| Estimated Parameters of Exponential Smoothing | |
| Parameter | Value |
| alpha | 0.971904589472015 |
| beta | 0.0881653247099089 |
| gamma | 1 |
| Interpolation Forecasts of Exponential Smoothing | |||
| t | Observed | Fitted | Residuals |
| 13 | 8 | 7.28231740602736 | 0.717682593972644 |
| 14 | 8 | 8.0362665291793 | -0.0362665291793043 |
| 15 | 8 | 8.04065730690637 | -0.0406573069063718 |
| 16 | 7.9 | 7.9281672157671 | -0.0281672157671071 |
| 17 | 7.9 | 7.92103776925931 | -0.021037769259312 |
| 18 | 8 | 8.02284163251019 | -0.0228416325101879 |
| 19 | 8.5 | 8.55843247582171 | -0.058432475821709 |
| 20 | 9.2 | 9.1652677515709 | 0.0347322484291013 |
| 21 | 9.4 | 9.36917791751489 | 0.0308220824851144 |
| 22 | 9.5 | 9.44220234594414 | 0.0577976540558627 |
| 23 | 9.5 | 9.53902370006006 | -0.0390237000600600 |
| 24 | 9.6 | 9.77818546511985 | -0.178185465119855 |
| 25 | 9.7 | 9.88516467844754 | -0.185164678447546 |
| 26 | 9.7 | 9.6652821708659 | 0.0347178291341006 |
| 27 | 9.6 | 9.67250712157846 | -0.0725071215784592 |
| 28 | 9.5 | 9.44294306600442 | 0.0570569339955789 |
| 29 | 9.4 | 9.45969820114468 | -0.0596982011446823 |
| 30 | 9.3 | 9.48328436836337 | -0.183284368363370 |
| 31 | 9.6 | 9.87650622595427 | -0.276506225954272 |
| 32 | 10.2 | 10.2671018501516 | -0.0671018501515608 |
| 33 | 10.2 | 10.2915578581767 | -0.0915578581767136 |
| 34 | 10.1 | 10.1462867132607 | -0.0462867132606632 |
| 35 | 9.9 | 10.0341740098443 | -0.134174009844285 |
| 36 | 9.8 | 10.0756990401418 | -0.275699040141788 |
| 37 | 9.8 | 9.97525673006184 | -0.175256730061840 |
| 38 | 9.7 | 9.65739241260358 | 0.0426075873964216 |
| 39 | 9.5 | 9.56018102582917 | -0.0601810258291717 |
| 40 | 9.3 | 9.24449188645717 | 0.0555081135428352 |
| 41 | 9.1 | 9.15745212963164 | -0.0574521296316384 |
| 42 | 9 | 9.07937646480935 | -0.0793764648093536 |
| 43 | 9.5 | 9.4589103555655 | 0.041089644434491 |
| 44 | 10 | 10.0836438004482 | -0.0836438004481508 |
| 45 | 10.2 | 10.0156865884149 | 0.184313411585148 |
| 46 | 10.1 | 10.0884121124512 | 0.0115878875488455 |
| 47 | 10 | 9.9842453578143 | 0.0157546421857049 |
| 48 | 9.9 | 10.1349752300051 | -0.234975230005077 |
| 49 | 10 | 10.0479909007913 | -0.047990900791314 |
| 50 | 9.9 | 9.83738140362743 | 0.0626185963725678 |
| 51 | 9.7 | 9.73616193857853 | -0.0361619385785339 |
| 52 | 9.5 | 9.42662574161964 | 0.0733742583803583 |
| 53 | 9.2 | 9.33732990375902 | -0.137329903759021 |
| 54 | 9 | 9.16105490811093 | -0.161054908110930 |
| 55 | 9.3 | 9.43723300816736 | -0.137233008167355 |
| 56 | 9.8 | 9.8284582381197 | -0.0284582381197023 |
| 57 | 9.8 | 9.78106593900861 | 0.0189340609913859 |
| 58 | 9.6 | 9.64018769879226 | -0.0401876987922645 |
| 59 | 9.4 | 9.4360099541609 | -0.0360099541609031 |
| 60 | 9.3 | 9.46160601444997 | -0.161606014449967 |
| 61 | 9.2 | 9.38679364012027 | -0.186793640120275 |
| 62 | 9.2 | 8.99100888274444 | 0.208991117255561 |
| 63 | 9 | 8.98866100775748 | 0.0113389922425178 |
| 64 | 8.8 | 8.70089627987883 | 0.0991037201211693 |
| 65 | 8.7 | 8.59950370408529 | 0.100496295914711 |
| 66 | 8.7 | 8.63195899956163 | 0.0680410004383649 |
| 67 | 9.1 | 9.11146593223397 | -0.0114659322339694 |
| 68 | 9.7 | 9.62207025720562 | 0.0779297427943799 |
| 69 | 9.8 | 9.69425570227011 | 0.105744297729890 |
| 70 | 9.6 | 9.65805465071792 | -0.058054650717919 |
| 71 | 9.4 | 9.45668213410107 | -0.0566821341010648 |
