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Some interesting/difficult series in Swiss QNA
Hello all,
in case we find a nice solution to seasonally adjust these series, we would be very happy to get your opinion.
# Changing patterns
s1 <- structure(c(2748.95219967717, 2777.95329628036, 2824.99428261349,
2806.85702451908, 2794.98210710454, 2809.80672061611, 2830.12065249941,
2830.67076629774, 2875.89964205303, 2936.0964610155, 3009.72283941721,
3027.36101839635, 3073.5548494395, 3133.52680818535, 3199.44568067348,
3199.10875771368, 3239.2068253766, 3289.66418698246, 3382.62215815776,
3436.97482495648, 3499.48814679899, 3581.09212363942, 3696.62707620236,
3782.94026232923, 3895.04650276686, 4007.44225464614, 4124.38390158616,
4203.01323307555, 4308.41615550041, 4414.0746525967, 4512.22669372636,
4583.53326237762, 4658.19984207685, 4775.27077591568, 4922.21553716941,
5089.79785236576, 5286.4397856178, 5429.91022884239, 5484.78630079163,
5483.09429665109, 5414.69166670325, 5402.80486307928, 5404.13444041258,
5434.60084058708, 5503.94494744447, 5571.26489918703, 5632.28832575799,
5682.65149739572, 5749.91994210101, 5819.49035278328, 5864.47884701221,
5900.88924419161, 5945.90913210023, 6011.9862571386, 6034.35830195975,
5986.28979778012, 5957.02616623421, 5965.59962611145, 5989.28823627077,
5966.43061353447, 5967.67898552472, 5995.53839377579, 6013.72103927692,
6023.79217832407, 6036.34154976122, 6064.99790696756, 6071.72556042416,
6064.41448718306, 6041.49519736445, 6262.93048287573, 6173.94638682299,
6836.06387522193, 6156.36518776499, 6082.11605321781, 6133.24541038409,
6887.43633057021, 6288.98647546723, 6648.48678751701, 6429.18198281063,
7442.85274421962, 6258.03450587738, 6831.15627229479, 6727.24907029709,
7551.03780435274, 6811.11527188242, 7106.63019270313, 7510.58546275778,
8651.61993503457, 8238.85580739585, 8235.46827753886, 8747.20756013025,
9179.76550911473, 8893.45512572506, 8595.66036506266, 8302.09965228383,
8819.32423513414, 8360.77329379198, 8319.04342456684, 8262.17122736939,
10115.0415213293, 8868.24408584367, 8506.76235233728, 8907.0941588898,
9299.60083840286, 8612.77397572337, 9070.57087140001),
.Tsp = c(1995, 2021.25, 4),
class = "ts"
)
plot.ts(s1)
# Bi-annual seasonality
s2 <- structure(c(469.204152273264, 472.1356798074, 470.231686255493,
483.146161052509, 490.227597091944, 484.74825848541, 487.503785112587,
474.52887188617, 458.626179769529, 446.900193750669, 461.321662682486,
454.158066349904, 530.152280373854, 597.768775620842, 564.541613521487,
521.248578290263, 488.417216740774, 496.176369256206, 507.548362175268,
516.057255142671, 668.915656812781, 825.698731406419, 968.872880778632,
761.884607641139, 567.803025862969, 555.517149760278, 566.495651909688,
588.246689444436, 649.184999678456, 726.988221416075, 701.948795849455,
689.185289695416, 681.931374995928, 693.24511894822, 719.38133184609,
745.824128557345, 938.17756099776, 1127.97793471303, 1318.07302209996,
1081.03756825206, 861.616165897904, 863.223433526174, 882.549128921091,
880.65373685798, 1009.9491742249, 1085.31813582232, 1043.8210931877,
978.337601059653, 937.056844080493, 946.470914551307, 963.479364651164,
979.934959168939, 1210.57894146597, 1430.63523525091, 1653.32436800723,
