| Estimated Parameters of Exponential Smoothing | |
| Parameter | Value |
| alpha | 0.873418950693836 |
| beta | 0.0296759775106365 |
| gamma | 1 |
| Interpolation Forecasts of Exponential Smoothing | |||
| t | Observed | Fitted | Residuals |
| 13 | 3.52 | 3.46502409710897 | 0.0549759028910324 |
| 14 | 3.52 | 3.51637916866576 | 0.00362083133424251 |
| 15 | 3.58 | 3.58007339645459 | -7.33964545860388e-05 |
| 16 | 3.6 | 3.59803506364187 | 0.00196493635812889 |
| 17 | 3.61 | 3.60741244019217 | 0.00258755980783043 |
| 18 | 3.61 | 3.60741060078114 | 0.00258939921886370 |
| 19 | 3.61 | 3.64964552079433 | -0.039645520794326 |
| 20 | 3.63 | 3.61742053476775 | 0.0125794652322471 |
| 21 | 3.68 | 3.62894473810215 | 0.051055261897853 |
| 22 | 3.69 | 3.6739557396976 | 0.0160442603024031 |
| 23 | 3.69 | 3.69092692300590 | -0.000926923005895475 |
| 24 | 3.69 | 3.69477467449461 | -0.00477467449460711 |
| 25 | 3.69 | 3.70288088133550 | -0.0128808813354953 |
| 26 | 3.69 | 3.6885750275598 | 0.00142497244019779 |
| 27 | 3.69 | 3.75299048235024 | -0.0629904823502381 |
| 28 | 3.69 | 3.71561636123817 | -0.0256163612381686 |
| 29 | 3.69 | 3.69930899812387 | -0.0093089981238701 |
| 30 | 3.78 | 3.68673093869279 | 0.0932690613072071 |
| 31 | 3.79 | 3.80424694387552 | -0.0142469438755199 |
| 32 | 3.79 | 3.80185326741977 | -0.0118532674197676 |
| 33 | 3.8 | 3.79707125002915 | 0.00292874997084658 |
| 34 | 3.8 | 3.79433025124074 | 0.00566974875926229 |
| 35 | 3.8 | 3.7987281476632 | 0.00127185233679983 |
| 36 | 3.8 | 3.80280392207294 | -0.00280392207293678 |
| 37 | 3.81 | 3.81066134800965 | -0.000661348009649565 |
| 38 | 3.95 | 3.80782061859225 | 0.142179381407754 |
| 39 | 3.99 | 3.99278607106964 | -0.00278607106963724 |
| 40 | 4 | 4.01831319290046 | -0.0183131929004636 |
| 41 | 4.06 | 4.01512783117502 | 0.0448721688249751 |
| 42 | 4.16 | 4.06869352788346 | 0.091306472116539 |
| 43 | 4.19 | 4.17807196660782 | 0.0119280333921798 |
| 44 | 4.2 | 4.20555035994741 | -0.00555035994741004 |
| 45 | 4.2 | 4.21472478598400 | -0.0147247859840043 |
| 46 | 4.2 | 4.20170280812858 | -0.00170280812857726 |
| 47 | 4.2 | 4.20408432051875 | -0.0040843205187473 |
| 48 | 4.2 | 4.20816490533 | -0.00816490533000191 |
| 49 | 4.23 | 4.21753393106047 | 0.0124660689395295 |
| 50 | 4.38 | 4.25044840952595 | 0.129551590474050 |
| 51 | 4.43 | 4.41493866768527 | 0.0150613323147262 |
| 52 | 4.44 | 4.46179694593563 | -0.0217969459356278 |
| 53 | 4.44 | 4.47062818506073 | -0.0306281850607295 |
| 54 | 4.44 | 4.46879802914675 | -0.0287980291467473 |
| 55 | 4.44 | 4.4647068575573 | -0.0247068575572955 |
| 56 | 4.44 | 4.45819796749402 | -0.0181979674940225 |
| 57 | 4.45 | 4.45496059279912 | -0.00496059279912053 |
| 58 | 4.45 | 4.45150519670828 | -0.00150519670828153 |
| 59 | 4.45 | 4.45328331929561 | -0.00328331929560921 |
| 60 | 4.45 | 4.45731156450628 | -0.00731156450628223 |
| 61 | 4.45 | 4.47054849457995 | -0.0205484945799475 |
| 62 | 4.45 | 4.48956230108177 | -0.0395623010817703 |
| 63 | 4.45 | 4.48728060425283 | -0.0372806042528264 |
| 64 | 4.45 | 4.47759229284161 | -0.0275922928416064 |
| 65 | 4.46 | 4.47388736617346 | -0.0138873661734555 |
| 66 | 4.46 | 4.48098975504584 | -0.0209897550458367 |
| 67 | 4.46 | 4.47850731393273 | -0.0185073139327319 |
| 68 | 4.48 | 4.47265444591991 | 0.00734555408009285 |
| 69 | 4.58 | 4.48847182153645 | 0.0915281784635482 |
| 70 | 4.67 | 4.56688434571314 | 0.103115654286857 |
| 71 | 4.68 | 4.65940996839529 | 0.0205900316047112 |
| 72 | 4.68 | 4.68410351827942 | -0.00410351827941913 |
| Extrapolation Forecasts of Exponential Smoothing | |||
| t | Forecast | 95% Lower Bound | 95% Upper Bound |
| 73 | 4.6994642720259 | 4.62041017000297 | 4.77851837404882 |
| 74 | 4.73647951725077 | 4.62998053074079 | 4.84297850376076 |
| 75 | 4.77261180698504 | 4.64312143238524 | 4.90210218158483 |
| 76 | 4.80085150748046 | 4.65089424252500 | 4.95080877243591 |
| 77 | 4.8278078425174 | 4.65889446600094 | 4.99672121903386 |
| 78 | 4.85106451220569 | 4.66431315058774 | 5.03781587382363 |
| 79 | 4.8725758773511 | 4.66877061335302 | 5.07638114134918 |
| 80 | 4.89180771201712 | 4.67157531882776 | 5.11204010520648 |
| 81 | 4.9176855681833 | 4.68115405196285 | 5.15421708440374 |
| 82 | 4.91924156963804 | 4.66783082303564 | 5.17065231624044 |
| 83 | 4.91023177593882 | 4.64475346653108 | 5.17571008534656 |
| 84 | 4.91292529328788 | 0.885039005800385 | 8.94081158077537 |
