| Structural Time Series Model -- Interpolation | |||||
| t | Observed | Level | Slope | Seasonal | Stand. Residuals |
| 1 | 3780 | 3780 | 0 | 0 | 0 |
| 2 | 3795 | 3793.37910821159 | 0.985466330327196 | 0.756984071903327 | 0.262429485142133 |
| 3 | 3840 | 3833.0580885375 | 4.43224795704527 | 1.15537858222645 | 1.17479318204581 |
| 4 | 3900 | 3890.93291132272 | 10.8228524220448 | 1.32548056702225 | 1.58880779979685 |
| 5 | 3940 | 3934.08941601953 | 15.4882897395531 | 1.3869078908694 | 0.942112139841346 |
| 6 | 3990 | 3983.88420681336 | 21.0449973174081 | 1.43722345733373 | 0.985188007526608 |
| 7 | 4050 | 4043.36778750806 | 27.7345113728801 | 1.48278912193378 | 1.09275551711176 |
| 8 | 4090 | 4086.46862660701 | 30.5317642840151 | 1.49752919614447 | 0.433863189578987 |
| 9 | 4145 | 4140.4105967886 | 34.9156743707818 | 1.51561968954627 | 0.657975830487531 |
| 10 | 4190 | 4186.95791567081 | 37.1331307737488 | 1.52283319354587 | 0.325945394856835 |
| 11 | 4175 | 4179.32634861135 | 28.5023488158051 | 1.50061199963996 | -1.25195632168522 |
| 12 | 4230 | 4226.11684411975 | 32.0535971885596 | 1.50786623343609 | 0.51082142367638 |
| 13 | 4220 | 4244.9200034248 | 29.6202195036449 | -23.2745998822314 | -0.434444798578576 |
| 14 | 4245 | 4246.19574374386 | 24.1971733686655 | 1.42704969934178 | -0.664269111761149 |
| 15 | 4295 | 4290.87002655595 | 28.2004906486946 | 1.48139046457019 | 0.571211795177397 |
| 16 | 4290 | 4292.01104346863 | 22.891885121881 | 1.48993566331914 | -0.753958166747014 |
| 17 | 4325 | 4322.52865207682 | 24.3889855620279 | 1.485359888631 | 0.212372593547551 |
| 18 | 4335 | 4335.04360903982 | 22.0570626084548 | 1.49163215499609 | -0.330691169952273 |
| 19 | 4360 | 4358.34766342451 | 22.3020128299907 | 1.49109828640788 | 0.0347313673474083 |
| 20 | 4360 | 4361.0381565915 | 18.4490447044807 | 1.49780890510256 | -0.54626251169472 |
| 21 | 4320 | 4325.47248519397 | 7.83583252206346 | 1.51254400679887 | -1.50462746726812 |
| 22 | 4310 | 4311.32555752431 | 3.51612850177399 | 1.5173227046311 | -0.612380046521561 |
| 23 | 4345 | 4340.20666484322 | 8.50076710394067 | 1.51292924896501 | 0.706628480204732 |
| 24 | 4315 | 4317.51672973497 | 2.37098792277812 | 1.51723381925035 | -0.868952846281989 |
| 25 | 4315 | 4328.4746892698 | 4.02802119283445 | -14.5589270855766 | 0.260777901459322 |
| 26 | 4335 | 4333.54951408836 | 4.22971813299954 | 1.34015293631601 | 0.0262345353425376 |
| 27 | 4365 | 4360.66378168183 | 8.71979174486626 | 1.37753456146937 | 0.637925434229906 |
| 28 | 4410 | 4404.13870026932 | 15.5525088543776 | 1.36735916558188 | 0.968066858221605 |
| 29 | 4435 | 4432.04181120621 | 17.9805029619519 | 1.36165346349602 | 0.34393492368038 |
| 30 | 4440 | 4439.93801233902 | 15.9982987777623 | 1.36569671368794 | -0.280847452594866 |
| 31 | 4390 | 4396.32280432173 | 4.28137236948845 | 1.38502207413286 | -1.66040217994062 |
| 32 | 4445 | 4438.69885957617 | 11.7685421177145 | 1.3751567331627 | 1.0611299525871 |