| 72 | 9.4 | 9.4770555350279 | -0.0770555350278972 |
| 73 | 9.5 | 9.51090376552828 | -0.0109037655282762 |
| 74 | 9.4 | 9.33244995989022 | 0.0675500401097775 |
| 75 | 9.3 | 9.21092765707405 | 0.0890723429259488 |
| 76 | 9.2 | 9.02568292409297 | 0.174317075907030 |
| 77 | 9 | 9.02844268097739 | -0.0284426809773919 |
| 78 | 8.9 | 8.96055111177748 | -0.0605511117774817 |
| 79 | 9.2 | 9.34007926671461 | -0.140079266714608 |
| 80 | 9.8 | 9.74117136560307 | 0.0588286343969315 |
| 81 | 9.9 | 9.80080288046499 | 0.0991971195350114 |
| 82 | 9.6 | 9.75676581130148 | -0.156765811301476 |
| 83 | 9.2 | 9.4556575709228 | -0.255657570922789 |
| 84 | 9.1 | 9.25949851228236 | -0.159498512282362 |
| 85 | 9.1 | 9.18292435657468 | -0.0829243565746776 |
| 86 | 9 | 8.90919559447721 | 0.0908044055227872 |
| 87 | 8.9 | 8.78729932556785 | 0.112700674432155 |
| 88 | 8.7 | 8.61067013191641 | 0.0893298680835883 |
| 89 | 8.5 | 8.50049891896919 | -0.000498918969190854 |
| 90 | 8.3 | 8.4295699778362 | -0.129569977836194 |
| 91 | 8.5 | 8.67105757501595 | -0.171057575015951 |
| 92 | 8.7 | 8.9611488807578 | -0.261148880757801 |
| 93 | 8.4 | 8.63816607288297 | -0.238166072882972 |
| 94 | 8.1 | 8.18307903223375 | -0.0830790322337478 |
| 95 | 7.8 | 7.8818531815114 | -0.081853181511403 |
| 96 | 7.7 | 7.76733169349048 | -0.067331693490484 |
| 97 | 7.5 | 7.69329636364513 | -0.193296363645126 |
| 98 | 7.2 | 7.26325261952877 | -0.0632526195287735 |
| 99 | 6.8 | 6.93639945251404 | -0.136399452514040 |
| 100 | 6.7 | 6.47001957550046 | 0.229980424499538 |
| 101 | 6.4 | 6.441561651945 | -0.0415616519450044 |
| 102 | 6.3 | 6.24376224430665 | 0.0562377556933535 |
| 103 | 6.8 | 6.48382889861912 | 0.316171101380883 |
| 104 | 7.3 | 7.0979452597597 | 0.202054740240297 |
| 105 | 7.1 | 7.2190224618741 | -0.119022461874098 |
| 106 | 7 | 6.90792008992367 | 0.0920799100763281 |
| 107 | 6.8 | 6.81250621937214 | -0.0125062193721384 |
| 108 | 6.6 | 6.78163892406428 | -0.181638924064285 |
| 109 | 6.3 | 6.59396813272725 | -0.293968132727254 |
| 110 | 6.1 | 6.09415013255625 | 0.00584986744375282 |
| 111 | 6.1 | 5.86572146740872 | 0.234278532591275 |
| 112 | 6.3 | 5.83170893722029 | 0.468291062779715 |
| 113 | 6.3 | 6.0976507986597 | 0.202349201340303 |
| 114 | 6 | 6.22196450180906 | -0.221964501809063 |
| 115 | 6.2 | 6.24486287082672 | -0.0448628708267229 |
| 116 | 6.4 | 6.50124236330985 | -0.101242363309847 |
| 117 | 6.8 | 6.32497785612964 | 0.47502214387036 |
| 118 | 7.5 | 6.65721782148455 | 0.842782178515454 |
| 119 | 7.5 | 7.39861955301892 | 0.101380446981081 |
| 120 | 7.6 | 7.60756432175886 | -0.00756432175886079 |
| 121 | 7.6 | 7.74264888465131 | -0.142648884651314 |
| 122 | 7.4 | 7.53580327153147 | -0.135803271531470 |
| 123 | 7.3 | 7.29260353418122 | 0.00739646581877818 |
| 124 | 7.1 | 7.12964522861433 | -0.0296452286143323 |
| 125 | 6.9 | 6.9591415971558 | -0.0591415971558034 |
| 126 | 6.8 | 6.86315668382605 | -0.0631566838260511 |
| 127 | 7.5 | 7.15288375286455 | 0.347116247135451 |
| 128 | 7.6 | 7.97063370996198 | -0.370633709961984 |
| 129 | 7.8 | 7.63343902225893 | 0.166560977741066 |
| 130 | 8 | 7.71693864167040 | 0.283061358329603 |
| 131 | 8.1 | 7.8927675668435 | 0.207232433156492 |
| 132 | 8.2 | 8.22368496904067 | -0.0236849690406729 |
| 133 | 8.3 | 8.36265630921508 | -0.0626563092150825 |
| 134 | 8.2 | 8.24687170493134 | -0.0468717049313376 |