1375.11620418815, 1087.17669309632, 1113.04338250164, 1112.36417754144,
1100.67746377289, 1178.13539075908, 1256.71790484714, 1179.856018912,
1079.20112283432, 1022.34300834865, 1024.94289447601, 1022.66333858163,
994.334523998076, 1266.74925426533, 1542.86474638389, 1791.9101658155,
1382.77011170323, 996.751779567994, 1002.01677384741, 990.497130119013,
979.795900742499, 1295.94321758486, 1619.54887005365, 1402.29684472329,
1142.59756476717, 924.334693632299, 944.716523040673, 970.453145734395,
986.248398065193, 1333.2535405725, 1681.81312950911, 2024.90382677556,
1560.8375538191, 1119.0053543496, 1163.78280619748, 1218.72154584179,
1232.60138767892, 1610.99536387937, 2020.18689698069, 1748.58912544328,
1480.58816184383, 1213.10419793364, 1223.19786318543, 1227.01894252051,
1216.00675333597, 1081.2731671739, 651.073841824608, 1128.35054692243,
992.739965079948, 937.419235101413, 1435.25500300426),
.Tsp = c(1995,2021.25, 4),
class = "ts"
)
plot.ts(s2)
# Changing specification from Level to Log during Covid
s3 <- structure(c(2224.00145592074, 1970.16909994317, 2875.24873118189,
1489.2259225028, 2217.77761272515, 1937.3236244396, 2915.56169175751,
1680.96999510892, 2614.73836344364, 2358.25126973773, 3447.68253467262,
2040.35761571327, 2804.24206476036, 2506.59369666525, 3519.16968243224,
2015.62978635932, 2813.78621445356, 2537.78703939676, 3537.87756326434,
2051.09323650229, 2942.70262472144, 2572.2322704062, 3672.91875090217,
2085.93484515553, 3132.04906675785, 2720.27042338961, 3763.62122501151,
2193.35310864108, 3146.98221694146, 2653.76576376071, 3638.90049031183,
2149.71419500596, 2955.65534672133, 2434.92529337123, 3416.3283289035,
1962.68182253025, 2771.59714181884, 2429.48545063095, 3325.04574297066,
1874.40880521532, 2892.90796131075, 2325.682798205, 3445.47890730444,
1963.89065167046, 2915.00685474643, 2522.61537964188, 3599.81536580797,
2067.53031784622, 3005.74258137271, 2656.40245261685, 3765.21018183305,
2268.32487808101, 3329.63989651068, 2718.82000350597, 3942.03920743922,
2301.78818495244, 3113.87560284163, 2679.67763629842, 3971.31242543785,
2295.37099194112, 3183.10219880644, 2755.37902276587, 4066.66380022911,
2332.26044141169, 3227.80134903588, 2883.50034912711, 4008.93025963956,
2324.45883584687, 3130.23959388562, 2769.82651161685, 3852.15887166433,
2350.15977482874, 3144.64281682951, 2828.59519441037, 4059.31897513095,
2411.4490325736, 3166.60219839768, 2872.71512212918, 4089.4205169342,
2488.46878336679, 3110.67690089301, 2830.03487294456, 4073.05597920744,
2363.90648929206, 3090.97691241218, 2784.00260350715, 4063.09248806243,
2362.84975747746, 3040.02676080475, 2950.56848986838, 4138.90468814108,
2421.17370728401, 3169.86711432648, 3029.39540048446, 4260.43972053279,
2549.48288262933, 3131.34485946874, 3172.95468578212, 4337.97064698468,
2626.89363930259, 2410.45386589763, 1002.41883823471, 3071.33600255101,
1419.21663205115, 926.510510652244, 1377.87501251091),
.Tsp = c(1995,2021.25, 4),
class = "ts")
plot.ts(s3)
# Large revisions due to model
s4 <- structure(c(3937.80176095905, 3753.30756093405, 3838.22467870605,
3653.75097953255, 4329.38992713028, 4190.32277266856, 4276.50936580442,
4267.53643502466, 4858.53324035314, 5110.48515864402, 5031.34673845616,
5291.58670089559, 5836.71817276752, 5554.87044315168, 5528.25475969655,
