#> 1982 -31.331771 -59.633989 -47.013818 -29.579572 41.687249 425.118885
#> 1983 -31.331771 -59.633989 -47.013818 -25.368171 43.328041 442.665246
#> 1984 -30.686490 -66.360333 -50.077006 -21.375437 39.898322 485.945075
#> 1985 -28.164159 -79.492689 -54.691319 -19.900135 32.682215 557.140490
#> 1986 -29.801505 -98.053742 -51.947531 -25.471103 28.863947 640.733198
#> 1987 -41.603569 -109.017052 -52.622357 -34.001582 41.569348 707.375135
#> 1988 -67.001794 -106.675868 -54.274923 -41.961863 69.969753 747.377353
#> 1989 -80.600000 -91.876254 -65.020313 -39.642612 91.954302 752.918133
#> 1990 -87.371566 -87.592458 -74.327546 -25.527469 99.979591 751.360340
#> 1991 -82.674344 -100.293499 -77.102450 -7.496566 92.933893 754.458893
#> 1992 -95.245583 -124.949518 -67.075174 3.789294 84.524846 780.449151
#> 1993 -105.960089 -135.078299 -62.334144 -1.409549 80.042882 818.740760
#> 1994 -109.603125 -125.742052 -71.158912 -12.574942 83.181250 855.537963
#> 1995 -87.615104 -113.220891 -88.090895 -25.471026 94.076601 875.810378
#> 1996 -56.211960 -114.002315 -96.186960 -26.635648 104.350540 888.091223
#> 1997 -25.060957 -132.636497 -85.630208 -22.696682 113.552296 905.898765
#> 1998 -33.651543 -142.015760 -75.892882 -21.044522 116.163812 942.821779
#> 1999 -61.484819 -149.478819 -75.102701 -25.460552 126.132311 990.949576
#> 2000 -110.742496 -147.686497 -95.039255 -32.456366 145.567843 1039.538021
#> 2001 -119.685069 -163.674633 -118.675405 -28.283951 178.691049 1073.858391
#> 2002 -121.583951 -176.701080 -128.178800 -23.187404 200.599190 1093.214043
#> 2003 -102.564718 -191.142747 -117.585320 -21.921219 198.596721 1106.681983
#> 2004 -85.437558 -190.879919 -111.783642 -36.746451 182.452180 1123.984279
#> 2005 -62.946644 -186.445814 -122.764853 -54.624267 170.454282 1151.880691
#> 2006 -30.633738 -191.441069 -147.325637 -70.068750 167.929128 1193.488638
#> 2007 -10.834664 -205.829128 -158.843345 -70.959799 165.407948 1233.567438
#> 2008 12.805710 -225.351505 -156.806539 -68.114448 160.613079 1258.221971
#> 2009 18.528241 -228.990895 -152.365992 -66.062384 160.460224 1249.578742
#> 2010 11.768538 -219.705883 -149.410667 -75.537789 157.422647 1232.177797
#> 2011 -21.286709 -203.831867 -154.488908 -80.845891 155.593287 1218.935648
#> 2012 -56.149151 -198.649113 -156.268519 -76.973650 152.258661 1221.626640
#> 2013 -69.437249 -207.461593 -161.041069 -58.627064 153.708102 1235.661535
#> 2014 -60.389815 -228.464082 -162.486722 -44.045306 153.237301 1257.964519
#> 2015 -50.245499 -243.472029 -164.790940 -35.388895 149.358410 1283.056154
#> 2016 -49.581391 -251.234774 -165.139095 -34.433230 145.419084 1298.523714
#> 2017 -49.581391 -251.234774
compare(s_1_f * b1 , "b5")
#> [1] TRUE
sa_1 <- 1- s_1_f
sa_1 * b1 # b6
#> Jan Feb Mar Apr May Jun Jul
#> 1982 483.5432 462.1424 495.1703 490.4318
#> 1983 485.7606 500.5489 517.1419 526.8432 470.1424 513.7703 499.6318
#> 1984 515.1176 545.9601 542.2655 518.8321 544.6576 561.9950 574.0865
#> 1985 608.2507 601.3758 602.2334 625.1562 639.7022 633.1775 630.9642
#> 1986 659.7190 646.2306 637.8349 638.5510 698.0442 630.1705 693.0015
#> 1987 712.3834 701.3117 691.6035 720.8089 690.9821 733.5555 762.5036
#> 1988 746.5866 755.1151 763.2942 771.7211 743.9214 765.1156 750.5018
#> 1989 762.1664 771.0992 803.5281 767.3923 782.0304 815.6406 795.7000
#> 1990 813.2097 808.4470 823.3005 817.0551 827.9115 863.1013 797.6716
#> 1991 826.0377 826.6349 833.4832 816.0959 831.2489 786.5707 877.1743
#> 1992 870.6217 885.8239 827.1568 888.8559 873.7512 862.0880 883.4456
#> 1993 900.3529 873.6768 879.7171 894.7984 901.4347 915.3074 877.4601
#> 1994 894.3606 903.9271 945.5393 889.0002 909.3183 938.5323 892.5031
#> 1995 905.3688 929.0120 938.2547 971.7182 932.2799 954.7816 968.2151
#> 1996 972.4138 984.9666 949.0720 969.0151 971.0954 992.6942 964.2120
#> 1997 960.7512 984.5076 999.7627 929.6642 1006.1190 954.9916 996.1610
#> 1998 1025.9336 988.0402 976.2069 1045.8859 993.1361 974.7339 1075.9515
#> 1999 1058.8714 1026.3080 1055.0151 1029.8609 1040.5720 1002.0140 1115.9848
#> 2000 1060.9127 1099.5908 1055.0601 1102.9217 1081.9756 1233.7130 970.0425
#> 2001 1120.9572 1132.8779 1161.6850 1124.7518 1148.6109 1091.3877 1220.4851
#> 2002 1182.4767 1176.8807 1200.4176 1163.0547 1222.3874 1196.7955 1197.2840