| 33 | 4470 | 4466.54857396437 | 14.9291142167535 | 1.37183705546822 | 0.447970487757857 |
| 34 | 4430 | 4434.67343603843 | 5.73026199397932 | 1.37953589470868 | -1.3038817223523 |
| 35 | 4450 | 4447.68032706516 | 7.16041246019159 | 1.37858221930915 | 0.20272136798151 |
| 36 | 4480 | 4475.89993292704 | 11.2994330954903 | 1.37638316574511 | 0.586710409004852 |
| 37 | 4565 | 4559.15281312339 | 25.2779237285676 | -3.31165338293803 | 2.12694809323031 |
| 38 | 4515 | 4522.35528775347 | 13.2590570006511 | -0.432740102072313 | -1.60170205620476 |
| 39 | 4490 | 4495.64881483923 | 5.41405689933943 | -0.481115767309923 | -1.11394241296439 |
| 40 | 4535 | 4531.54599761548 | 11.4066892522704 | -0.487885280941598 | 0.8491409764971 |
| 41 | 4545 | 4545.19833079283 | 11.8481442043563 | -0.488665009894533 | 0.0625443971132483 |
| 42 | 4555 | 4555.66665699147 | 11.5769232217967 | -0.488249524952866 | -0.0384323620695134 |
| 43 | 4575 | 4574.54578212657 | 13.0121789370886 | -0.490027104615387 | 0.203405309276456 |
| 44 | 4585 | 4585.72651197822 | 12.6522158703622 | -0.48967096316952 | -0.0510187849913124 |
| 45 | 4600 | 4600.24819072826 | 13.0196466995393 | -0.489960744484837 | 0.05208021964504 |
| 46 | 4690 | 4681.65394878061 | 26.4604951024626 | -0.498407309087224 | 1.90519668278576 |
| 47 | 4720 | 4719.08111026427 | 28.6159336240103 | -0.499486540806028 | 0.305533533006332 |
| 48 | 4780 | 4776.74477935006 | 34.3251496168276 | -0.501764122223222 | 0.809293648773226 |
| 49 | 4775 | 4777.81688743119 | 27.8457058046238 | 1.43311523946109 | -0.969212257070168 |
| 50 | 4830 | 4827.42015946859 | 32.071266167024 | 0.0747074889839892 | 0.570749031649876 |
| 51 | 4865 | 4864.29898249051 | 33.0152182907145 | 0.0793369104589692 | 0.133989748371902 |
| 52 | 4945 | 4939.47575663707 | 41.3034289597282 | 0.0718708191118461 | 1.17451627275416 |
| 53 | 5005 | 5002.16841579751 | 45.5080728448447 | 0.0659519409763159 | 0.595771339643047 |
| 54 | 5065 | 5062.9612676176 | 48.5124753194497 | 0.0622840586512518 | 0.42576086820419 |
| 55 | 5105 | 5105.68515917058 | 47.3747157370905 | 0.0634070236905674 | -0.161252087683521 |
| 56 | 5080 | 5088.30144663167 | 34.6465852819863 | 0.073442560448881 | -1.8040588258976 |
| 57 | 5045 | 5053.85399973081 | 21.0664097978222 | 0.0819776673643413 | -1.92491443738406 |
| 58 | 5115 | 5110.34046061226 | 28.0280895670614 | 0.0784912879192929 | 0.986808278317122 |
| 59 | 5095 | 5099.89463395216 | 20.4661529865937 | 0.0815085863139401 | -1.07191372679374 |
| 60 | 5075 | 5080.12065691068 | 12.5570260391682 | 0.0840229697749707 | -1.12114159280111 |
| 61 | 5080 | 5083.0926634021 | 10.6860637024723 | -1.86464370304303 | -0.276960769007268 |
| 62 | 5115 | 5112.48528003913 | 14.3264852193616 | 0.316022235012959 | 0.495975543644424 |
| 63 | 5115 | 5116.08034864552 | 12.2190171171097 | 0.307430853537928 | -0.29907788270523 |
| 64 | 5115 | 5116.2491935193 | 9.85021908607052 | 0.309203961486001 | -0.335699262921572 |
| 65 | 5065 | 5071.71115527973 | -0.841106127784492 | 0.321709776902216 | -1.51500519234404 |
