| | | *The author of this computation has been verified* | | R Software Module: /rwasp_exponentialsmoothing.wasp (opens new window with default values) | | Title produced by software: Exponential Smoothing | | Date of computation: Wed, 08 Dec 2010 14:59:13 +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/Dec/08/t12918213179865yosk2e5j6ec.htm/, Retrieved Wed, 08 Dec 2010 16:15:17 +0100 | | | | 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/Dec/08/t12918213179865yosk2e5j6ec.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: | | | | | Dataseries X: | | » Textbox « » Textfile « » CSV « | | 235.1
280.7
264.6
240.7
201.4
240.8
241.1
223.8
206.1
174.7
203.3
220.5
299.5
347.4
338.3
327.7
351.6
396.6
438.8
395.6
363.5
378.8
357
369
464.8
479.1
431.3
366.5
326.3
355.1
331.6
261.3
249
205.5
235.6
240.9
264.9
253.8
232.3
193.8
177
213.2
207.2
180.6
188.6
175.4
199
179.6
225.8
234
200.2
183.6
178.2
203.2
208.5
191.8
172.8
148
159.4
154.5
213.2
196.4
182.8
176.4
153.6
173.2
171
151.2
161.9
157.2
201.7
236.4
356.1
398.3
403.7
384.6
365.8
368.1
367.9
347
343.3
292.9
311.5
300.9
366.9
356.9
329.7
316.2
269
289.3
266.2
253.6
233.8
228.4
253.6
260.1
306.6
309.2
309.5
271
279.9
317.9
298.4
246.7
227.3
209.1
259.9
266
320.6
308.5
282.2
262.7
263.5
313.1
284.3
252.6
250.3
246.5
312.7
333.2
446.4
511.6
515.5
506.4
483.2
522.3
509.8
460.7
405.8
375
378.5
406.8
467.8
469.8
429.8
355.8
332.7
378
360.5
334.7
319.5
323.1
363.6
352.1
411.9
388.6
416.4
360.7
338
417.2
388. etc... | | | | Output produced by software: |
| Estimated Parameters of Exponential Smoothing | | Parameter | Value | | alpha | 0.859089779897674 | | beta | 0.0739551466119535 | | gamma | 1 |
| Interpolation Forecasts of Exponential Smoothing | | t | Observed | Fitted | Residuals | | 13 | 299.5 | 239.394497863248 | 60.105502136752 | | 14 | 347.4 | 339.492568454785 | 7.90743154521482 | | 15 | 338.3 | 339.929368367977 | -1.62936836797678 | | 16 | 327.7 | 329.223847139343 | -1.52384713934293 | | 17 | 351.6 | 353.166328513730 | -1.56632851373035 | | 18 | 396.6 | 400.389465951146 | -3.78946595114559 | | 19 | 438.8 | 384.599468387819 | 54.2005316121809 | | 20 | 395.6 | 427.763334305495 | -32.1633343054951 | | 21 | 363.5 | 393.901916821003 | -30.4019168210031 | | 22 | 378.8 | 345.076323015715 | 33.7236769842847 | | 23 | 357 | 410.295475302627 | -53.2954753026268 | | 24 | 369 | 383.104615914129 | -14.1046159141288 | | 25 | 464.8 | 456.976411932666 | 7.82358806733362 | | 26 | 479.1 | 502.592180774858 | -23.4921807748580 | | 27 | 431.3 | 470.502913550706 | -39.202913550706 | | 28 | 366.5 | 420.938862378819 | -54.4388623788188 | | 29 | 326.3 | 389.460350164271 | -63.1603501642712 | | 30 | 355.1 | 369.585850194136 | -14.4858501941362 | | 31 | 331.6 | 338.228916187246 | -6.62891618724552 | | 32 | 261.3 | 298.551363583577 | -37.2513635835773 | | 33 | 249 | 241.829900212188 | 7.17009978781158 | | 34 | 205.5 | 217.967924422901 | -12.4679244229012 | | 35 | 235.6 | 211.957644808095 | 23.6423551919051 | | 36 | 240.9 | 241.98904722745 | -1.08904722745021 | | 37 | 264.9 | 