#> 2003 1252.6804 1250.8369 1255.6300 1322.9051 1289.7287 1273.7323 1284.5647
#> 2004 1340.5865 1346.4669 1303.5756 1388.9221 1361.3579 1380.0204 1391.3376
#> 2005 1409.1264 1399.8279 1456.9363 1284.2835 1367.7872 1426.3776 1353.0466
#> 2006 1359.5704 1406.9417 1358.2841 1472.5524 1379.2438 1414.2589 1442.6337
#> 2007 1421.6250 1438.2146 1479.8967 1424.2399 1468.6846 1509.4863 1473.1347
#> 2008 1530.5885 1556.2429 1513.7566 1509.3349 1517.0721 1453.0081 1569.4943
#> 2009 1565.8629 1498.4143 1559.4300 1617.1995 1611.7488 1555.1044 1552.1718
#> 2010 1581.5675 1550.7139 1563.6267 1498.9402 1524.4349 1579.8767 1569.2315
#> 2011 1534.6419 1541.6533 1501.7231 1582.0851 1502.6225 1470.8298 1553.7867
#> 2012 1485.6081 1540.1534 1521.3663 1510.6555 1544.7123 1595.9365 1479.5492
#> 2013 1504.2815 1529.7552 1561.4819 1456.3857 1527.7868 1533.7425 1460.0372
#> 2014 1534.1004 1498.2652 1459.6386 1553.0635 1507.4481 1476.6378 1561.9898
#> 2015 1543.9975 1501.4292 1530.2011 1546.8300 1536.6739 1511.2340 1591.1455
#> 2016 1597.0567 1605.6828 1612.1914 1554.6024 1565.4077 1624.0066 1517.8814
#> 2017 1515.5783 1540.5505 1530.9914 1626.2024 1568.1077 1585.1066 1495.0814
#> Aug Sep Oct Nov Dec
#> 1982 498.0340 512.1138 482.2796 481.2128 464.1811
#> 1983 517.8340 529.7138 510.6682 525.3720 521.0348
#> 1984 569.7603 572.8770 577.9754 583.3017 553.4549
#> 1985 661.9927 617.7913 657.0001 664.4178 630.3595
#> 1986 679.1537 713.8475 691.0711 672.0361 727.1668
#> 1987 710.6171 724.9224 743.1016 701.6307 752.7249
#> 1988 757.5759 777.5749 771.5619 800.3302 822.6226
#> 1989 815.6763 822.9203 791.3426 831.8457 816.4819
#> 1990 846.9925 815.4275 812.1275 831.5204 811.7397
#> 1991 870.6935 818.6024 866.0966 851.7661 845.8411
#> 1992 848.5495 886.8752 898.7107 884.0752 870.4508
#> 1993 863.7783 907.0341 888.3095 889.9571 891.7592
#> 1994 924.5421 958.1589 947.1749 917.2187 961.9620
#> 1995 987.1209 944.8909 946.0710 973.3234 981.3896
#> 1996 1002.9023 929.8870 960.3356 977.2495 949.5088
#> 1997 968.6365 1024.7302 999.5967 997.7477 973.2012
#> 1998 1011.9158 1015.2929 1042.3445 1021.5362 1032.8782
#> 1999 1048.9788 1077.4027 1069.1606 1081.0677 1078.6504
#> 2000 1156.8865 1149.6393 1102.8564 1086.9322 1137.9620
#> 2001 1126.6746 1131.5754 1160.2840 1166.1090 1195.6416
#> 2002 1242.6011 1188.2788 1234.5874 1294.5008 1245.3860
#> 2003 1292.3427 1315.7853 1338.0212 1329.6033 1317.5180
#> 2004 1357.6799 1429.6836 1395.0465 1354.2478 1376.8157
#> 2005 1397.1458 1400.5649 1369.0243 1369.9457 1384.1193
#> 2006 1430.6411 1366.4256 1414.6687 1455.3709 1417.6114
#> 2007 1521.3291 1512.1433 1511.5598 1522.4921 1513.4326
#> 2008 1493.7515 1540.1065 1520.5144 1515.2869 1627.8780
#> 2009 1570.4909 1552.2660 1600.3624 1576.1398 1545.5213
#> 2010 1543.7059 1571.4107 1540.4378 1548.0774 1520.2222
#> 2011 1497.3319 1500.1889 1485.5459 1504.4067 1511.5644
#> 2012 1557.6491 1524.0685 1519.5736 1520.6413 1531.6734
#> 2013 1544.6616 1520.4411 1521.9271 1515.1919 1489.8385
#> 2014 1482.6641 1518.8867 1522.7453 1534.4627 1498.9355
#> 2015 1575.3720 1564.8909 1601.6889 1581.1416 1630.5438
#> 2016 1545.1348 1558.6391 1531.8332 1538.8809 1551.8763
#> 2017 1554.3348
compare(sa_1 * b1 , "b6")
#> [1] TRUE
h13 <- lp_filter(horizon = 6, ic = 3.5)
tc_2 <- h13 * sa_1
tc_2 * b1 # b7
#> Jan Feb Mar Apr May Jun Jul
#> 1982 478.2765 482.8008 487.6970 492.0921
#> 1983 489.2404 495.6111 501.2316 504.7038 505.7864 506.4552 508.5027
#> 1984 526.2366 529.2061 534.0533 540.4488 547.9069 556.7454 564.5273
#> 1985 590.1932 600.2107 611.4806 621.9800 629.8612 635.5527 639.4848
#> 1986 647.1107 646.9835 648.1251 651.8062 659.7331 668.7500 677.3090
#> 1987 703.0687 703.8874 706.4011 710.7287 716.7933 723.2959 728.3548
#> 1988 747.0877 754.6823 758.6458 759.8470 758.5857 756.6617 758.6509
#> 1989 787.9300 784.3449 782.2924 784.4335 790.0580 797.6288 804.5296
#> 1990 815.1236 816.9223 820.5208 824.9422 828.5787 830.8131 830.0138
#> 1991 823.5193 822.5066 822.5614 823.5336 826.9730 832.9334 839.6391
#> 1992 860.1441 864.4782 867.0668 867.7926 868.4994 869.7528 872.0361
#> 1993 884.1122 886.0296 888.8678 892.1340 893.7556 893.1806 891.3135
#> 1994 901.9831 906.8510 910.3225 912.4865 914.3848 917.0651 922.2012
#> 1995 933.3637 933.5731 938.2310 945.9664 953.3952 958.5753 961.2950