5383.18868843163, 5968.09117609059, 5670.70810348975, 6234.31808663314,
7023.85539593159, 7431.00640673489, 6706.46096564077, 7139.39665328307,
6765.12773582756, 8615.98205649115, 8317.68001093172, 8173.99280959904,
7927.3403743894, 9200.27240847718, 9499.13164036878, 9401.03702939016,
8386.52900842303, 9812.30558904616, 9043.85229846914, 9207.68083753431,
9196.09354346217, 10961.8834440798, 10176.29548198, 10417.0966444502,
9865.90362818397, 11579.1404849843, 11655.224174793, 11683.8459030742,
11430.6803505265, 13652.9711091128, 12837.1795822732, 13572.9576884898,
13617.747713284, 15119.3820373629, 14173.3900314132, 14784.4682725528,
13744.8322312044, 15352.1249999132, 16013.4746709293, 15602.2818715209,
13011.3055843785, 14667.1476962317, 14320.537649306, 15679.6785244463,
14994.7550450947, 16882.5114177377, 15954.5868929309, 16537.2164242669,
15802.4933169269, 17636.3298744937, 17516.0182338752, 16937.2408216408,
16901.0888254583, 18536.5810703164, 17544.8902552325, 17615.7818477101,
17532.6162607638, 18565.3717458897, 18887.5727639645, 18457.9115208314,
17894.1768898062, 20213.2196310496, 19243.9169501724, 19997.6863419221,
19470.0496513446, 20897.3407369083, 19943.5646466971, 20616.7807432764,
22836.0951981183, 23273.639450895, 24671.2019939183, 24385.1352550811,
24042.8000602485, 27184.1173332545, 25809.6050452171, 25118.6153270455,
24929.8938304959, 27925.9632063132, 27351.1352809109, 25303.6434807121,
29419.5533537817, 31153.1777231213, 30552.0665461881, 31454.6920440232,
30740.3899048503, 35890.8320853405, 33031.5789572423, 31471.1783572708,
31881.5792015077, 36700.3827370838, 36957.0593207029),
.Tsp = c(1995, 2021.25, 4), class = "ts")
plot.ts(s4)
# Does this series even have a season
s5 <- structure(c(126.533263546597, 124.827191097829, 126.530129977648,
123.132682302581, 121.889433661116, 119.032128204219, 117.81696399102,
111.741522359767, 100.598753021161, 101.240261681216, 107.746035875873,
102.728081199004, 102.33166305119, 102.386412080762, 98.1914563918161,
99.277072071332, 98.8066317068652, 93.0092378565665, 100.332270141323,
92.884860387453, 88.8063680906986, 87.7204614544844, 96.1082053077533,
86.8478289306274, 90.2429264151742, 90.090278512047, 115.688408457459,
95.0807586878487, 96.3507434164097, 83.1617540355808, 80.9117091920351,
84.9250177927506, 86.6943704353939, 74.7603423427271, 76.7457472610892,
93.2627225297734, 87.046614892611, 92.6678437853354, 88.506249350551,
83.902937756436, 75.9450598243245, 80.0921563585365, 78.7503776797469,
112.235482933208, 73.059813277435, 71.9963100464643, 73.5132216882338,
71.1200355138491, 65.3682541726117, 58.2612668739728, 71.8617129435073,
55.8662542698461, 186.740172274869, 97.8441206227095, 109.783906359741,
102.209392238934, 68.7167003187089, 69.9753229623161, 101.382156997142,
160.027341740454, 61.7050320683144, 53.2333762663846, 55.2955996844403,
54.678765605391, 54.3000509076175, 60.0196670456877, 59.1241498250882,
54.9951203824529, 51.7738063358092, 59.8875664755438, 55.8376396753865,
64.2376298389621, 50.3308524319249, 53.4497711291206, 53.5274770975974,
51.1841122044864, 47.4910917857037, 51.2332005666284, 51.3020429388563,
49.3421478254651, 48.493310722297, 53.4821873909699, 56.131895462165,
