| Estimated Parameters of Exponential Smoothing | |
| Parameter | Value |
| alpha | 0.904344694666365 |
| beta | 0.465568295859685 |
| gamma | 1 |
| Interpolation Forecasts of Exponential Smoothing | |||
| t | Observed | Fitted | Residuals |
| 13 | 4.7 | 4.90931356837607 | -0.209313568376067 |
| 14 | 4.73 | 4.67056656418675 | 0.0594334358132533 |
| 15 | 4.57 | 4.5340496643026 | 0.035950335697402 |
| 16 | 4.61 | 4.61351560223803 | -0.00351560223802849 |
| 17 | 4.69 | 4.70997720640782 | -0.0199772064078152 |
| 18 | 4.53 | 4.52480742536258 | 0.00519257463741774 |
| 19 | 4.55 | 4.43166938720862 | 0.118330612791376 |
| 20 | 4.31 | 4.55400170402283 | -0.244001704022828 |
| 21 | 4.03 | 4.15759431235348 | -0.127594312353484 |
| 22 | 3.72 | 3.79482108952395 | -0.0748210895239509 |
| 23 | 3.64 | 3.48910414516911 | 0.150895854830892 |
| 24 | 3.81 | 3.13896210689787 | 0.671037893102132 |
| 25 | 3.95 | 3.62963238959929 | 0.320367610400714 |
| 26 | 4.26 | 4.27087395236728 | -0.0108739523672803 |
| 27 | 4.55 | 4.41419396596922 | 0.135806034030784 |
| 28 | 4.54 | 4.96789672457306 | -0.427896724573057 |
| 29 | 4.55 | 4.88802587432993 | -0.338025874329933 |
| 30 | 4.39 | 4.49275772045436 | -0.102757720454365 |
| 31 | 4.21 | 4.34248652067432 | -0.132486520674322 |
| 32 | 4 | 4.12740095081224 | -0.127400950812239 |
| 33 | 3.67 | 3.82073498898702 | -0.150734988987023 |
| 34 | 3.6 | 3.40549881274811 | 0.194501187251888 |
| 35 | 3.53 | 3.44174311406491 | 0.0882568859350923 |
| 36 | 3.35 | 3.13514510305551 | 0.21485489694449 |
| 37 | 3.1 | 3.03809349017706 | 0.0619065098229372 |
| 38 | 2.89 | 3.16345939733002 | -0.273459397330024 |
| 39 | 2.97 | 2.72233220049034 | 0.247667799509655 |
| 40 | 3.03 | 3.00936284946455 | 0.0206371505354483 |
| 41 | 2.71 | 3.21865341840654 | -0.508653418406536 |
| 42 | 2.44 | 2.49467932795565 | -0.0546793279556463 |
| 43 | 2.6 | 2.20838202888369 | 0.391617971116307 |
| 44 | 2.93 | 2.51175814139021 | 0.418241858609791 |
| 45 | 2.86 | 2.97004773270316 | -0.110047732703156 |
| 46 | 2.88 | 2.91549965762313 | -0.035499657623133 |
| 47 | 3 | 2.92761198302832 | 0.0723880169716775 |
| 48 | 2.9 | 2.8061223781212 | 0.0938776218787987 |
| 49 | 2.64 | 2.72144927340619 | -0.0814492734061854 |
| 50 | 2.75 | 2.76114890987356 | -0.0111489098735649 |
| 51 | 2.7 | 2.79358738248179 | -0.0935873824817892 |
| 52 | 2.87 | 2.79310691386389 | 0.0768930861361143 |
| 53 | 3.03 | 3.0691463444185 | -0.0391463444184956 |
| 54 | 3.14 | 3.07737561527735 | 0.0626243847226551 |
| 55 | 3.02 | 3.25342298742656 | -0.233422987426561 |
| 56 | 2.86 | 3.04450068637003 | -0.184500686370026 |
| 57 | 3.07 | 2.70380166157492 | 0.366198338425084 |
| 58 | 2.93 | 3.08422311432215 | -0.154223114322146 |
| 59 | 2.83 | 2.94644990335422 | -0.116449903354222 |
| 60 | 2.72 | 2.52389545895523 | 0.196104541044773 |
| 61 | 2.73 | 2.42559494673312 | 0.304405053266877 |
| 62 | 2.72 | 2.89411754220865 | -0.174117542208651 |