#> 1996 971.0399 971.3401 971.7342 972.5164 973.8616 975.0545 974.3662
#> 1997 967.7838 971.5350 973.2678 973.3591 974.9790 978.9540 984.0581
#> 1998 997.2415 997.3743 999.8649 1004.4566 1009.6485 1015.2631 1020.1678
#> 1999 1038.7254 1039.2019 1037.8463 1038.3668 1041.8716 1048.2719 1057.3997
#> 2000 1074.6140 1080.8931 1087.4445 1095.4638 1104.0200 1110.6335 1113.9968
#> 2001 1128.0249 1130.8177 1136.9392 1140.6839 1142.1090 1142.8506 1144.5974
#> 2002 1181.7393 1186.5206 1188.9181 1192.1846 1195.6908 1200.6014 1207.9087
#> 2003 1260.8824 1267.6421 1273.8295 1278.8051 1284.2755 1289.7706 1294.8380
#> 2004 1333.1753 1338.3093 1345.8059 1355.5295 1366.9878 1377.8001 1385.3081
#> 2005 1392.4503 1389.8997 1385.2683 1380.8591 1377.3673 1376.9966 1380.5528
#> 2006 1380.2916 1387.3415 1398.5500 1409.3835 1415.7647 1417.9376 1417.2443
#> 2007 1433.4930 1441.1823 1448.8879 1458.5260 1471.1088 1484.1563 1495.3979
#> 2008 1528.8771 1526.3858 1521.0243 1514.4016 1509.8919 1507.2434 1508.6551
#> 2009 1559.1936 1567.0935 1572.8798 1576.2199 1576.5864 1576.0230 1573.7841
#> 2010 1560.7677 1550.8381 1543.3420 1540.9041 1543.7216 1549.4946 1555.5850
#> 2011 1534.1555 1531.9071 1529.4026 1526.4197 1521.5278 1515.2128 1509.0566
#> 2012 1507.9353 1517.1258 1525.8547 1533.6003 1538.7680 1540.2603 1538.3190
#> 2013 1523.3436 1521.1137 1518.1472 1513.7359 1510.4123 1510.0511 1511.6092
#> 2014 1505.8189 1503.2206 1504.3506 1506.4647 1508.7807 1511.4399 1513.5703
#> 2015 1521.9322 1523.4604 1525.7922 1531.1163 1539.1194 1548.3359 1558.7293
#> 2016 1604.9908 1602.4616 1595.4172 1586.0690 1576.1816 1566.1880 1557.9160
#> 2017 1540.3165 1549.5424 1559.8416 1566.1639 1566.6342 1562.0955 1555.1216
#> Aug Sep Oct Nov Dec
#> 1982 494.1801 492.3454 487.5649 484.3054 484.6338
#> 1983 512.0796 516.0279 519.8319 522.4752 524.0864
#> 1984 570.2071 573.7676 575.4125 577.2838 582.0523
#> 1985 642.7917 645.2273 647.4582 648.0337 647.9295
#> 1986 685.3008 692.0373 697.1898 701.3603 703.5648
#> 1987 729.9434 729.4201 729.2137 732.1640 738.3674
#> 1988 764.9226 773.6153 782.4425 788.5955 789.9578
#> 1989 809.6214 813.3235 815.1347 815.1223 814.4282
#> 1990 827.0127 823.2620 820.8291 820.2630 822.3032
#> 1991 845.6198 850.8945 854.1429 855.6841 857.4731
#> 1992 875.5525 879.1870 882.0800 884.2732 884.1707
#> 1993 889.1061 886.6276 887.1560 891.0795 896.2862
#> 1994 929.0619 935.2239 937.5880 936.5172 934.7606
#> 1995 961.6451 963.0434 965.4486 968.0275 969.5027
#> 1996 970.7972 965.1632 961.4199 960.8795 963.6944
#> 1997 990.3254 996.2855 998.5630 998.2472 998.5402
#> 1998 1024.6400 1027.5494 1030.6820 1033.9446 1037.0511
#> 1999 1065.9959 1072.4856 1075.7269 1075.9588 1072.7769
#> 2000 1114.5689 1113.5674 1113.6102 1116.8862 1123.2065
#> 2001 1147.9822 1153.4453 1160.8738 1168.0531 1175.1897
#> 2002 1217.3961 1228.5466 1238.4462 1246.4771 1254.1158
#> 2003 1301.3925 1310.6686 1319.9787 1327.1247 1330.6477
#> 2004 1388.6168 1387.2256 1387.6884 1391.0740 1392.5169
#> 2005 1384.0256 1384.9608 1380.6550 1375.4039 1375.9441
#> 2006 1415.5131 1414.3555 1415.9911 1420.9595 1426.0610
#> 2007 1504.3033 1511.4876 1517.3394 1521.8845 1527.2877
#> 2008 1516.9330 1528.8439 1539.0051 1546.1290 1552.1924
#> 2009 1569.6415 1567.6048 1570.3348 1573.0643 1569.8358
#> 2010 1558.5893 1556.6240 1549.2444 1540.7244 1536.4873
#> 2011 1503.7305 1499.9448 1498.9432 1500.4005 1501.7981
#> 2012 1533.8484 1527.9859 1524.0638 1522.9803 1523.1034
#> 2013 1514.3497 1517.9286 1517.7686 1513.9166 1510.5018
#> 2014 1515.7317 1516.9847 1518.1428 1519.6370 1520.8240
#> 2015 1570.2753 1581.1962 1592.2694 1601.1666 1604.7084
#> 2016 1550.6404 1545.0351 1538.8459 1534.2685 1534.2199
#> 2017 1546.0510
compare(tc_2 * b1 , "b7")
#> [1] TRUE
si_2 <- 1 - tc_2
si_2 * b1 # b8
#> Jan Feb Mar Apr May
#> 1982 -18.1764686 19.7991942
#> 1983 -110.0404355 -117.6110797 -29.1316445 -1.3037913 4.8135647
#> 1984 -111.5366186 -114.7061493 -49.3533483 -53.1487757 49.9930754
#> 1985 -73.8932195 -147.7107406 -85.6805524 -34.2799629 70.4388188
#> 1986 -76.6107479 -168.7834557 -100.7250581 -57.5061620 91.8668920
#> 1987 -89.1686548 -190.6874404 -106.5011209 -36.6286817 -2.7933472
#> 1988 -116.0877205 -203.5823499 -80.5458466 -44.1469853 -17.7856636
#> 1989 -156.4299699 -232.3448709 -63.2924005 -86.8335163 -25.2580321