56.5492679345682, 58.334516837374, 59.1749368196284, 69.1010577701589,
131.637314117131, 118.77433258926, 153.724276549064, 168.11581226013,
142.203101991527, 130.227497012326, 167.306452611908, 180.071154640537,
154.659115395262, 139.677951497382, 173.500262902165, 188.345555189974,
149.736031707187, 123.0141285209, 48.947507302937, 50.5386426051299,
67.3925042063494, 77.5061798672659, 62.7030348881647), .Tsp = c(1995,
2021.25, 4), class = "ts")
plot.ts(s5)
# Similar to R&D
s6 <- structure(c(684.121873326244, 702.380296427645, 701.117512233649,
680.582402941876, 641.249867121037, 644.196349305869, 688.770040098114,
774.967221348301, 903.422230335338, 963.949974164205, 956.11132313431,
880.144164545896, 736.954090914206, 655.246866236813, 634.237808790488,
673.147760497642, 771.207850542923, 847.872748710588, 903.641260561925,
938.851581154764, 953.687796408554, 939.182700468676, 895.945612510625,
825.447933332748, 729.923213822089, 716.2527030071, 782.915275687664,
936.706616313436, 1156.38238030641, 1290.79185168014, 1405.29060469231,
1389.05603742484, 1273.18363999607, 1393.37653278596, 1569.04888032381,
1893.6820906974, 2296.66501255144, 2550.54108032214, 2719.36720937423,
2827.0637303227, 2708.47907531554, 2680.21063156459, 2705.951102228,
2968.20391125755, 4258.58179931538, 3017.95670918887, 2986.67269322981,
4206.90088830461, 3950.71099789685, 4070.51346445126, 4932.99055984922,
3578.35409168576, 4357.66150354392, 5773.33478889362, 6054.19659248602,
3604.67457415649, 5669.50396389008, 5504.21194090622, 7096.0271083747,
6349.57188319242, 5244.04250891635, 8793.70882600001, 6180.2937667387,
9333.85926304771, 10211.3315623662, 8370.74580955524, 4929.63106191969,
4454.10112947704, 6467.80956335861, 7450.18837137925, 5908.43478235912,
7200.46919830961, 6120.77629614074, 5431.05484156181, 6621.42451940549,
5093.58532954918, 6675.58132789848, 7458.24159879014, 5569.36871503762,
5458.00403035996, 7553.16837101911, 8558.22629657546, 7916.83308342004,
7202.00874298539, 10187.5046124712, 9953.71436150321, 7733.4414444647,
9002.18277437977, 7000.56661398864, 9274.09402608789, 11973.0732700555,
9389.20039059625, 11939.9807281783, 9736.26093543729, 8903.26744661931,
8813.27488727661, 8942.61903891382, 10303.7859232127, 9623.98160898762,
9091.51718532616, 8298.23927484928, 11743.3805110921, 11823.6994673069,
9510.64972519834, 8965.01016971329, 7777.62638891031), .Tsp = c(1995,
2021.25, 4), class = "ts", tstype = "PCY")
plot.ts(s6)
# Is there even a seasonality
s7 <- structure(c(2595.68650497152, 2690.86419454777, 2081.86200909916,
2518.80300572038, 2792.70550033098, 2847.93679306625, 2356.29134534318,
2626.15850353984, 2492.33139179912, 3028.88972428224, 2498.21977208649,
2626.43012231635, 2767.73390910286, 3048.98476615721, 2401.99263626848,
3716.32637953541, 3978.80277153656, 3440.92086407035, 3091.61588254979,
3354.67881070396, 3267.3340115993, 3540.2415306051, 2716.41741157516,
3621.66842359284, 3115.260339444, 3459.41704383036, 2715.8901867553,
2970.33840437219, 2774.00555759906, 3205.23985806043, 2777.38341950782,
2667.28645604004, 2773.01805310978, 3019.32331277437, 2999.11059476684,
3788.82840739972, 3048.40306249331, 3649.85416602646, 3119.75204295131,
3051.40938468299, 3013.77487602464, 3489.90202176545, 2805.55893440501,