| 63 | 2.77 | 2.77582819179425 | -0.0058281917942451 |
| 64 | 2.61 | 2.91250693751264 | -0.302506937512643 |
| 65 | 2.47 | 2.71608508450967 | -0.246085084509671 |
| 66 | 2.3 | 2.34152392527821 | -0.0415239252782134 |
| 67 | 2.38 | 2.14583543321028 | 0.234164566789723 |
| 68 | 2.43 | 2.31209210332012 | 0.117907896679879 |
| 69 | 2.39 | 2.37251529055661 | 0.017484709443393 |
| 70 | 2.6 | 2.31594131076508 | 0.284058689234917 |
| 71 | 2.84 | 2.69081372897927 | 0.149186271020734 |
| 72 | 2.87 | 2.76289995678558 | 0.107100043214416 |
| 73 | 2.92 | 2.781510794924 | 0.138489205075996 |
| 74 | 3.08 | 3.17140137610073 | -0.0914013761007335 |
| 75 | 3.33 | 3.29602638496385 | 0.0339736150361536 |
| 76 | 3.48 | 3.60909137424452 | -0.129091374244525 |
| 77 | 3.57 | 3.81667848828993 | -0.246678488289928 |
| 78 | 3.66 | 3.70268267720468 | -0.0426826772046751 |
| 79 | 3.77 | 3.77336409621469 | -0.0033640962146877 |
| 80 | 3.75 | 3.85473147321074 | -0.10473147321074 |
| 81 | 3.75 | 3.75150618412767 | -0.0015061841276709 |
| 82 | 3.81 | 3.74256155719096 | 0.0674384428090424 |
| 83 | 3.82 | 3.85673325758296 | -0.0367332575829571 |
| 84 | 3.89 | 3.62647980682169 | 0.263520193178308 |
| 85 | 4.05 | 3.72523058488877 | 0.324769415111225 |
| 86 | 4.1 | 4.27570244193343 | -0.175702441933433 |
| 87 | 4.07 | 4.31469938879119 | -0.244699388791188 |
| 88 | 4.26 | 4.22143540040574 | 0.0385645995942632 |
| 89 | 4.4 | 4.50126788175432 | -0.101267881754323 |
| 90 | 4.61 | 4.53138391202895 | 0.0786160879710467 |
| 91 | 4.63 | 4.75969043664461 | -0.129690436644611 |
| 92 | 4.48 | 4.70809939845644 | -0.22809939845644 |
| 93 | 4.46 | 4.44221937723124 | 0.0177806227687629 |
| 94 | 4.45 | 4.40447034679594 | 0.0455296532040625 |
| 95 | 4.32 | 4.42679877929415 | -0.106798779294147 |
| 96 | 4.52 | 4.07033720459649 | 0.449662795403507 |
| 97 | 4.21 | 4.33009069888729 | -0.120090698887294 |
| 98 | 3.97 | 4.22988838171736 | -0.259888381717364 |
| 99 | 4.12 | 3.9502126332381 | 0.169787366761899 |
| 100 | 4.5 | 4.19745669038361 | 0.302543309616387 |
| 101 | 4.73 | 4.75235871262396 | -0.0223587126239559 |
| 102 | 5.26 | 4.95398366143489 | 0.30601633856511 |
| 103 | 5.2 | 5.54669703281501 | -0.346697032815014 |
| 104 | 4.94 | 5.3767609495731 | -0.436760949573101 |
| 105 | 4.95 | 4.94516209523332 | 0.00483790476667689 |
| 106 | 4.52 | 4.89237680637264 | -0.372376806372637 |
| 107 | 3.85 | 4.34026388496181 | -0.490263884961809 |
| 108 | 3.41 | 3.34685540556038 | 0.0631445944396218 |
| 109 | 2.95 | 2.69643510969163 | 0.253564890308374 |
| 110 | 2.68 | 2.57196747987753 | 0.108032520122472 |
| 111 | 2.53 | 2.47222072894606 | 0.0577792710539433 |
| 112 | 2.44 | 2.38981134519681 | 0.0501886548031889 |
| 113 | 2.16 | 2.33811090317119 | -0.178110903171188 |
| 114 | 2.2 | 2.01740772988735 | 0.182592270112646 |
| 115 | 2.1 | 1.97121667606911 | 0.12878332393089 |
| 116 | 2.29 | 1.95800611289755 | 0.331993887102453 |
| 117 | 2.03 | 2.32288245511187 | -0.292882455111869 |