| 66 | 5045 | 5047.67335068575 | -5.40067093476686 | 0.326335138526031 | -0.6461800417627 |
| 67 | 5080 | 5075.39546545718 | 1.10971616999062 | 0.320995848712103 | 0.922733291913088 |
| 68 | 5115 | 5110.31124669478 | 7.75427859198593 | 0.316642728236027 | 0.941806570555111 |
| 69 | 5080 | 5084.07587916694 | 1.07367783508273 | 0.320131525575902 | -0.946950861367222 |
| 70 | 5100 | 5098.01671689439 | 3.60269388394121 | 0.319079157232591 | 0.358487534097383 |
| 71 | 5085 | 5086.61997066158 | 0.654572151813744 | 0.320056586975421 | -0.417902127793455 |
| 72 | 5120 | 5115.96991590238 | 6.29464022631564 | 0.318566739562882 | 0.799498710464049 |
| 73 | 5195 | 5185.27390287156 | 18.6082291411434 | 1.64041499229607 | 1.81001505766694 |
| 74 | 5135 | 5142.83728698893 | 6.71130285403384 | -0.558199989328364 | -1.63062629653609 |
| 75 | 5200 | 5194.68951501788 | 15.5773518931434 | -0.527304676280821 | 1.25800843937055 |
| 76 | 5150 | 5157.36269752937 | 5.17771895385977 | -0.520646279753818 | -1.47386430730309 |
| 77 | 5105 | 5112.04101490165 | -4.7490330830443 | -0.510714206119701 | -1.40673613479301 |
| 78 | 5105 | 5105.71445157375 | -5.05911302636605 | -0.5104451484204 | -0.04394604853903 |
| 79 | 5030 | 5038.535625053 | -17.268972441247 | -0.501880016593309 | -1.73057479587447 |
| 80 | 5060 | 5056.01201652698 | -10.4397528934551 | -0.505706944088351 | 0.967994710151578 |
| 81 | 5075 | 5072.07967070803 | -5.22973772156063 | -0.508034193269151 | 0.738507808308285 |
| 82 | 5030 | 5034.66814476609 | -11.5550493014733 | -0.505782853545043 | -0.896617165454834 |
| 83 | 5090 | 5082.79037125668 | 0.174518317475574 | -0.50910917781138 | 1.66269602065737 |
| 84 | 5070 | 5071.93522943018 | -1.99337020437972 | -0.508619357792954 | -0.307306280848178 |
| 85 | 5160 | 5140.4225150604 | 11.7917637266272 | 10.5226749965575 | 2.01607690616218 |
| 86 | 5110 | 5115.58547951231 | 4.64552805588819 | -1.17109574361496 | -0.98383152756993 |
| 87 | 5145 | 5143.18836793193 | 9.15497463726586 | -1.15737222833064 | 0.639770900238251 |
| 88 | 5075 | 5084.87566339847 | -4.10732692671807 | -1.14995405779432 | -1.87962492348171 |
| 89 | 5125 | 5120.9593988787 | 3.7930234384661 | -1.15685982440334 | 1.11961556012107 |
| 90 | 5055 | 5064.00402312653 | -8.1476795874373 | -1.14780807808093 | -1.69234153952799 |
| 91 | 5050 | 5051.68657991135 | -8.96726382839602 | -1.14730579832313 | -0.116166533976011 |
| 92 | 5040 | 5041.32721784239 | -9.24088262176082 | -1.14717184533902 | -0.0387840134608262 |
| 93 | 5020 | 5022.39932476608 | -11.1448681789998 | -1.14642883651215 | -0.269887565422421 |
| 94 | 5025 | 5024.44160453444 | -8.55292922325365 | -1.14723478956125 | 0.36741076511246 |
| 95 | 4960 | 4967.41462150455 | -18.0805471749955 | -1.14487435252529 | -1.35056797231933 |
| 96 | 4965 | 4964.22004329398 | -15.1546862649771 | -1.1454518878324 | 0.414752455785124 |
| 97 | 4875 | 4876.22002118815 | -29.4111950801171 | 8.14661047258915 | -2.0770537094564 |