3314.81940759625, 3411.06909051812, 3712.06521384474, 2921.20971760409,
3605.8170334435, 3436.29910974707, 4062.04554438963, 3159.18456501798,
3723.65427668062, 3520.11673109805, 4309.41444907176, 3175.28563546475,
3102.76779344007, 2956.04893167044, 3338.47976217506, 3132.42368790036,
3408.89875050527, 3597.90310219004, 3832.94874894482, 3253.00803658214,
3958.23642506736, 4238.68729394803, 3951.29345258024, 3624.54970496882,
4020.91847646545, 4641.43562443613, 4242.49101296001, 3379.12338369251,
3874.26387927676, 3531.03167718482, 4213.73297525263, 3219.01464756868,
3736.20584106122, 3596.22221649466, 3856.92072422277, 3396.53444619832,
3903.42091723818, 4387.0063010264, 4398.76773227814, 3801.45818298329,
4048.23351071216, 4472.15319907699, 4720.37228260087, 3883.02069985224,
4239.54241038166, 4379.50095675784, 4736.44240399343, 3504.6079259428,
4183.00056641194, 4383.12499794949, 4861.61450456661, 3816.88910693882,
3986.49563848067, 4354.90372382823, 4129.62280276886, 3620.81243394272,
4534.2709191679, 3915.68272818192, 2528.7475765217, 3801.26666257281,
4693.31998347599, 3847.60575707209, 3908.04455614142), .Tsp = c(1995,
2021.25, 4), class = "ts", tstype = "PCY")
plot.ts(s7)
# Outliers and large volatility
s8 <- structure(c(1351.14980214999, 1541.50979130484, 1335.1296468058,
1524.77307361208, 1443.72501544665, 1615.59574461741, 1437.44901144544,
1532.97202260594, 1645.33411710747, 1673.74063194765, 1739.16455648203,
1780.16544930199, 1563.13695415904, 1792.65002734286, 1651.4938433918,
1636.41085041514, 1492.15405684524, 1637.0627444213, 1619.07950598611,
1685.64785812572, 1552.42714195183, 1511.2361856444, 1427.61541476071,
1614.91070423383, 1581.99653791708, 1547.22012211493, 1514.9746801275,
1705.54707188187, 1749.18178849336, 2305.65943065503, 1675.23604738162,
1921.18494405234, 1993.78466742098, 1778.43423356755, 1751.67076058903,
1858.87962625115, 1935.23691189743, 2019.49514273672, 1930.93493315278,
2133.77298634765, 2129.35841136632, 2137.21646049845, 2198.32713129833,
2440.31336805445, 2441.69024889489, 2396.69361302471, 2379.55645058587,
2687.72229592843, 2659.88095620519, 2795.52104863273, 2618.2912768901,
3016.10019458771, 2892.04580320168, 3283.8700296328, 3036.04768312073,
3011.8238116081, 4788.74665597453, 2492.67222805688, 2436.49428446073,
2835.48531061187, 2799.0519366543, 4668.65378567803, 4327.31512277468,
3689.9630209203, 3387.03669085841, 3789.83804368554, 4144.8316650986,
4198.45133385996, 4004.97862732557, 3982.88806507517, 3933.9034318149,
4107.66187149337, 3646.14739053063, 3847.73706661858, 3522.4299048541,
3571.17764478658, 3165.953352273, 3441.28318021639, 3867.80438083902,
3773.08871564376, 3414.44614131345, 3548.85313054148, 3752.56026263831,
3712.95563450677, 3500.5476725587, 3776.23528355677, 3828.34436621291,
3471.4639480026, 3607.2281168807, 4194.74119020942, 4481.6001498943,
6291.09626513034, 5777.96535795054, 7204.65969343604, 6196.86615514892,
6443.28800957593, 6302.02766686754, 6494.69841928534, 7715.53533526028,
6203.43800710893, 5687.92063486138, 2904.36890565887, 4058.59595736808,
3650.59068213921, 3794.85507750815, 3578.68942505224), .Tsp = c(1995,
2021.25, 4), class = "ts", tstype = "PCY")
plot.ts(s8)
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