#> 1990 -136.9236148 -230.7223472 -93.7208319 -80.8422036 -13.0787333
#> 1991 -129.5192622 -217.8065914 -103.3613724 -75.3336339 1.2270063
#> 1992 -120.1440573 -198.5782340 -165.5668002 -36.3926471 10.1006068
#> 1993 -122.0122054 -243.0296430 -134.7677611 -51.4340242 12.8443733
#> 1994 -156.2830838 -242.4509755 -88.8225033 -80.7864796 -6.3847632
#> 1995 -180.9636517 -251.0731476 -127.0310398 -39.9663905 -26.1951561
#> 1996 -137.9398843 -234.2401280 -159.7341885 -77.3164087 -11.0616385
#> 1997 -126.8838117 -244.1350230 -115.3678003 -124.3590905 19.8210415
#> 1998 -79.9415030 -281.1742815 -176.9649165 -34.3565596 -39.4485387
#> 1999 -96.7253985 -300.8018804 -134.6463470 -85.1668007 -30.6716176
#> 2000 -149.7140027 -282.6930982 -185.5444590 -70.7638080 -51.7199624
#> 2001 -156.1248673 -316.2176975 -119.4392287 -101.4838671 -18.6089911
#> 2002 -153.8392796 -345.1206498 -145.0180591 -116.8846359 -4.7907999
#> 2003 -161.5823583 -367.1421069 -181.1294542 -56.4051416 -47.1755318
#> 2004 -150.2752590 -348.5093452 -214.4059212 -78.4295141 -86.6878451
#> 2005 -146.1502728 -352.5996850 -84.4682566 -227.1591109 -113.1672899
#> 2006 -186.5915528 -349.6415245 -194.0500121 -60.7835213 -148.1646817
#> 2007 -166.1929550 -394.1822823 -117.2879170 -155.9259891 -106.0088366
#> 2008 -131.0771088 -385.8858216 -169.3243286 -117.8015696 -88.7918791
#> 2009 -108.1935911 -510.4934932 -185.9798346 -67.1198953 -57.1863970
#> 2010 -91.6676551 -438.9381235 -163.4420188 -151.2041251 -116.5216452
#> 2011 -121.5554959 -414.4070549 -207.8026117 -53.8196846 -112.6278111
#> 2012 -145.5353046 -385.4257916 -176.6547095 -142.4003250 -81.8679545
#> 2013 -125.9436127 -407.5137112 -120.8472402 -174.6358630 -68.5123233
#> 2014 -54.8188912 -438.3206141 -211.1505783 -63.5646932 -96.9807260
#> 2015 -50.7322106 -469.6603880 -158.5921864 -88.9162589 -110.4194381
#> 2016 -85.7907753 -446.6616037 -143.9171518 -135.0689866 -126.4815884
#> 2017 -111.8164676 -457.1423868 -189.5415609 -43.5639476 -114.2342005
#> Jun Jul Aug Sep Oct
#> 1982 -43.8970391 -32.9921126 -55.7801050 -27.2454317 -34.8649125
#> 1983 -44.0551555 -40.2026621 -53.8795948 -33.3278857 -34.5318651
#> 1984 -56.3454166 -21.1273459 -66.8071010 -50.9675667 -18.8124641
#> 1985 -73.7526892 -36.6847860 -60.2917427 -82.1273489 -10.3582220
#> 1986 -115.3499551 -14.1090159 -104.2007942 -30.1372951 -31.5897613
#> 1987 -52.7959394 -7.4547509 -128.3434398 -57.1201292 -20.1136970
#> 1988 -34.6617370 -75.1509369 -114.0226230 -50.3152727 -52.8424932
#> 1989 -11.3288169 -89.4296034 -85.8213988 -55.4234577 -63.4347249
#> 1990 1.5869248 -119.7137856 -67.6126719 -82.1620372 -34.2291240
#> 1991 -86.0333588 -45.1391245 -75.2198137 -109.3944650 4.4571237
#> 1992 -43.7527784 -83.8360641 -151.9525021 -59.3869927 20.4199717
#> 1993 -6.0805897 -119.8134633 -160.4061399 -41.9275854 -0.2560126
#> 1994 -4.4651486 -139.3011830 -130.2618597 -48.2238998 -2.9879990
#> 1995 -51.7753166 -80.6949961 -87.7450910 -106.2434307 -44.8485715
#> 1996 -66.4545138 -66.3661733 -81.8972266 -131.4632146 -27.7199209
#> 1997 -148.7540370 -12.9581383 -154.3254317 -57.1855374 -21.6630156
#> 1998 -165.8631278 22.1321705 -154.7399670 -88.1493825 -9.3820488
#> 1999 -153.8718787 -2.8997072 -166.4958907 -70.1855552 -32.0268549
#> 2000 54.8665166 -254.6967639 -105.3689384 -58.9674043 -43.2101768
#> 2001 -117.9506458 -43.7973742 -184.9822462 -140.5453478 -28.8738249
#> 2002 -57.6013951 -132.2087241 -151.4961133 -168.4466077 -27.0462154
#> 2003 -51.8706425 -112.8380291 -200.1924915 -112.4686118 -3.8786900
#> 2004 6.2999164 -79.4080820 -221.8168278 -69.3256234 -29.3883826
#> 2005 77.2033598 -90.4527781 -173.3255912 -107.1608477 -66.2549619
#> 2006 11.0623648 -5.2442758 -176.3130588 -195.2554702 -71.3910628
#> 2007 7.3436723 -33.0979075 -188.8032629 -158.1875984 -76.7394194
#> 2008 -105.6434119 73.6448655 -248.5330029 -145.5439469 -86.6051256
#> 2009 -75.5229964 -3.0840881 -228.1415472 -167.7048264 -36.0348421
#> 2010 1.9053858 25.4149821 -234.5893390 -134.6239965 -84.3444376
#> 2011 -43.3127668 23.4433680 -210.2305394 -154.2447662 -94.2432152
#> 2012 76.1396654 -114.9190105 -174.8484215 -160.1858704 -81.4638254
#> 2013 27.3488773 -121.0092456 -177.1496674 -158.5285510 -54.4686108
#> 2014 -49.8399134 -11.9702832 -261.5317153 -160.5847103 -39.4428174
