| opgave 10 oefening 2 P Fieremans | | *Unverified author* | | R Software Module: /rwasp_exponentialsmoothing.wasp (opens new window with default values) | | Title produced by software: Exponential Smoothing | | Date of computation: Mon, 31 May 2010 18:02:53 +0000 | | | | Cite this page as follows: | | Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/May/31/t127532902476ftibhyo3qa8hr.htm/, Retrieved Mon, 31 May 2010 20:03:48 +0200 | | | | BibTeX entries for LaTeX users: | @Manual{KEY,
author = {{YOUR NAME}},
publisher = {Office for Research Development and Education},
title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2010/May/31/t127532902476ftibhyo3qa8hr.htm/},
year = {2010},
}
@Manual{R,
title = {R: A Language and Environment for Statistical Computing},
author = {{R Development Core Team}},
organization = {R Foundation for Statistical Computing},
address = {Vienna, Austria},
year = {2010},
note = {{ISBN} 3-900051-07-0},
url = {http://www.R-project.org},
}
| | | | Original text written by user: | | | | | IsPrivate? | | No (this computation is public) | | | | User-defined keywords: | | KDGP2W62 | | | | Dataseries X: | | » Textbox « » Textfile « » CSV « | | 93,2
96
95,2
77,1
70,9
64,8
70,1
77,3
79,5
100,6
100,7
107,1
95,9
82,8
83,3
80
80,4
67,5
75,7
71,1
89,3
101,1
105,2
114,1
96,3
84,4
91,2
81,9
80,5
70,4
74,8
75,9
86,3
98,7
100,9
113,8
89,8
84,4
87,2
85,6
72
69,2
77,5
78,1
94,3
97,7
100,2
116,4
97,1
93
96
80,5
76,1
69,9
73,6
92,6
94,2
93,5
108,5
109,4
105,1
92,5
97,1
81,4
79,1
72,1
78,7
87,1
91,4
109,9
116,3
113
100
84,8
94,3
87,1
90,3
72,4
84,9
92,7
92,2
114,9
112,5
118,3
106
91,2
96,6
96,3
88,2
70,2
86,5
88,2
102,8
119,1
119,2
125,1
106,1
102,1
105,2
101
84,3
87,5
92,7
94,4
113
113,9
122,9
132,7
106,9
96,6
127,3
98,2
100,2
89,4
95,3
104,2
106,4
116,2
135,9
134
104,6
107,1
123,5
98,8
98,6
90,6
89,1
105,2
114
122,1
138
142,2
116,4
112,6
123,8
103,6
113,9
98,6
95
116
113,9
127,5
131,4
145,9
131,5
131
130,5
118,9
114,3
85,7
104,6
105,1
117,3
142,5
140
159,8
131,2
125,4
126,5
119,4
113,5
98,7
114,5
113, etc... | | | | Output produced by software: |
| Estimated Parameters of Exponential Smoothing | | Parameter | Value | | alpha | 0.0754804609554412 | | beta | 0.0688123430653692 | | gamma | 0.145742399878318 |
| Interpolation Forecasts of Exponential Smoothing | | t | Observed | Fitted | Residuals | | 13 | 95.9 | 95.2328359670504 | 0.667164032949628 | | 14 | 82.8 | 82.4158966582214 | 0.384103341778626 | | 15 | 83.3 | 82.9246934871367 | 0.375306512863276 | | 16 | 80 | 79.3934177269914 | 0.60658227300857 | | 17 | 80.4 | 79.7706270115215 | 0.629372988478465 | | 18 | 67.5 | 66.7505147737472 | 0.749485226252816 | | 19 | 75.7 | 70.1054628480633 | 5.59453715193669 | | 20 | 71.1 | 78.3313164076358 | -7.23131640763584 | | 21 | 89.3 | 81.1177274645233 | 8.18227253547673 | | 22 | 101.1 | 104.108334074047 | -3.00833407404703 | | 23 | 105.2 | 103.554013259526 | 1.6459867404744 | | 24 | 114.1 | 109.834171797475 | 4.2658282025245 | | 25 | 96.3 | 98.5504247616478 | -2.25042476164776 | | 26 | 84.4 | 85.1190236495592 | -0.719023649559205 | | 27 | 91.2 | 85.6035768631725 | 5.59642313682754 | | 28 | 81.9 | 82.4375712706993 | -0.537571270699274 | | 29 | 80.5 | 82.8062143801282 | -2.30621438012822 | | 30 | 70.4 | 69.1745629699802 | 1.22543703001980 | | 31 | 74.8 | 73.3972470526686 | 1.40275294733138 | | 32 | 75.9 | 79.7844650759951 | -3.88446507599514 | | 33 | 86.3 | 85.1245475950229 | 1.17545240497712 | | 34 | 98.7 | 106.684221053253 | -7.98422105325315 | | 35 | 100.9 | 106.372333849685 | -5.47233384968494 | | 36 | 113.8 | 112.539853560906 | 1.26014643909421 | | 37 | 89.8 | 99.8730401800989 | -10.0730401800989 | | 38 | 84.4 | 85.8313336836083 | -1.43133368360833 | | 39 | 87.2 | 87.0287095177412 | 0.17129048225884 | | 40 | 85.6 | 82.499303029043 | 3.10069697095707 | | 41 | 72 | 82.8089361438132 | -10.8089361438132 | | 42 | 69.2 | 68.9469015220223 | 0.253098477977744 | | 43 | 77.5 | 72.9643822326154 | 4.53561776738461 | | 44 | 78.1 | 78.724978298194 | -0.624978298194009 | | 45 | 94.3 | 84.8582858999982 | 9.44171410000176 | | 46 | 97.7 | 105.763165615604 | -8.06316561560416 | | 47 | 100.2 | 105.695209545937 | -5.49520954593746 | | 48 | 116.4 | 112.679424637046 | 3.72057536295389 | | 49 | 97.1 | 98.571293424571 | -1.47129342457094 | | 50 | 93 | 86.2325069906795 | 6.76749300932048 | | 51 | 96 | 88.3054513151034 | 7.69454868489662 | | 52 | 80.5 | 84.7055128367741 | -4.20551283677415 | | 53 | 76.1 | 82.564714764164 | -6.464714764164 | | 54 | 69.9 | 70.3334361292525 | -0.433436129252485 | | 55 | 73.6 | 74.9911615105482 | -1.39116151054817 | | 56 | 92.6 | 79.6715416379072 | 12.9284583620928 | | 57 | 94.2 | 88.447289844766 | 5.752710155234 | | 58 | 93.5 | 107.194717238848 | -13.6947172388478 | | 59 | 108.5 | 107.101967349896 | 1.39803265010393 | | 60 | 109.4 | 116.148772516106 | -6.74877251610637 | | 61 | 105.1 | 100.284407077200 | 4.81559292279955 | | 62 | 92.5 | 89.3042417028188 | 3.19575829718121 | | 63 | 97.1 | 91.2924278877996 | 5.8075721122004 | | 64 | 81.4 | 85.8464236098148 | -4.44642360981481 | | 65 | 79.1 | 83.3516892599446 | -4.25168925994457 | | 66 | 72.1 | 71.8790144383867 | 0.220985561613318 | | 67 | 78.7 | 76.5939424696098 | 2.10605753039022 | | 68 | 87.1 | 83.682796342581 | 3.41720365741902 | | 69 | 91.4 | 90.899124382917 | 0.500875617082926 | | 70 | 109.9 | 106.804299604056 | 3.09570039594412 | | 71 | 116.3 | 110.145382888560 | 6.15461711143966 | | 72 | 113 | 118.769132691297 | -5.76913269129663 | | 73 | 100 | 104.180827536405 | -4.18082753640485 | | 74 | 84.8 | 92.0380475987584 | -7.23804759875838 | | 75 | 94.3 | 93.597171340214 | 0.70282865978595 | | 76 | 87.1 | 86.245192432662 | 0.854807567337929 | | 77 | 90.3 | 84.1197456533712 | 6.1802543466288 | | 78 | 72.4 | 73.7941374110453 | -1.39413741104534 | | 79 | 84.9 | 78.7843858805643 | 6.11561411943569 | | 80 | 92.7 | 86.6012040357212 | 6.09879596427876 | | 81 | 92.2 | 93.8976216603754 | -1.69762166037536 | | 82 | 114.9 | 110.539900240134 | 4.36009975986578 | | 83 | 112.5 | 114.566241004821 | -2.06624100482074 | | 84 | 118.3 | 121.162805671396 | -2.86280567139642 | | 85 | 106 | 106.642302070862 | -0.642302070862158 | | 86 | 91.2 | 94.0084018548739 | -2.80840185487386 | | 87 | 96.6 | 97.1623620908655 | -0.562362090865463 | | 88 | 96.3 | 89.532741133076 | 6.76725886692391 | | 89 | 88.2 | 88.59615162711 | -0.396151627110029 | | 90 | 70.2 | 76.3665398557712 | -6.16653985577119 | | 91 | 86.5 | 82.2293512070977 | 4.27064879290229 | | 92 | 88.2 | 90.145222205961 | -1.94522220596106 | | 93 | 102.8 | 95.8968797627026 | 6.9031202372974 | | 94 | 119.1 | 114.564370453497 | 4.53562954650255 | | 95 | 119.2 | 117.846482727276 | 1.35351727272449 | | 96 | 125.1 | 124.856062373998 | 0.243937626001724 | | 97 | 106.1 | 110.418087158746 | -4.31808715874625 | | 98 | 102.1 | 96.8081770357873 | 5.29182296421268 | | 99 | 105.2 | 101.096314016265 | 4.1036859837355 | | 100 | 101 | 94.5926582844397 | 6.40734171556026 | | 101 | 84.3 | 92.636238706759 | -8.33623870675895 | | 102 | 87.5 | 78.5479177507134 | 8.95208224928658 | | 103 | 92.7 | 87.5079593143408 | 5.19204068565925 | | 104 | 94.4 | 95.1805074953356 | -0.780507495335584 | | 105 | 113 | 102.786851450214 | 10.2131485497857 | | 106 | 113.9 | 122.718823778725 | -8.81882377872508 | | 107 | 122.9 | 124.838131482188 | -1.9381314821876 | | 108 | 132.7 | 131.946206633851 | 0.75379336614887 | | 109 | 106.9 | 116.182157130141 | -9.28215713014103 | | 110 | 96.6 | 102.910309520757 | -6.31030952075689 | | 111 | 127.3 | 106.348264586809 | 20.9517354131912 | | 112 | 98.2 | 101.132896397176 | -2.93289639717567 | | 113 | 100.2 | 96.2882899882601 | 3.91171001173991 | | 114 | 89.4 | 84.8354324615593 | 4.56456753844076 | | 115 | 95.3 | 93.4847417648008 | 1.81525823519918 | | 116 | 104.2 | 100.520750431423 | 3.67924956857736 | | 117 | 106.4 | 110.575977702752 | -4.17597770275157 | | 118 | 116.2 | 127.705656998035 | -11.5056569980346 | | 119 | 135.9 | 130.73341124387 | 5.16658875612998 | | 120 | 134 | 139.188646836532 | -5.18864683653229 | | 121 | 104.6 | 120.753601953077 | -16.1536019530766 | | 122 | 107.1 | 106.772528954680 | 0.327471045320110 | | 123 | 123.5 | 114.744120000408 | 8.7558799995924 | | 124 | 98.8 | 104.918906987847 | -6.11890698784731 | | 125 | 98.6 | 100.547530009895 | -1.94753000989479 | | 126 | 90.6 | 88.2629380760567 | 2.33706192394331 | | 127 | 89.1 | 96.518502420977 | -7.41850242097696 | | 128 | 105.2 | 103.112103318784 | 2.08789668121581 | | 129 | 114 | 111.981886405564 | 2.01811359443602 | | 130 | 122.1 | 128.781136471756 | -6.68113647175619 | | 131 | 138 | 134.417538434051 | 3.58246156594913 | | 132 | 142.2 | 141.339505586341 | 0.860494413658586 | | 133 | 116.4 | 121.281615501989 | -4.88161550198879 | | 134 | 112.6 | 110.00266315173 | 2.59733684826999 | | 135 | 123.8 | 119.517870467601 | 4.28212953239934 | | 136 | 103.6 | 106.939765300306 | -3.33976530030630 | | 137 | 113.9 | 103.198904774264 | 10.7010952257364 | | 138 | 98.6 | 92.0176184962678 | 6.58238150373215 | | 139 | 95 | 99.601517462436 | -4.60151746243601 | | 140 | 116 | 108.131573617209 | 7.86842638279057 | | 141 | 113.9 | 117.960030852564 | -4.0600308525642 | | 142 | 127.5 | 133.922164212146 | -6.42216421214579 | | 143 | 131.4 | 141.399907179708 | -9.9999071797076 | | 144 | 145.9 | 147.197977553068 | -1.29797755306834 | | 145 | 131.5 | 125.379731561904 | 6.12026843809555 | | 146 | 131 | 115.531397826611 | 15.4686021733894 | | 147 | 130.5 | 126.900924925775 | 3.59907507422508 | | 148 | 118.9 | 112.568822097604 | 6.3311779023956 | | 149 | 114.3 | 111.488568862143 | 2.81143113785735 | | 150 | 85.7 | 98.5039597334794 | -12.8039597334794 | | 151 | 104.6 | 103.360198512349 | 1.23980148765125 | | 152 | 105.1 | 114.551508528088 | -9.45150852808788 | | 153 | 117.3 | 121.684416224237 | -4.3844162242371 | | 154 | 142.5 | 137.809028400856 | 4.69097159914432 | | 155 | 140 | 145.936978429468 | -5.93697842946821 | | 156 | 159.8 | 153.565245826811 | 6.23475417318915 | | 157 | 131.2 | 132.348159955103 | -1.14815995510347 | | 158 | 125.4 | 122.790308082030 | 2.60969191796958 | | 159 | 126.5 | 131.821789672770 | -5.32178967276957 | | 160 | 119.4 | 116.658746568187 | 2.74125343181279 | | 161 | 113.5 | 114.661535221815 | -1.16153522181524 | | 162 | 98.7 | 98.7969112500533 | -0.0969112500532958 | | 163 | 114.5 | 106.685149231439 | 7.81485076856107 | | 164 | 113.8 | 117.235502044247 | -3.43550204424663 | | 165 | 133.1 | 125.840037548489 | 7.2599624515108 | | 166 | 143.4 | 144.957714999671 | -1.55771499967111 | | 167 | 137.3 | 151.49431237477 | -14.1943123747700 | | 168 | 165.2 | 160.520272784680 | 4.67972721532024 | | 169 | 126.9 | 137.303535637755 | -10.4035356377552 | | 170 | 124 | 127.202626974008 | -3.20262697400842 | | 171 | 135.7 | 134.867742692728 | 0.8322573072723 | | 172 | 130 | 120.765105707162 | 9.23489429283825 | | 173 | 109.4 | 118.618374126380 | -9.21837412638044 | | 174 | 117.8 | 101.762756492383 | 16.0372435076169 | | 175 | 120.3 | 112.345434738981 | 7.95456526101921 | | 176 | 121 | 121.786312429892 | -0.786312429891609 | | 177 | 132.3 | 132.543558005469 | -0.243558005468628 | | 178 | 142.9 | 150.62853366763 | -7.72853366762996 | | 179 | 147.4 | 155.155224560388 | -7.75522456038814 | | 180 | 175.9 | 167.747459455240 | 8.15254054475955 | | 181 | 132.6 | 141.697494772399 | -9.09749477239902 | | 182 | 123.7 | 132.338655230114 | -8.63865523011422 | | 183 | 153.3 | 140.493725121465 | 12.8062748785346 | | 184 | 134 | 127.865029834123 | 6.1349701658773 | | 185 | 119.6 | 122.790403784752 | -3.19040378475178 | | 186 | 116.2 | 109.191945483937 | 7.00805451606345 | | 187 | 118.6 | 118.377638177415 | 0.222361822584546 | | 188 | 130.7 | 126.327797314632 | 4.37220268536844 | | 189 | 129.3 | 138.000924457495 | -8.70092445749481 | | 190 | 144.4 | 155.016682399648 | -10.6166823996484 | | 191 | 163.2 | 159.437382507700 | 3.76261749230017 | | 192 | 179.4 | 175.656136324161 | 3.74386367583855 | | 193 | 128.1 | 145.814815896969 | -17.7148158969692 | | 194 | 138.4 | 135.514828167827 | 2.88517183217309 | | 195 | 152.7 | 147.885269666006 | 4.81473033399402 | | 196 | 120 | 133.201586468767 | -13.2015864687667 | | 197 | 140.5 | 125.122926183154 | 15.3770738168465 | | 198 | 116.2 | 113.856340843052 | 2.34365915694816 | | 199 | 121.4 | 121.952780204266 | -0.552780204265744 | | 200 | 127.8 | 130.585659578754 | -2.78565957875357 | | 201 | 143.6 | 140.077422881536 | 3.522577118464 | | 202 | 157.6 | 158.229649746253 | -0.629649746252994 | | 203 | 166.2 | 165.590624645950 | 0.609375354049632 | | 204 | 182.3 | 182.084508373576 | 0.215491626424296 | | 205 | 153.1 | 147.972158830709 | 5.1278411692912 | | 206 | 147.6 | 141.978410040908 | 5.62158995909178 | | 207 | 157.7 | 155.487489708773 | 2.21251029122649 | | 208 | 137.2 | 137.448950487248 | -0.248950487248436 | | 209 | 151.5 | 134.144342366703 | 17.355657633297 | | 210 | 98.7 | 120.613075888685 | -21.9130758886849 | | 211 | 145.8 | 126.797616946527 | 19.0023830534734 | | 212 | 151.7 | 137.154458537139 | 14.5455414628607 | | 213 | 129.4 | 149.685219241002 | -20.2852192410020 | | 214 | 174.1 | 166.486348985370 | 7.61365101462951 | | 215 | 197 | 175.216054849226 | 21.7839451507737 | | 216 | 193.9 | 194.636601696513 | -0.736601696512736 | | 217 | 164.1 | 159.047103883118 | 5.05289611688175 | | 218 | 142.8 | 152.881948834189 | -10.0819488341889 | | 219 | 157.9 | 165.676549288060 | -7.77654928806027 | | 220 | 159.2 | 145.545083942813 | 13.6549160571870 | | 221 | 162.2 | 145.722716921373 | 16.4772830786271 | | 222 | 123.1 | 125.563638027374 | -2.46363802737426 | | 223 | 130 | 140.015136307893 | -10.0151363078928 | | 224 | 150.1 | 148.193702873056 | 1.90629712694391 | | 225 | 169.4 | 155.461651624815 | 13.9383483751854 | | 226 | 179.7 | 180.511521336569 | -0.811521336568518 | | 227 | 182.1 | 191.415316212980 | -9.31531621297975 | | 228 | 194.3 | 206.379110257327 | -12.0791102573266 | | 229 | 161.4 | 168.728188593815 | -7.32818859381541 | | 230 | 169.4 | 159.072209525697 | 10.3277904743029 | | 231 | 168.8 | 174.576852082780 | -5.77685208277958 | | 232 | 158.1 | 156.479380994632 | 1.62061900536807 | | 233 | 158.5 | 156.054075962605 | 2.44592403739512 | | 234 | 135.3 | 131.065471921700 | 4.23452807830043 | | 235 | 149.3 | 145.630349988117 | 3.66965001188274 | | 236 | 143.4 | 157.071332800774 | -13.6713328007744 | | 237 | 142.2 | 165.141905273146 | -22.9419052731463 | | 238 | 188.4 | 185.834788828588 | 2.56521117141241 | | 239 | 166.2 | 195.874064125495 | -29.6740641254952 | | 240 | 199.2 | 208.855213423628 | -9.65521342362817 | | 241 | 182.7 | 170.946119495629 | 11.7538805043706 | | 242 | 145.2 | 164.701891098602 | -19.5018910986019 | | 243 | 182.1 | 175.551280973688 | 6.5487190263116 | | 244 | 158.7 | 158.830764636220 | -0.130764636219794 | | 245 | 141.6 | 158.081036694607 | -16.4810366946066 | | 246 | 132.6 | 131.535137507642 | 1.06486249235797 | | 247 | 139.6 | 145.372698202468 | -5.77269820246832 | | 248 | 147 | 153.222013245283 | -6.22201324528265 | | 249 | 166.6 | 160.075562077040 | 6.52443792296032 | | 250 | 157 | 186.144982254351 | -29.1449822543510 | | 251 | 180.4 | 188.837027777461 | -8.43702777746122 | | 252 | 210.2 | 205.552711413196 | 4.64728858680371 | | 253 | 159.8 | 171.458398622834 | -11.6583986228344 | | 254 | 157.8 | 159.015207908992 | -1.21520790899234 | | 255 | 168.2 | 174.265920592401 | -6.06592059240054 | | 256 | 158.4 | 155.669082919605 | 2.73091708039533 | | 257 | 152 | 152.647651348802 | -0.647651348802128 | | 258 | 142.2 | 129.753184768845 | 12.4468152311552 | | 259 | 137.2 | 143.259107675992 | -6.05910767599235 | | 260 | 152.6 | 150.772284275781 | 1.82771572421908 | | 261 | 166.8 | 159.747538899656 | 7.05246110034437 | | 262 | 165.6 | 180.698354700027 | -15.0983547000267 | | 263 | 198.6 | 187.12632072931 | 11.4736792706899 | | 264 | 201.5 | 207.214128316498 | -5.71412831649809 | | 265 | 170.7 | 170.053816848923 | 0.64618315107731 | | 266 | 164.4 | 159.908219327289 | 4.4917806727108 | | 267 | 179.7 | 175.134022558505 | 4.56597744149488 | | 268 | 157 | 158.386925147099 | -1.38692514709891 | | 269 | 168 | 154.634003892909 | 13.3659961070913 | | 270 | 139.3 | 134.250390752676 | 5.04960924732367 | | 271 | 138.6 | 144.974503955605 | -6.37450395560478 | | 272 | 153.4 | 153.791455120714 | -0.391455120713687 | | 273 | 138.9 | 163.564208150216 | -24.6642081502156 | | 274 | 172.1 | 179.103326021629 | -7.00332602162894 | | 275 | 198.4 | 189.749653467146 | 8.65034653285392 | | 276 | 217.8 | 207.332551107878 | 10.4674488921222 | | 277 | 173.7 | 171.909863318466 | 1.79013668153414 | | 278 | 153.8 | 162.292610114483 | -8.49261011448337 | | 279 | 175.6 | 176.581133624842 | -0.981133624841817 | | 280 | 147.1 | 158.509455759079 | -11.4094557590793 | | 281 | 160.3 | 155.869004748775 | 4.43099525122517 | | 282 | 135.2 | 133.730554641587 | 1.46944535841308 | | 283 | 148.8 | 142.383561876337 | 6.41643812366257 | | 284 | 151 | 152.813397235032 | -1.8133972350316 | | 285 | 148.2 | 159.009787032605 | -10.8097870326053 | | 286 | 182.2 | 177.893990476923 | 4.30600952307728 | | 287 | 189.2 | 191.547511503034 | -2.34751150303362 | | 288 | 183.1 | 208.464412193103 | -25.3644121931027 | | 289 | 170 | 169.500809177604 | 0.4991908223964 | | 290 | 158.4 | 158.381632053845 | 0.0183679461547115 | | 291 | 176.1 | 173.949801572865 | 2.15019842713500 | | 292 | 156.2 | 154.818607436064 | 1.38139256393626 | | 293 | 153.2 | 155.207642157460 | -2.00764215745963 | | 294 | 117.9 | 132.353309114108 | -14.4533091141084 | | 295 | 149.8 | 140.098296458894 | 9.70170354110607 | | 296 | 156.6 | 149.317174965689 | 7.28282503431109 | | 297 | 166.7 | 154.765729744963 | 11.9342702550370 | | 298 | 156.8 | 177.240271089512 | -20.4402710895122 | | 299 | 158.6 | 187.761750279868 | -29.1617502798684 | | 300 | 210.8 | 198.80780529114 | 11.9921947088597 | | 301 | 203.6 | 166.611165296203 | 36.9888347037968 | | 302 | 175.2 | 158.27762798104 | 16.9223720189598 | | 303 | 168.7 | 175.714405059563 | -7.01440505956339 | | 304 | 155.9 | 155.825745034868 | 0.0742549651322975 | | 305 | 147.3 | 155.776615023442 | -8.47661502344232 | | 306 | 137 | 130.756675657504 | 6.2433243424957 | | 307 | 141.1 | 143.687069540194 | -2.58706954019408 | | 308 | 167.4 | 151.865121528125 | 15.5348784718751 | | 309 | 160.2 | 158.821973280508 | 1.37802671949214 | | 310 | 191.9 | 