| Estimated Parameters of Exponential Smoothing | |
| Parameter | Value |
| alpha | 0.589894328918783 |
| beta | 0.0757352352628603 |
| gamma | 1 |
| Interpolation Forecasts of Exponential Smoothing | |||
| t | Observed | Fitted | Residuals |
| 13 | 4.07 | 3.86178952991453 | 0.208210470085469 |
| 14 | 4.07 | 3.98743931282398 | 0.0825606871760192 |
| 15 | 4.3 | 4.2747407982728 | 0.0252592017271969 |
| 16 | 4.44 | 4.44228560376877 | -0.00228560376876974 |
| 17 | 4.52 | 4.53389644023381 | -0.0138964402338084 |
| 18 | 4.52 | 4.53803727572711 | -0.0180372757271146 |
| 19 | 4.52 | 4.43684629304614 | 0.0831537069538548 |
| 20 | 4.53 | 4.53364558771849 | -0.00364558771848777 |
| 21 | 4.53 | 4.62949626788018 | -0.099496267880177 |
| 22 | 4.53 | 4.598943434775 | -0.0689434347749973 |
| 23 | 4.53 | 4.56416677586129 | -0.0341667758612916 |
| 24 | 4.53 | 4.54504490992699 | -0.0150449099269885 |
| 25 | 4.53 | 4.62191907565322 | -0.0919190756532204 |
| 26 | 4.53 | 4.51200440027563 | 0.017995599724367 |
| 27 | 4.53 | 4.7278450938572 | -0.1978450938572 |
| 28 | 4.61 | 4.73264375118202 | -0.122643751182022 |
| 29 | 4.63 | 4.72327532585192 | -0.093275325851919 |
| 30 | 4.63 | 4.6501275093584 | -0.0201275093584039 |
| 31 | 4.63 | 4.56034380533604 | 0.0696561946639598 |
| 32 | 4.63 | 4.58412239885952 | 0.0458776011404822 |
| 33 | 4.63 | 4.64262839494087 | -0.0126283949408705 |
| 34 | 4.63 | 4.65247998322762 | -0.022479983227619 |
| 35 | 4.63 | 4.6380814127892 | -0.00808141278920438 |
| 36 | 4.63 | 4.62206198121658 | 0.00793801878341593 |
| 37 | 4.63 | 4.6618667362831 | -0.0318667362831047 |
| 38 | 4.63 | 4.61603573385104 | 0.013964266148963 |
| 39 | 4.66 | 4.72438327794075 | -0.0643832779407454 |
| 40 | 4.7 | 4.82811571601387 | -0.128115716013867 |
| 41 | 4.72 | 4.81668401841936 | -0.0966840184193574 |
| 42 | 4.73 | 4.76049193284289 | -0.0304919328428861 |
| 43 | 4.73 | 4.68992024657183 | 0.0400797534281674 |
| 44 | 4.74 | 4.67368390453066 | 0.0663160954693387 |
| 45 | 4.74 | 4.70834969296161 | 0.0316503070383947 |
| 46 | 4.74 | 4.73035591125511 | 0.00964408874488587 |
| 47 | 4.76 | 4.73232231928803 | 0.027677680711971 |
| 48 | 4.88 | 4.73707443471615 | 0.142925565283852 |
| 49 | 4.88 | 4.83932189766139 | 0.0406781023386102 |
| 50 | 4.88 | 4.85745971131533 | 0.0225402886846666 |
| 51 | 4.88 | 4.94149804404472 | -0.061498044044721 |
| 52 | 4.89 | 5.02368694476422 | -0.133686944764221 |
| 53 | 4.97 | 5.02450174315693 | -0.0545017431569272 |
| 54 | 4.97 | 5.02486563330458 | -0.0548656333045763 |
| 55 | 4.97 | 4.97229611498373 | -0.00229611498373217 |
| 56 | 4.97 | 4.94336721279324 | 0.0266327872067631 |
| 57 | 4.97 | 4.94017957497066 | 0.0298204250293423 |
| 58 | 4.97 | 4.95177189857791 | 0.0182281014220864 |
| 59 | 4.97 | 4.96627156011035 | 0.00372843988965421 |
| 60 | 4.97 | 5.00316392885212 | -0.0331639288521224 |
| 61 | 4.97 | 4.95074196051219 | 0.0192580394878084 |
| 62 | 4.97 | 4.93898584928086 | 0.0310141507191419 |
| 63 | 4.97 | 4.98411691372887 | -0.0141169137288708 |
| 64 | 4.98 | 5.05732603157429 | -0.0773260315742936 |
| 65 | 5 | 5.1190555159884 | -0.1190555159884 |
| 66 | 5.03 | 5.073499680406 | -0.0434996804059988 |
| 67 | 5.04 | 5.04201112589581 | -0.00201112589581154 |
| 68 | 5.04 | 5.01794417117364 | 0.0220558288263559 |
| 69 | 5.05 | 5.00598932787011 | 0.0440106721298896 |
| 70 | 5.05 | 5.01445772851819 | 0.0355422714818143 |
| 71 | 5.05 | 5.02725745991073 | 0.0227425400892649 |
| 72 | 5.06 | 5.05511877131162 | 0.00488122868837504 |
| Extrapolation Forecasts of Exponential Smoothing | |||
| t | Forecast | 95% Lower Bound | 95% Upper Bound |
| 73 | 5.04322007188387 | 4.91074413300739 | 5.17569601076035 |
| 74 | 5.02064673194247 | 4.86374917207657 | 5.17754429180837 |
| 75 | 5.02331036942331 | 4.84244047843186 | 5.20418026041477 |
| 76 | 5.07389139127077 | 4.86916926153699 | 5.27861352100455 |
| 77 | 5.16254300054471 | 4.93389786153308 | 5.39118813955635 |
| 78 | 5.22194354962021 | 4.96918611345784 | 5.47470098578258 |
| 79 | 5.23881361807846 | 4.96167759962676 | 5.51594963653017 |
| 80 | 5.23157657506147 | 4.9297441552443 | 5.53340899487864 |
| 81 | 5.22040313300355 | 4.89352136719364 | 5.54728489881345 |
| 82 | 5.20225894110279 | 4.84995074262088 | 5.5545671395847 |
| 83 | 5.1900773592553 | 4.8119490743522 | 5.56820564415839 |
| 84 | 5.1974160228611 | 4.79306278039491 | 5.60176926532728 |