#> 2015 -67.4359487 -17.8293397 -238.3753196 -181.0962490 -25.9693782
#> 2016 29.9120329 -89.6160373 -256.7404030 -151.5351013 -41.4458743
#> 2017 -4.8954782 -109.6215511 -242.9509913
#> Nov Dec
#> 1982 38.5945852 404.6661840
#> 1983 46.2247879 439.6135712
#> 1984 45.9161917 457.3476972
#> 1985 49.0662718 539.5705460
#> 1986 -0.4602892 664.3351777
#> 1987 11.0359789 721.7326365
#> 1988 81.7044971 780.0422080
#> 1989 108.6776656 754.9718433
#> 1990 111.2370154 740.7968343
#> 1991 89.0158584 742.8268712
#> 1992 84.3267984 766.7292635
#> 1993 78.9204581 814.2137760
#> 1994 63.8827944 882.7394450
#> 1995 99.3724992 887.6973047
#> 1996 120.7205304 873.9056411
#> 1997 113.0527949 880.5598374
#> 1998 103.7554241 938.6489156
#> 1999 131.2412072 996.8231443
#> 2000 115.6137521 1054.2935304
#> 2001 176.7469189 1094.3103056
#> 2002 248.6228906 1084.4841513
#> 2003 201.0752559 1093.5522516
#> 2004 145.6260479 1108.2830607
#> 2005 164.9960575 1160.0558607
#> 2006 202.3404846 1185.0389948
#> 2007 166.0155197 1219.7122960
#> 2008 129.7709981 1333.9075549
#> 2009 163.5357444 1225.2641538
#> 2010 164.7755809 1215.9127030
#> 2011 159.5994852 1228.7019297
#> 2012 149.9196972 1230.1966005
#> 2013 154.9834303 1214.9982333
#> 2014 168.0630054 1236.0759793
#> 2015 129.3334405 1308.8916168
#> 2016 150.0315061 1316.1801312
#> 2017
compare(si_2 * b1 , "b8")
#> [1] TRUE
M3X5 <- macurves("S3x5")
M3X5_s <- to_seasonal(M3X5, 12)
s_2 <- M3X5_s * si_2
s_2_norm <- M2X12 * s_2
s_2_norm <- impute_last_obs(s_2_norm, n = 6, nperiod = 1)
s_2_demean <- s_2 - s_2_norm
s_2_f <- impute_last_obs(s_2_demean, n = 6, nperiod = 12)
s_2_f * b1 # b10
#> Jan Feb Mar Apr May
#> 1982 -25.3309999 32.0933639
#> 1983 -94.8072734 -132.5039611 -60.9632263 -27.5940738 38.4656216
#> 1984 -93.4405758 -138.0283886 -65.5174833 -30.9065186 43.4537317
#> 1985 -92.4337834 -149.1214588 -73.5035784 -36.5738092 44.6224107
#> 1986 -95.5356416 -166.0543860 -80.3480411 -42.5403612 36.7625160
#> 1987 -103.0997690 -185.0082069 -85.3507755 -50.8318103 24.4439216
#> 1988 -113.7534696 -201.8431048 -87.2564140 -57.6127241 7.2730851
#> 1989 -123.6783205 -211.2668323 -91.9945746 -62.2209366 -4.0749069
#> 1990 -129.8902698 -217.9137026 -99.8605123 -64.2529559 -7.6213725
#> 1991 -132.5851010 -221.7316606 -109.1395798 -64.6523764 -3.4888467
#> 1992 -135.8907643 -226.7066413 -116.9408237 -62.0710633 -0.7454942
#> 1993 -139.2985328 -229.9282476 -124.7429692 -58.8762733 -0.8425102
#> 1994 -142.8672723 -235.4919708 -127.5525229 -62.0264307 -1.6861693
#> 1995 -140.6730544 -242.1250096 -130.7447905 -66.7947310 -5.3598522
#> 1996 -133.9630161 -251.5667909 -133.1560787 -71.7115206 -9.8237326
#> 1997 -125.4175867 -259.6983452 -142.5984048 -72.8382258 -16.6374929
#> 1998 -121.0108043 -270.9625923 -146.4699895 -76.5219806 -20.2976231
#> 1999 -122.4555763 -285.1852187 -149.4387760 -79.2832036 -23.9936050
#> 2000 -131.1162123 -303.3536215 -148.9702556 -81.6413266 -26.6639892
#> 2001 -142.2276090 -319.1567974 -156.8612899 -82.5213435 -32.8067509
#> 2002 -150.8928624 -333.2099007 -156.1773556 -94.5541164 -41.4499832
#> 2003 -156.1909040 -343.8459604 -160.3630860 -102.2329381 -58.0002798
#> 2004 -158.6064505 -354.3417373 -157.1625026 -112.8418890 -77.3600917
#> 2005 -159.3833392 -361.1624942 -159.6694996 -116.8692263 -95.0632488
#> 2006 -155.2393337 -376.4166073 -154.9106033 -122.5613025 -102.4472736
#> 2007 -146.7424243 -394.1754213 -157.2765040 -120.6028258 -103.5612662
#> 2008 -136.0005933 -414.6812314 -161.4423165 -114.5721692 -99.9459013
#> 2009 -126.8608201 -423.9934186 -171.7282723 -108.5620128 -96.5213635
#> 2010 -120.9315101 -428.8009541 -173.4115152 -111.2051564 -91.6211973
#> 2011 -115.7193339 -424.8101620 -175.6855092 -113.6852201 -91.3279376
#> 2012 -108.8142014 -423.2709682 -173.4179330 -112.7458749 -92.0048849
#> 2013 -100.0959639 -422.5104882 -170.0823348 -113.4426486 -94.8050819
#> 2014 -92.5919383 -431.2902656 -166.0354812 -107.8903331 -97.3653281
#> 2015 -84.5750842 -441.3151357 -166.2890203 -100.5779022 -103.2950393
#> 2016 -80.0912322 -450.1595025 -168.6683661 -89.2050778 -109.2962109
#> 2017 -77.9742516 -454.1664141 -170.3570895 -84.6103901 -113.3055046
#> Jun Jul Aug Sep Oct
#> 1982 -51.5580052 -31.8380974 -58.6534670 -43.5331315 -26.1571304