| 118 | 2.05 | 1.89843685617811 | 0.151563143821891 |
| 119 | 1.94 | 1.96313047820039 | -0.0231304782003925 |
| 120 | 1.87 | 1.79604797641295 | 0.0739520235870541 |
| 121 | 1.89 | 1.52910623321984 | 0.360893766780161 |
| 122 | 1.94 | 1.88845928965493 | 0.0515407103450678 |
| 123 | 1.79 | 2.10971182493531 | -0.31971182493531 |
| 124 | 1.71 | 1.90315196454926 | -0.193151964549263 |
| 125 | 1.66 | 1.7250526090442 | -0.0650526090442045 |
| 126 | 1.74 | 1.70420063546927 | 0.0357993645307328 |
| 127 | 1.83 | 1.62141060788522 | 0.208589392114776 |
| 128 | 1.64 | 1.83471101587233 | -0.19471101587233 |
| 129 | 1.69 | 1.57663165731026 | 0.113368342689738 |
| 130 | 1.78 | 1.64627569984924 | 0.133724300150756 |
| 131 | 1.89 | 1.75480103118923 | 0.135198968810766 |
| 132 | 1.95 | 1.88352604083847 | 0.0664739591615251 |
| 133 | 2.05 | 1.77745718847524 | 0.272542811524765 |
| 134 | 2.24 | 2.13030862946077 | 0.109691370539229 |
| 135 | 2.38 | 2.4961099121968 | -0.116109912196803 |
| 136 | 2.53 | 2.6989786367314 | -0.168978636731399 |
| 137 | 2.36 | 2.77836763636126 | -0.418367636361264 |
| 138 | 2.22 | 2.52226035365533 | -0.302260353655335 |
| 139 | 2.12 | 2.0825576221324 | 0.0374423778675981 |
| 140 | 1.75 | 1.96272708857666 | -0.212727088576665 |
| 141 | 1.76 | 1.57046180873363 | 0.189538191266367 |
| 142 | 1.81 | 1.59564431108889 | 0.214355688911113 |
| 143 | 1.71 | 1.69588535073744 | 0.0141146492625623 |
| 144 | 1.74 | 1.57620992455523 | 0.163790075444774 |
| 145 | 1.48 | 1.48650881754583 | -0.00650881754583255 |
| 146 | 1.24 | 1.36258236229749 | -0.122582362297495 |
| 147 | 1.16 | 1.1900924152013 | -0.0300924152012998 |
| 148 | 1.11 | 1.19527312123142 | -0.0852731212314246 |
| 149 | 0.98 | 1.0913279535301 | -0.111327953530101 |
| 150 | 0.94 | 1.01809344420984 | -0.0780934442098431 |
| 151 | 0.65 | 0.80208796355857 | -0.15208796355857 |
| 152 | 0.42 | 0.395606602487347 | 0.024393397512653 |
| 153 | 0.41 | 0.264774590852937 | 0.145225409147063 |
| 154 | 0.4 | 0.242115597972844 | 0.157884402027156 |
| Extrapolation Forecasts of Exponential Smoothing | |||
| t | Forecast | 95% Lower Bound | 95% Upper Bound |
| 155 | 0.238215275871042 | -0.162203771955309 | 0.638634323697392 |
| 156 | 0.0802321045158322 | -0.584587640802581 | 0.745051849834245 |
| 157 | -0.282703392846695 | -1.24758768866519 | 0.682180902971802 |
| 158 | -0.517927960914044 | -1.81570679538249 | 0.779850873554407 |
| 159 | -0.625183952852479 | -2.28606177739979 | 1.03569387169483 |
| 160 | -0.639867629531615 | -2.69186731194623 | 1.412132052883 |
| 161 | -0.675085854905756 | -3.14442540355854 | 1.79425369374703 |
| 162 | -0.603486654566728 | -3.51487218992313 | 2.30789888078967 |
| 163 | -0.682090890977925 | -4.05894323319416 | 2.69476145123831 |
| 164 | -0.796260873121688 | -4.66089294890375 | 3.06837120266037 |
| 165 | -0.809975098987915 | -5.18373309563744 | 3.56378289766161 |
| 166 | -0.896282284532126 | -5.79965977306837 | 4.00709520400412 |