176.439662314221 | 15.4603376857787 | | 311 | 174.4 | 189.096550260132 | -14.6965502601316 | | 312 | 208.2 | 207.908365654612 | 0.291634345387564 | | 313 | 159.4 | 177.490585575635 | -18.0905855756352 | | 314 | 161.1 | 162.190382656486 | -1.09038265648621 | | 315 | 172.1 | 175.013447861397 | -2.91344786139672 | | 316 | 158.4 | 156.307126141605 | 2.09287385839485 | | 317 | 114.6 | 155.235345762939 | -40.6353457629387 | | 318 | 159.6 | 129.879828487425 | 29.7201715125748 | | 319 | 159.7 | 143.361285707579 | 16.3387142924211 | | 320 | 159.4 | 155.570623830657 | 3.82937616934296 | | 321 | 160.7 | 159.759992705524 | 0.94000729447626 | | 322 | 165.5 | 179.319665823398 | -13.819665823398 | | 323 | 205 | 185.479944180646 | 19.5200558193542 | | 324 | 205.2 | 209.029456781255 | -3.82945678125478 | | 325 | 141.6 | 175.685047034729 | -34.0850470347292 | | 326 | 148.1 | 161.430675030397 | -13.3306750303968 | | 327 | 184.9 | 172.813291526024 | 12.0867084739758 | | 328 | 132.5 | 155.917198925 | -23.4171989249999 | | 329 | 137.3 | 146.981489970683 | -9.68148997068278 | | 330 | 135.5 | 133.379973322293 | 2.12002667770696 | | 331 | 121.7 | 142.584204036107 | -20.8842040361067 | | 332 | 166.1 | 149.522649578926 | 16.5773504210744 | | 333 | 146.8 | 153.809689736714 | -7.00968973671411 | | 334 | 162.8 | 169.607494808112 | -6.80749480811232 | | 335 | 186.8 | 179.858344034479 | 6.94165596552057 | | 336 | 185.5 | 197.8576040439 | -12.3576040438998 | | 337 | 151.5 | 161.267548450630 | -9.76754845063033 | | 338 | 158.1 | 151.711560632387 | 6.38843936761333 | | 339 | 143 | 167.088154391356 | -24.0881543913558 | | 340 | 151.2 | 143.545233512191 | 7.6547664878089 | | 341 | 147.6 | 138.806146175922 | 8.79385382407759 | | 342 | 130.7 | 128.485552885035 | 2.21444711496531 | | 343 | 137.5 | 134.202467648771 | 3.29753235122871 | | 344 | 146.1 | 147.615246453815 | -1.51524645381460 | | 345 | 133.6 | 147.252161274955 | -13.6521612749548 | | 346 | 167.9 | 161.755345849111 | 6.14465415088901 | | 347 | 181.9 | 174.285476638414 | 7.61452336158573 | | 348 | 202 | 189.092769105883 | 12.9072308941172 | | 349 | 166.5 | 155.714185405355 | 10.7858145946449 | | 350 | 151.3 | 150.121909688815 | 1.17809031118546 | | 351 | 146.2 | 160.869258858163 | -14.6692588581630 | | 352 | 148.3 | 142.690373874223 | 5.60962612577745 | | 353 | 144.7 | 138.139355913426 | 6.56064408657414 | | 354 | 123.6 | 127.035205388819 | -3.43520538881944 | | 355 | 151.6 | 132.449500066821 | 19.1504999331786 | | 356 | 133.9 | 146.492844078083 | -12.5928440780827 | | 357 | 137.4 | 143.782992727413 | -6.38299272741304 | | 358 | 181.6 | 161.536374332517 | 20.0636256674827 | | 359 | 182 | 175.579694942619 | 6.42030505738052 | | 360 | 190 | 191.30070031177 | -1.30070031177007 | | 361 | 161.2 | 156.836432104226 | 4.36356789577425 | | 362 | 155.5 | 149.634934210359 | 5.86506578964148 | | 363 | 141.9 | 158.735187114784 | -16.8351871147838 | | 364 | 164.6 | 143.290897932204 | 21.3091020677962 | | 365 | 136.2 | 140.230768655027 | -4.03076865502723 | | 366 | 126.8 | 127.086133693249 | -0.286133693248814 | | 367 | 152.5 | 135.978286479825 | 16.5217135201749 | | 368 | 126.6 | 145.747217413100 | -19.1472174131003 | | 369 | 150.1 | 143.504510593641 | 6.5954894063587 | | 370 | 186.3 | 166.245745027873 | 20.0542549721269 | | 371 | 147.5 | 178.820459049232 | -31.3204590492318 | | 372 | 200.4 | 190.662563222386 | 9.73743677761405 | | 373 | 177.2 | 157.815989345257 | 19.3840106547429 | | 374 | 127.4 | 152.036268159643 | -24.6362681596433 | | 375 | 177.1 | 155.730461601357 | 21.3695383986428 | | 376 | 154.4 | 148.339599575485 | 6.06040042451454 | | 377 | 135.2 | 140.755226446009 | -5.55522644600893 | | 378 | 126.4 | 127.998353906702 | -1.59835390670202 | | 379 | 147.3 | 139.193225524307 | 8.1067744756931 | | 380 | 140.6 | 143.542221776613 | -2.94222177661291 | | 381 | 152.3 | 146.141836333723 | 6.15816366627732 | | 382 | 151.2 | 171.064457327278 | -19.8644573272776 | | 383 | 172.2 | 173.555411973667 | -1.35541197366652 | | 384 | 215.3 | 193.41727014621 | 21.88272985379 | | 385 | 154.1 | 162.496053594127 | -8.39605359412732 | | 386 | 159.3 | 148.632513442267 | 10.6674865577334 | | 387 | 160.4 | 161.545361181224 | -1.14536118122368 | | 388 | 151.9 | 150.358137718704 | 1.54186228129578 | | 389 | 148.4 | 140.838101379886 | 7.56189862011433 | | 390 | 139.6 | 129.538148200398 | 10.0618517996021 | | 391 | 148.2 | 143.339709840559 | 4.86029015944146 | | 392 | 153.5 | 146.146521303914 | 7.35347869608623 | | 393 | 145.1 | 151.060318899433 | -5.96031889943262 | | 394 | 183.7 | 172.151902134628 | 11.5480978653715 | | 395 | 210.5 | 180.086042879421 | 30.4139571205789 | | 396 | 203.3 | 207.238303697958 | -3.93830369795774 | | 397 | 153.3 | 168.983678191185 | -15.6836781911848 | | 398 | 144.3 | 156.956345105342 | -12.6563451053421 | | 399 | 169.6 | 167.057267351793 | 2.54273264820660 | | 400 | 143.7 | 156.303219173420 | -12.6032191734197 | | 401 | 160.1 | 146.35743236885 | 13.7425676311499 | | 402 | 135.6 | 135.577766600603 | 0.0222333993969244 | | 403 | 141.8 | 148.367365687373 | -6.56736568737313 | | 404 | 159.9 | 150.732835949363 | 9.16716405063664 | | 405 | 145.7 | 154.082058602173 | -8.38205860217306 | | 406 | 183.5 | 177.944218476874 | 5.55578152312552 | | 407 | 198.2 | 188.111863506676 | 10.0881364933243 | | 408 | 186.8 | 209.227402537999 | -22.4274025379993 | | 409 | 172 | 167.583075132478 | 4.41692486752248 | | 410 | 150.6 | 157.254950644472 | -6.6549506444722 | | 411 | 163.3 | 170.017244445381 | -6.7172444453808 | | 412 | 153.7 | 156.276884726660 | -2.57688472665981 | | 413 | 152.9 | 150.503656395929 | 2.39634360407106 | | 414 | 135.5 | 136.801781825397 | -1.30178182539714 | | 415 | 148.5 | 148.599094607332 | -0.099094607332006 | | 416 | 148.4 | 153.552637480464 | -5.15263748046357 | | 417 | 133.6 | 153.310556948823 | -19.7105569488233 | | 418 | 194.1 | 177.874012851900 | 16.2259871480995 | | 419 | 208.6 | 189.262074056446 | 19.3379259435538 | | 420 | 197.3 | 206.556548526833 | -9.256548526833 | | 421 | 164.4 | 169.210519559140 | -4.81051955914026 | | 422 | 148.1 | 156.556086862315 | -8.45608686231517 | | 423 | 152 | 169.046528016972 | -17.0465280169716 | | 424 | 144.1 | 154.978579659446 | -10.8785796594455 | | 425 | 155 | 149.093739473351 | 5.90626052664871 | | 426 | 124.5 | 135.129908403824 | -10.6299084038238 | | 427 | 153 | 145.956169645207 | 7.04383035479299 | | 428 | 146 | 150.502603038921 | -4.50260303892091 | | 429 | 138 | 148.152089424049 | -10.1520894240486 | | 430 | 190 | 177.712651301005 | 12.2873486989951 | | 431 | 192 | 188.834001841098 | 3.16599815890208 | | 432 | 192 | 200.472299877024 | -8.47229987702445 | | 433 | 147 | 164.368288641132 | -17.3682886411324 | | 434 | 133 | 150.364193581064 | -17.3641935810645 | | 435 | 163 | 160.19442486749 | 2.80557513250983 | | 436 | 150 | 148.561365290672 | 1.43863470932777 | | 437 | 129 | 145.752440032313 | -16.7524400323126 | | 438 | 131 | 128.218584042153 | 2.7814159578472 | | 439 | 145 | 141.739553927189 | 3.26044607281077 | | 440 | 137 | 144.104710687596 | -7.1047106875962 | | 441 | 138 | 140.643121127480 | -2.64312112747984 | | 442 | 168 | 172.240937376648 | -4.24093737664813 | | 443 | 176 | 180.094610093677 | -4.09461009367749 | | 444 | 188 | 188.676334780369 | -0.676334780369046 | | 445 | 139 | 153.479480209668 | -14.4794802096682 | | 446 | 143 | 140.043648158909 | 2.95635184109068 | | 447 | 150 | 153.310711924240 | -3.31071192423963 | | 448 | 154 | 141.389428761313 | 12.6105712386875 | | 449 | 137 | 137.033897157788 | -0.0338971577880898 | | 450 | 129 | 123.827513984973 | 5.17248601502693 | | 451 | 128 | 137.059923483735 | -9.05992348373476 | | 452 | 140 | 136.941461596336 | 3.05853840366436 | | 453 | 143 | 134.866746650031 | 8.13325334996932 | | 454 | 151 | 166.007828434087 | -15.0078284340870 | | 455 | 177 | 172.680227685543 | 4.31977231445731 | | 456 | 184 | 181.997354408142 | 2.00264559185834 | | 457 | 151 | 146.365684693923 | 4.63431530607733 | | 458 | 134 | 137.046300187522 | -3.04630018752235 | | 459 | 164 | 148.731380910241 | 15.2686190897588 | | 460 | 126 | 140.658736853849 | -14.6587368538486 | | 461 | 131 | 132.755076320922 | -1.75507632092206 | | 462 | 125 | 120.507374017629 | 4.49262598237134 | | 463 | 127 | 131.392057650653 | -4.3920576506533 | | 464 | 143 | 133.197841251031 | 9.80215874896928 | | 465 | 143 | 132.39691207622 | 10.6030879237800 | | 466 | 160 | 159.983289250016 | 0.0167107499840995 | | 467 | 190 | 170.366734125451 | 19.6332658745486 | | 468 | 182 | 180.693844499038 | 1.30615550096203 | | 469 | 138 | 145.880962898054 | -7.88096289805372 | | 470 | 136 | 134.856652074421 | 1.14334792557946 | | 471 | 152 | 149.320779769235 | 2.67922023076454 | | 472 | 127 | 136.550252906727 | -9.55025290672728 | | 473 | 151 | 130.945697982197 | 20.0543020178033 | | 474 | 130 | 121.388144675785 | 8.61185532421496 | | 475 | 119 | 131.681550320279 | -12.6815503202795 | | 476 | 153 | 134.989039690101 | 18.0109603098986 |
| Extrapolation Forecasts of Exponential Smoothing | | t | Forecast | 95% Lower Bound | 95% Upper Bound | | 477 | 135.151601073994 | 131.000321391756 | 139.302880756231 | | 478 | 160.847118808214 | 156.282918281663 | 165.411319334765 | | 479 | 174.176650351491 | 169.176766941744 | 179.176533761238 | | 480 | 180.697626543404 | 175.275004310943 | 186.120248775865 | | 481 | 144.718396240073 | 139.460979532342 | 149.975812947803 | | 482 | 135.625274846243 | 130.175441510890 | 141.075108181596 | | 483 | 150.428828785048 | 144.305842627938 | 156.551814942157 | | 484 | 135.882174682901 | 129.740078407166 | 142.024270958637 | | 485 | 135.131309944456 | 128.630480234669 | 141.632139654243 | | 486 | 122.583049334962 | 116.090909171625 | 129.075189498299 | | 487 | 129.334822439710 | 122.212881538455 | 136.456763340964 | | 488 | 137.827254274072 | 90.2473389036252 | 185.407169644518 |
| | | Charts produced by software: |  | | http://www.freestatistics.org/blog/date/2010/May/31/t127532902476ftibhyo3qa8hr/1i7uj1275328967.png (open in new window) | | http://www.freestatistics.org/blog/date/2010/May/31/t127532902476ftibhyo3qa8hr/1i7uj1275328967.ps (open in new window) |
 | | http://www.freestatistics.org/blog/date/2010/May/31/t127532902476ftibhyo3qa8hr/2i7uj1275328967.png (open in new window) | | http://www.freestatistics.org/blog/date/2010/May/31/t127532902476ftibhyo3qa8hr/2i7uj1275328967.ps (open in new window) |
 | | http://www.freestatistics.org/blog/date/2010/May/31/t127532902476ftibhyo3qa8hr/3sztm1275328967.png (open in new window) | | http://www.freestatistics.org/blog/date/2010/May/31/t127532902476ftibhyo3qa8hr/3sztm1275328967.ps (open in new window) |
| | | | Parameters (Session): | | par1 = 12 ; par2 = Triple ; par3 = multiplicative ; | | | | Parameters (R input): | | par1 = 12 ; par2 = Triple ; par3 = multiplicative ; | | | | R code (references can be found in the software module): | par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')
| | |
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