#> 1983 -57.1820610 -31.9862541 -62.6764735 -45.0666053 -25.8073950
#> 1984 -63.4092885 -30.4625299 -71.4920497 -48.6091303 -24.6162610
#> 1985 -67.7702906 -30.7403735 -83.8238451 -50.8166491 -25.6678276
#> 1986 -65.1270320 -36.3862520 -94.1357535 -54.4425762 -29.0961350
#> 1987 -56.6319284 -48.5078110 -99.5763577 -55.7879556 -35.0015517
#> 1988 -46.6197286 -59.9422814 -99.0205364 -61.1712048 -36.9335754
#> 1989 -38.9643687 -72.0197920 -98.8115926 -66.2623046 -33.0542658
#> 1990 -34.2625768 -81.6023255 -101.2454485 -70.8823193 -24.1901127
#> 1991 -31.0879057 -92.8884678 -108.6951969 -69.8521049 -13.9945633
#> 1992 -32.0113641 -96.5945847 -116.1543793 -70.5384230 -7.2957803
#> 1993 -33.8325641 -99.0098491 -121.0634036 -73.4060180 -6.3391974
#> 1994 -43.0484020 -93.2625481 -123.3627004 -76.6155965 -12.1867028
#> 1995 -59.4512128 -80.6716864 -123.8429421 -81.1890320 -17.9359129
#> 1996 -87.1223359 -57.5067563 -126.2999731 -85.5855448 -23.1403084
#> 1997 -100.7441783 -50.6482746 -129.3214929 -86.8954992 -25.6061099
#> 1998 -107.2176678 -51.8660627 -139.6412972 -85.5967913 -27.3710320
#> 1999 -97.7538610 -70.1370216 -147.2607713 -90.2287768 -27.6337245
#> 2000 -87.7146377 -85.6538144 -157.0449390 -99.7049349 -27.2869984
#> 2001 -63.1943052 -107.3187053 -163.3619350 -108.9231389 -27.2478711
#> 2002 -43.2126767 -110.1222693 -174.5533067 -113.5929573 -28.1129888
#> 2003 -22.1494111 -101.3440372 -181.9455544 -120.4423747 -32.5258204
#> 2004 -7.4047580 -81.0327125 -188.4180208 -126.5456477 -40.1523819
#> 2005 2.3584815 -59.5807655 -193.5521705 -131.6454306 -51.9507661
#> 2006 -2.2316344 -35.5915732 -199.9044269 -139.5459505 -61.0656919
#> 2007 -16.3822971 -10.3131253 -207.5676347 -149.8762401 -68.0845230
#> 2008 -30.5119057 4.9881727 -214.1734615 -155.6008573 -71.0885228
#> 2009 -34.5104510 9.6632936 -219.1383904 -154.9145233 -74.2017143
#> 2010 -24.6984141 -6.3535300 -215.5559880 -153.3736462 -74.0508431
#> 2011 -9.5888516 -25.3978932 -212.0597208 -153.9334798 -72.8000472
#> 2012 -3.5914372 -42.1226284 -210.1072365 -157.7638732 -67.3093996
#> 2013 -1.7274909 -53.7611458 -215.8578673 -160.0126969 -60.2298887
#> 2014 -6.8238388 -63.8845959 -223.7922058 -162.9476846 -49.8263996
#> 2015 -10.6308210 -66.4783415 -235.8340136 -162.7649201 -42.2357143
#> 2016 -17.3317478 -64.2804670 -243.9402740 -162.9686889 -38.0389358
#> 2017 -18.7648967 -62.5679202 -247.6187409
#> Nov Dec
#> 1982 44.6479839 449.9493658
#> 1983 41.8696870 468.8986557
#> 1984 37.2538632 508.9761226
#> 1985 34.7750371 566.5014430
#> 1986 39.5183326 630.1424226
#> 1987 50.2134775 686.2290368
#> 1988 64.3993582 724.4655805
#> 1989 79.3343640 745.8651875
#> 1990 89.8823887 756.0165090
#> 1991 91.5136365 769.9749487
#> 1992 87.5264250 790.6841665
#> 1993 85.9292510 818.1365901
#> 1994 89.1530511 844.6477366
#> 1995 94.6872760 869.6232842
#> 1996 102.8331315 892.7078147
#> 1997 110.0216813 919.2499713
#> 1998 119.4367599 952.0949678
#> 1999 133.2827565 991.4102721
#> 2000 153.0082760 1030.0368607
#> 2001 169.9059936 1062.0955740
#> 2002 180.9376484 1087.4931585
#> 2003 186.9298245 1108.4480955
#> 2004 186.1592063 1130.4571844
#> 2005 177.1085586 1161.1923800
#> 2006 167.6066328 1193.7126062
#> 2007 163.7734197 1220.7873036
#> 2008 162.2805753 1234.9944738
#> 2009 158.5778422 1241.9182656
#> 2010 156.4018121 1237.6532587
#> 2011 156.8765806 1231.1447120
#> 2012 156.3427928 1230.2440175
#> 2013 153.2538480 1242.8809986
#> 2014 150.6042613 1257.8915970
#> 2015 149.9371535 1270.2649518
#> 2016 150.3874691 1276.8386358
#> 2017
compare(s_2_f * b1 , "b10")
#> [1] TRUE
sa_2 <- 1 - s_2_f
sa_2 * b1 # b11
#> Jan Feb Mar Apr May Jun Jul
#> 1982 485.4310 470.5066 495.3580 490.9381
#> 1983 474.0073 510.5040 533.0632 530.9941 472.1344 519.5821 500.2863
#> 1984 508.1406 552.5284 550.2175 518.2065 554.4463 563.8093 573.8625
#> 1985 608.7338 601.6215 599.3036 624.2738 655.6776 629.5703 633.5404
#> 1986 666.0356 644.2544 627.7480 636.8404 714.8375 618.5270 699.5863
#> 1987 716.9998 698.2082 685.2508 724.9318 689.5561 727.1319 769.4078
#> 1988 744.7535 752.9431 765.3564 773.3127 733.5269 768.6197 743.4423
#> 1989 755.1783 763.2668 810.9946 759.8209 768.8749 825.2644 787.1198
#> 1990 808.0903 804.1137 826.6605 808.3530 823.1214 866.6626 791.9023