| 98 | 4805 | 4810.35900782448 | -36.528466044436 | -0.930129558478966 | -0.983180333324698 |
| 99 | 4735 | 4740.28620820625 | -43.1179702135662 | -0.947939126292615 | -0.934788806457037 |
| 100 | 4775 | 4766.93195193397 | -29.4044530110623 | -0.95474908759621 | 1.9436187662532 |
| 101 | 4815 | 4806.98317987685 | -15.7516609080635 | -0.965344307045288 | 1.93489461891263 |
| 102 | 4870 | 4861.8427671365 | -1.87233952933449 | -0.974685278541401 | 1.96714162144877 |
| 103 | 4860 | 4860.85976121499 | -1.69753704590804 | -0.974780387063062 | 0.0247765606523839 |
| 104 | 4875 | 4874.05046724503 | 1.22877683905195 | -0.976052266845072 | 0.414793122192352 |
| 105 | 4900 | 4898.03446385301 | 5.70134096471374 | -0.977601814366032 | 0.633983892246694 |
| 106 | 4855 | 4861.44522743044 | -2.61091990290219 | -0.975307136631054 | -1.17827811116185 |
| 107 | 4880 | 4878.44025983463 | 1.24266091074782 | -0.97615473447583 | 0.546257684577432 |
| 108 | 4850 | 4854.26318168788 | -3.75364492506729 | -0.975279164243198 | -0.708247293759726 |
| 109 | 4880 | 4866.36982575818 | -0.648138384904984 | 11.5894620513682 | 0.451095354621109 |
| 110 | 4900 | 4897.07285482444 | 5.47764846487449 | -0.906985722234634 | 0.848496912519707 |
| 111 | 4910 | 4909.94687600761 | 6.93069028464172 | -0.903459415411949 | 0.206113567959478 |
| 112 | 4935 | 4933.72585993648 | 10.2425512851783 | -0.904938139706613 | 0.469399104751418 |
| 113 | 4965 | 4963.39522992319 | 14.061227768955 | -0.907602694561857 | 0.541201879237145 |
| 114 | 4945 | 4949.51758489073 | 8.56958026696667 | -0.904279555544845 | -0.778354524813572 |
| 115 | 4965 | 4965.00963686131 | 9.9302247555014 | -0.904945192273999 | 0.192860313736235 |
| 116 | 4950 | 4953.65609511767 | 5.74684707341982 | -0.903310363941919 | -0.592980971925961 |
| Structural Time Series Model -- Extrapolation | |||
| t | Observed | Level | Seasonal |
| 1 | 4945.32988225227 | 4947.58456455147 | -2.25468229919641 |
| 2 | 4945.32225124689 | 4947.55162832936 | -2.22937708247368 |
| 3 | 4941.79126781437 | 4947.51869210726 | -5.72742429289831 |
| 4 | 4941.95915399646 | 4947.48575588516 | -5.52660188870635 |
| 5 | 4953.29997091556 | 4947.45281966306 | 5.84715125250273 |
| 6 | 4935.66124725026 | 4947.41988344096 | -11.7586361906999 |
| 7 | 4941.85150297164 | 4947.38694721886 | -5.53544424721967 |
| 8 | 4947.87073947044 | 4947.35401099676 | 0.516728473684813 |
| 9 | 4956.71895740987 | 4947.32107477466 | 9.39788263521615 |
| 10 | 4954.39615864239 | 4947.28813855256 | 7.10802008983151 |
| 11 | 4950.4023427879 | 4947.25520233046 | 3.14714045744212 |
| 12 | 4954.23750920087 | 4947.22226610836 | 7.01524309251699 |
| 13 | 4944.93464758706 | 4947.18932988625 | -2.25468229919641 |
| 14 | 4944.92701658168 | 4947.15639366415 | -2.22937708247368 |
| 15 | 4941.39603314915 | 4947.12345744205 | -5.72742429289831 |
| 16 | 4941.56391933125 | 4947.09052121995 | -5.52660188870635 |
| 17 | 4952.90473625035 | 4947.05758499785 | 5.84715125250273 |
| 18 | 4935.26601258505 | 4947.02464877575 | -11.7586361906999 |