| 135 | 8 | 8.1097455751538 | -0.109745575153797 |
| 136 | 7.9 | 7.8323801871011 | 0.067619812898907 |
| 137 | 7.6 | 7.7641174856201 | -0.164117485620098 |
| 138 | 7.6 | 7.57823545195936 | 0.0217645480406423 |
| 139 | 8.3 | 8.02921317888177 | 0.270786821118232 |
| 140 | 8.4 | 8.81703316351684 | -0.417033163516837 |
| 141 | 8.4 | 8.46950483167575 | -0.0695048316757507 |
| 142 | 8.4 | 8.31561407794768 | 0.0843859220523164 |
| 143 | 8.4 | 8.26884121380901 | 0.131158786190989 |
| 144 | 8.6 | 8.49495351957274 | 0.105046480427259 |
| 145 | 8.9 | 8.74693622858642 | 0.153063771413583 |
| 146 | 8.8 | 8.83584461365424 | -0.0358446136542394 |
| 147 | 8.3 | 8.70044001488269 | -0.400440014882685 |
| 148 | 7.5 | 8.11674836326688 | -0.616748363266876 |
| 149 | 7.2 | 7.30878384413295 | -0.108783844132947 |
| 150 | 7.4 | 7.11297159659089 | 0.287028403409114 |
| 151 | 8.8 | 7.76588816615986 | 1.03411183384014 |
| 152 | 9.3 | 9.31484844905075 | -0.0148484490507474 |
| 153 | 9.3 | 9.420749066177 | -0.120749066176991 |
| 154 | 8.7 | 9.2537902441492 | -0.553790244149202 |
| 155 | 8.2 | 8.5715355439778 | -0.371535543977798 |
| 156 | 8.3 | 8.25314828692511 | 0.0468517130748882 |
| 157 | 8.5 | 8.38681669908764 | 0.113183300912356 |
| 158 | 8.6 | 8.37546461042496 | 0.224535389575037 |
| 159 | 8.5 | 8.44738787395259 | 0.0526121260474106 |
| 160 | 8.2 | 8.29088745303601 | -0.0908874530360073 |
| 161 | 8.1 | 8.03620318206955 | 0.0637968179304504 |
| 162 | 7.9 | 8.07159710384127 | -0.171597103841272 |
| 163 | 8.6 | 8.34375794401563 | 0.256242055984373 |
| 164 | 8.7 | 9.04760945095619 | -0.347609450956186 |
| 165 | 8.7 | 8.74649310803348 | -0.0464931080334825 |
| 166 | 8.5 | 8.57619532644035 | -0.0761953264403452 |
| 167 | 8.4 | 8.33695780324588 | 0.0630421967541217 |
| 168 | 8.5 | 8.46203897616968 | 0.0379610238303165 |
| 169 | 8.7 | 8.59830386973191 | 0.101696130268092 |
| 170 | 8.7 | 8.58196435683023 | 0.118035643169767 |
| 171 | 8.6 | 8.5405445069983 | 0.059455493001705 |
| 172 | 8.5 | 8.381493608208 | 0.118506391792002 |
| 173 | 8.3 | 8.3433611518528 | -0.0433611518527997 |
| 174 | 8 | 8.2724765068037 | -0.272476506803693 |
| 175 | 8.2 | 8.46160505340703 | -0.261605053407033 |
| 176 | 8.1 | 8.5768582038509 | -0.476858203850897 |
| 177 | 8.1 | 8.09483183098223 | 0.00516816901776984 |
| 178 | 8 | 7.92684288044915 | 0.0731571195508538 |
| 179 | 7.9 | 7.80365801078055 | 0.0963419892194537 |
| 180 | 7.9 | 7.91694966441791 | -0.0169496644179112 |
| Extrapolation Forecasts of Exponential Smoothing | |||
| t | Forecast | 95% Lower Bound | 95% Upper Bound |
| 181 | 7.94977588228965 | 7.54688558804596 | 8.35266617653335 |
| 182 | 7.79300586995586 | 7.2109897501952 | 8.37502198971652 |
| 183 | 7.59209262568915 | 6.86102492406567 | 8.32316032731262 |
| 184 | 7.34004233108736 | 6.47830259468733 | 8.20178206748738 |
| 185 | 7.13492398294717 | 6.14676903372821 | 8.12307893216613 |
| 186 | 7.03949513249486 | 5.9159513131087 | 8.16303895188102 |
| 187 | 7.39145815814608 | 6.06179994626884 | 8.72111637002332 |
| 188 | 7.6896291457255 | 6.15251335927928 | 9.22674493217172 |
| 189 | 7.69573333069134 | 6.00075534014136 | 9.39071132124132 |
| 190 | 7.54350258661117 | 5.72386453217716 | 9.36314064104518 |
| 191 | 7.36484011387838 | 5.42882868326941 | 9.30085154448734 |
| 192 | 7.3758840739992 | -2.3644308879373 | 17.1161990359357 |