#> 1991 826.5851 826.4317 828.3396 812.8524 831.6888 777.9879 887.3885
#> 1992 875.8908 892.6066 818.4408 893.4711 879.3455 858.0114 884.7946
#> 1993 901.3985 872.9282 878.8430 899.5763 907.4425 920.9326 870.5098
#> 1994 888.5673 899.8920 949.0525 893.7264 909.6862 955.6484 876.1625
#> 1995 893.0731 924.6250 941.9448 972.7947 932.5599 966.2512 961.2717
#> 1996 967.0630 988.6668 945.1561 966.9115 972.6237 995.7223 965.5068
#> 1997 966.3176 987.0983 1000.4984 921.8382 1011.4375 930.9442 1021.7483
#> 1998 1038.3108 987.1626 969.3700 1046.6220 990.4976 956.6177 1094.1661
#> 1999 1064.4556 1023.5852 1052.6388 1032.4832 1035.1936 992.1539 1124.6370
#> 2000 1056.0162 1101.5536 1050.8703 1106.3413 1078.9640 1253.2146 944.9538
#> 2001 1114.1276 1133.7568 1174.3613 1121.7213 1156.3068 1088.0943 1208.1187
#> 2002 1178.7929 1174.6099 1200.0774 1169.8541 1232.3500 1186.2127 1185.8223
#> 2003 1255.4909 1244.3460 1253.0631 1324.6329 1295.1003 1260.0494 1283.3440
#> 2004 1341.5065 1344.1417 1288.5625 1389.9419 1357.6601 1391.5048 1386.9327
#> 2005 1405.6833 1398.4625 1460.4695 1270.5692 1359.2632 1451.8415 1349.6808
#> 2006 1348.9393 1414.1166 1359.4106 1471.1613 1370.0473 1431.2316 1447.5916
#> 2007 1414.0424 1441.1754 1488.8765 1423.2028 1468.6613 1507.8823 1472.6131
#> 2008 1533.8006 1555.1812 1513.1423 1511.1722 1521.0459 1432.1119 1577.3118
#> 2009 1577.8608 1480.5934 1558.6283 1617.6620 1615.9214 1535.0105 1561.0367
#> 2010 1590.0315 1540.7010 1553.3115 1500.9052 1518.8212 1576.0984 1587.3535
#> 2011 1528.3193 1542.3102 1497.2855 1586.2852 1500.2279 1481.4889 1557.8979
#> 2012 1471.2142 1554.9710 1522.6179 1503.9459 1548.9049 1619.9914 1465.5226
#> 2013 1497.4960 1536.1105 1567.3823 1452.5426 1536.7051 1539.1275 1444.3611
#> 2014 1543.5919 1496.1903 1459.2355 1550.7903 1509.1653 1468.4238 1565.4846
#> 2015 1555.7751 1495.1151 1533.4890 1542.7779 1531.9950 1491.5308 1607.3783
#> 2016 1599.2912 1605.9595 1620.1684 1540.2051 1558.9962 1613.4317 1532.5805
#> 2017 1506.4743 1546.5664 1540.6571 1607.2104 1565.7055 1575.9649 1508.0679
#> Aug Sep Oct Nov Dec
#> 1982 497.0535 508.6331 478.8571 478.2520 439.3506
#> 1983 520.8765 527.7666 511.1074 526.8303 494.8013
#> 1984 574.8920 571.4091 581.2163 585.9461 530.4239
#> 1985 666.3238 613.9166 662.7678 662.3250 620.9986
#> 1986 675.2358 716.3426 694.6961 661.3817 737.7576
#> 1987 701.1764 728.0880 744.1016 692.9865 773.8710
#> 1988 749.9205 784.4712 766.5336 805.9006 845.5344
#> 1989 822.6116 824.1623 784.7543 844.4656 823.5348
#> 1990 860.6454 811.9823 810.7901 841.6176 807.0835
#> 1991 879.0952 811.3521 872.5946 853.1864 830.3251
#> 1992 839.7544 890.3384 909.7958 881.0736 860.2158
#> 1993 849.7634 918.1060 893.2392 884.0707 892.3634
#> 1994 922.1627 963.6156 946.7867 911.2469 972.8523
#> 1995 997.7429 937.9890 938.5359 972.7127 987.5767
#> 1996 1015.2000 919.2855 956.8403 978.7669 944.8922
#> 1997 965.3215 1025.9955 1002.5061 1001.2783 959.8500
#> 1998 1009.5413 1024.9968 1048.6710 1018.2632 1023.6050
#> 1999 1046.7608 1092.5288 1071.3337 1073.9172 1078.1897
#> 2000 1166.2449 1154.3049 1097.6870 1079.4917 1147.4631
#> 2001 1126.3619 1121.8231 1159.2479 1174.8940 1207.4044
#> 2002 1240.4533 1173.6930 1239.5130 1314.1624 1251.1068
#> 2003 1283.1456 1318.6424 1348.6258 1341.2702 1315.7519
#> 2004 1355.2180 1444.4456 1398.4524 1350.5408 1370.3428
#> 2005 1404.2522 1409.4454 1366.3508 1363.2914 1374.8076
#> 2006 1439.1044 1358.6460 1405.6657 1455.6934 1417.3874
#> 2007 1523.0676 1503.1762 1508.6845 1524.1266 1526.2127
#> 2008 1482.5735 1538.9009 1523.4885 1513.6194 1651.1055
#> 2009 1560.6384 1554.8145 1608.5017 1578.0222 1553.1817
#> 2010 1539.5560 1575.3736 1538.9508 1549.0982 1514.7467
#> 2011 1505.5597 1499.6335 1477.5000 1503.1234 1499.3553
#> 2012 1569.1072 1525.5639 1509.9094 1516.5572 1523.0560
#> 2013 1553.0579 1519.4127 1523.5299 1515.6462 1482.6190
#> 2014 1477.9922 1519.3477 1528.5264 1537.0957 1499.0084
#> 2015 1567.7340 1562.8649 1608.5357 1580.5628 1643.3350
#> 2016 1537.8403 1556.4687 1535.4389 1533.9125 1573.5614
#> 2017 1550.7187
compare(sa_2 * b1 , "b11")
#> [1] TRUE
if (!exists("sa_2")) {
# we redefined the moving averages if they don't exist
tc_1 <- M2X12 <- (simple_ma(12, - 6) + simple_ma(12, - 5))/2
si_1 <- 1 - tc_1
M3X3 <- macurves("S3x3")
M3X3_s <- to_seasonal(M3X3, 12)
s_1 <- M3X3_s * si_1
s_1_norm <- M2X12 * s_1
s_1_norm <- impute_last_obs(s_1_norm, n = 6, nperiod = 1)
s_1_demean <- s_1 - s_1_norm
s_1_f <- impute_last_obs(s_1_demean, n = 6, nperiod = 12)
sa_1 <- 1- s_1_f
h13 <- lp_filter(horizon = 6, ic = 3.5)
tc_2 <- h13 * sa_1
si_2 <- 1 - tc_2
M3X5 <- macurves("S3x5")
M3X5_s <- to_seasonal(M3X5, 12)
s_2 <- M3X5_s * si_2
s_2_norm <- M2X12 * s_2
s_2_norm <- impute_last_obs(s_2_norm, n = 6, nperiod = 1)
s_2_demean <- s_2 - s_2_norm
s_2_f <- impute_last_obs(s_2_demean, n = 6, nperiod = 12)
sa_2 <- 1 - s_2_f
}
compare <- function(x, id, na.rm = TRUE){
if (na.rm)
x <- na.omit(x)
res <- cbind(x, x11_step$user_defined[[id]])
all.equal(res[,1], res[,2], check.attributes = FALSE)
}
ud_var <- c("b1", "b2", "b3", "b4", "b4a", "b4d", "b5",
"b6", "b7", "b8", "b9", "b10", "b11", "b13", "b17", "b20", "c1",
"c2", "c4", "c5", "c6", "c7", "c9", "c10", "c11", "c13",
"c17", "c20", "d1", "d2", "d4", "d5", "d6", "d7", "d8",
"d10", "d11", "d12", "d13", "d10bis", "d11bis")
b1 <- rjd3toolkit::ABS$X0.2.09.10.M # b1
x11_step <- x11plus_trend(b1, trend.coefs = lp_filter(horizon = 6, ic = 3.5),
mul = FALSE,
seas.s0 = "S3X3",
seas.s1 = "S3X5",
userdefined = ud_var)
# B tables
compare(b1, "b1")
#> [1] TRUE
b2 <- tc_1 * b1
compare(b2, "b2")
#> [1] TRUE
b3 <- si_1 * b1
compare(b3, "b3")
#> [1] TRUE
b4a <- M3X3_s *
b3
#compare(b4a, "b4a")
b4norm <- b4a -
impute_last_obs(finite_filters(M2X12), n = 6, nperiod = 1) *
b4a
b4d <- b3 - b4norm
#compare(b4d, "b4d")
corr <- x11_extreme_values_corr(x = b4d,
corrected_s = b3, mul = FALSE, start = 6)
b4 <- corr[, "correction_factors"]
b4g <- b3
b4g[!is.nan(b4)] <- b4[!is.nan(b4)]
compare(window(b4, start = start(na.omit(b3)), end = end(na.omit(b3))),
"b4",
na.rm = FALSE)
#> [1] TRUE
b5a <- M3X3_s * b4g
b5 <- b5a -
impute_last_obs(finite_filters(M2X12), n = 6, nperiod = 1) *
b5a
b5 <- filter(b5, impute_last_obs(moving_average(c(rep(0,6),1, rep(0,6)), lags = -6),
n = 6, nperiod = 12), remove_missing = FALSE)
compare(b5, "b5")
#> [1] TRUE
b6 <- b1 - b5
compare(b6, "b6")
#> [1] TRUE
b7 <- h13 * b6
compare(b7, "b7")
#> [1] TRUE
b8 <- b1 - b7
compare(b8, "b8")
#> [1] TRUE
b9a <- M3X5_s * b8
b9c <- b9a - impute_last_obs(finite_filters(M2X12), n = 6, nperiod = 1) *
b9a
b9d <- b8 - b9c
corr <- x11_extreme_values_corr(x = b9d,
corrected_s = b8, mul = FALSE, start = 0)
b9 <- corr[, "correction_factors"]
b9g <- b8
b9g[!is.nan(b9)] <- b9[!is.nan(b9)]
compare(b9, "b9", na.rm = FALSE)
#> [1] TRUE
b10a <- M3X5_s * b9g
b10 <- b10a - impute_last_obs(finite_filters(M2X12), n = 6, nperiod = 1) *
b10a
b11 <- b1 - b10
b13 <- b11 - b7
compare(b10, "b10")
#> [1] TRUE
compare(b11, "b11")
#> [1] TRUE
compare(b13, "b13")
#> [1] TRUE
corr <- x11_extreme_values_corr(x = b13, mul = FALSE, start = 0)
b17 <- corr[, "obs_weight"]
b20 <- corr[, "correction_factors"]
compare(b17, "b17")
#> [1] TRUE
compare(b20, "b20")
#> [1] TRUE
# C tables
c1 <- b1 - b20
compare(c1, "c1")
#> [1] TRUE
c2 <- tc_1 * c1
compare(c2, "c2")
#> [1] TRUE
c4 <- c1 - c2
compare(c4, "c4")
#> [1] TRUE
c5 <- s_1_f * c1
compare(c5, "c5")
#> [1] TRUE
c6 <- sa_1 * c1
compare(c6 , "c6")
#> [1] TRUE
c7 <- tc_2 * c1
compare(c7 , "c7")
#> [1] TRUE
c9 <- si_2 * c1
compare(c9 , "c9")
#> [1] TRUE
c10 <- s_2_f * c1
compare(c10 , "c10")
#> [1] TRUE
c11 <- b1 - c10
compare(c11 , "c11")
#> [1] TRUE
c13 <- c11 - c7
compare(c13 , "c13")
#> [1] TRUE
corr <- x11_extreme_values_corr(x = c13, mul = FALSE, start = 0)
c17 <- corr[, "obs_weight"]
c20 <- corr[, "correction_factors"]
compare(c17, "c17")
#> [1] TRUE
compare(c20, "c20")
#> [1] TRUE
# D tables
d1 <- b1 - c20
compare(d1, "d1")
#> [1] TRUE
d2 <- tc_1 * d1
compare(d2, "d2")
#> [1] TRUE
d4 <- d1 - d2
compare(d4, "d4")
#> [1] TRUE
d5 <- s_1_f * d1
compare(d5, "d5")
#> [1] TRUE
d6 <- sa_1 * d1
compare(d6 , "d6")
#> [1] TRUE
d7 <- tc_2 * d1
compare(d7 , "d7")
#> [1] TRUE
d8 <- b1 - d7
compare(d8 , "d8")
#> [1] TRUE
d9bis <- d1 - d7
d10bis <- M3X5_s * d9bis
#compare(d10bis , "d10bis")
d10 <- d10bis - impute_last_obs(finite_filters(M2X12), n = 6, nperiod = 1) *
d10bis
compare(d10 , "d10")
#> [1] TRUE
d11bis <- d1 - d10
#compare(d11bis , "d11bis")
d11 <- b1 - d10
compare(d11 , "d11")
#> [1] TRUE
d12 <- h13 * d11bis
compare(d12 , "d12")
#> [1] TRUE
d13 <- d11 - d12
compare(d13 , "d13")
#> [1] TRUE