316.562591234604 | -51.6625912346038 | | 38 | 253.8 | 289.312575917534 | -35.5125759175336 | | 39 | 232.3 | 226.570098552231 | 5.72990144776912 | | 40 | 193.8 | 198.202426353210 | -4.40242635320968 | | 41 | 177 | 196.401736377519 | -19.4017363775191 | | 42 | 213.2 | 211.679691597586 | 1.52030840241380 | | 43 | 207.2 | 186.898687006962 | 20.301312993038 | | 44 | 180.6 | 159.470671269898 | 21.1293287301018 | | 45 | 188.6 | 156.301135563512 | 32.2988644364878 | | 46 | 175.4 | 149.994593438554 | 25.4054065614463 | | 47 | 199 | 182.750228339167 | 16.2497716608326 | | 48 | 179.6 | 203.617164709325 | -24.0171647093253 | | 49 | 225.8 | 250.581684813321 | -24.7816848133213 | | 50 | 234 | 249.622954887637 | -15.6229548876367 | | 51 | 200.2 | 211.965074818564 | -11.7650748185640 | | 52 | 183.6 | 168.214511591807 | 15.3854884081933 | | 53 | 178.2 | 183.631681264515 | -5.43168126451542 | | 54 | 203.2 | 217.078693406992 | -13.8786934069917 | | 55 | 208.5 | 183.956032762703 | 24.5439672372974 | | 56 | 191.8 | 162.800100601192 | 28.999899398808 | | 57 | 172.8 | 170.976629955543 | 1.82337004445708 | | 58 | 148 | 138.591946465025 | 9.40805353497475 | | 59 | 159.4 | 156.372321819668 | 3.02767818033197 | | 60 | 154.5 | 159.424241468732 | -4.92424146873239 | | 61 | 213.2 | 223.114591521913 | -9.91459152191297 | | 62 | 196.4 | 237.594179120147 | -41.1941791201465 | | 63 | 182.8 | 178.262882364703 | 4.53711763529682 | | 64 | 176.4 | 153.129849185552 | 23.2701508144476 | | 65 | 153.6 | 173.674936082875 | -20.0749360828750 | | 66 | 173.2 | 193.709097448662 | -20.5090974486619 | | 67 | 171 | 160.240503322417 | 10.7594966775835 | | 68 | 151.2 | 126.930608984476 | 24.2693910155242 | | 69 | 161.9 | 125.973456778233 | 35.9265432217675 | | 70 | 157.2 | 124.881635601938 | 32.3183643980615 | | 71 | 201.7 | 163.826966358072 | 37.8730336419277 | | 72 | 236.4 | 200.289538262072 | 36.1104617379277 | | 73 | 356.1 | 305.732164758813 | 50.367835241187 | | 74 | 398.3 | 378.625119516164 | 19.6748804838356 | | 75 | 403.7 | 392.930042429074 | 10.7699575709265 | | 76 | 384.6 | 391.087477668013 | -6.4874776680125 | | 77 | 365.8 | 393.365923368252 | -27.5659233682523 | | 78 | 368.1 | 419.833142168581 | -51.7331421685811 | | 79 | 367.9 | 374.89222873197 | -6.99222873197033 | | 80 | 347 | 338.053724532858 | 8.94627546714219 | | 81 | 343.3 | 334.419745556591 | 8.88025444340911 | | 82 | 292.9 | 316.710436241821 | -23.8104362418211 | | 83 | 311.5 | 311.778835654345 | -0.278835654344562 | | 84 | 300.9 | 316.353255060838 | -15.4532550608384 | | 85 | 366.9 | 377.367067087161 | -10.4670670871610 | | 86 | 356.9 | 387.667374574820 | -30.7673745748205 | | 87 | 329.7 | 348.173219823229 | -18.4732198232289 | | 88 | 316.2 | 307.708594744637 | 8.49140525536296 | | 89 | 269 | 309.768950771735 | -40.7689507717352 | | 90 | 289.3 | 310.533206458106 | -21.2332064581061 | | 91 | 266.2 | 289.081745239821 | -22.8817452398206 | | 92 | 253.6 | 230.811908838495 | 22.7880911615046 | | 93 | 233.8 | 229.912707575474 | 3.88729242452641 | | 94 | 228.4 | 193.843038149833 | 34.5569618501666 | | 95 | 253.6 | 236.613931438545 | 16.9860685614551 | | 96 | 260.1 | 249.222948841631 | 10.8770511583691 | | 97 | 306.6 | 330.573061287800 | -23.9730612877995 | | 98 | 309.2 | 322.565493664962 | -13.3654936649622 | | 99 | 309.5 | 297.014609303718 | 12.4853906962820 | | 100 | 271 | 286.173849460292 | -15.1738494602924 | | 101 | 279.9 | 258.686836584542 | 21.2131634154579 | | 102 | 317.9 | 317.114554808372 | 0.785445191628298 | | 103 | 298.4 | 317.408207348347 | -19.0082073483469 | | 104 | 246.7 | 272.208947367314 | -25.5089473673142 | | 105 | 227.3 | 227.393941712298 | -0.0939417122979478 | | 106 | 209.1 | 192.211763945066 | 16.8882360549335 | | 107 | 259.9 | 216.191209606794 | 43.7087903932063 | | 108 | 266 | 251.457918172993 | 14.5420818270065 | | 109 | 320.6 | 331.840035391451 | -11.2400353914510 | | 110 | 308.5 | 337.869127744946 | -29.3691277449465 | | 111 | 282.2 | 302.798694924629 | -20.5986949246292 | | 112 | 262.7 | 258.122653888003 | 4.57734611199737 | | 113 | 263.5 | 252.470256166133 | 11.0297438338667 | | 114 | 313.1 | 298.363296829439 | 14.7367031705608 | | 115 | 284.3 | 307.831853745127 | -23.5318537451273 | | 116 | 252.6 | 257.521597984580 | -4.92159798457968 | | 117 | 250.3 | 234.973450068096 | 15.3265499319041 | | 118 | 246.5 | 217.410790950303 | 29.0892090496972 | | 119 | 312.7 | 258.405405469605 | 54.2945945303951 | | 120 | 333.2 | 302.083089947340 | 31.1169100526596 | | 121 | 446.4 | 397.551282945143 | 48.8487170548572 | | 122 | 511.6 | 460.944893522612 | 50.6551064773881 | | 123 | 515.5 | 509.240034140055 | 6.25996585994528 | | 124 | 506.4 | 506.273724748613 | 0.126275251387142 | | 125 | 483.2 | 512.512040675153 | -29.312040675153 | | 126 | 522.3 | 536.512509971341 | -14.2125099713409 | | 127 | 509.8 | 526.121695403856 | -16.3216954038557 | | 128 | 460.7 | 495.489111659899 | -34.7891116598992 | | 129 | 405.8 | 459.098776494406 | -53.2987764944056 | | 130 | 375 | 389.123568567087 | -14.1235685670874 | | 131 | 378.5 | 398.404206937121 | -19.9042069371205 | | 132 | 406.8 | 372.216314957998 | 34.5836850420023 | | 133 | 467.8 | 470.525458397287 | -2.72545839728718 | | 134 | 469.8 | 483.954127951157 | -14.1541279511571 | | 135 | 429.8 | 460.286358805320 | -30.4863588053195 | | 136 | 355.8 | 412.522482908257 | -56.7224829082571 | | 137 | 332.7 | 349.797741990305 | -17.0977419903055 | | 138 | 378 | 371.218383121015 | 6.78161687898495 | | 139 | 360.5 | 364.699360233611 | -4.19936023361089 | | 140 | 334.7 | 328.78204248591 | 5.91795751409 | | 141 | 319.5 | 314.244160340019 | 5.2558396599814 | | 142 | 323.1 | 293.302654217216 | 29.7973457827839 | | 143 | 363.6 | 335.501068763852 | 28.0989312361477 | | 144 | 352.1 | 357.280238295066 | -5.18023829506632 | | 145 | 411.9 | 412.695151719774 | -0.79515171977448 | | 146 | 388.6 | 422.818141734829 | -34.2181417348292 | | 147 | 416.4 | 374.983885952752 | 41.4161140472477 | | 148 | 360.7 | 385.233692068623 | -24.5336920686227 | | 149 | 338 | 357.730570008506 | -19.7305700085058 | | 150 | 417.2 | 382.071973480155 | 35.1280265198452 | | 151 | 388.4 | 401.97644570551 | -13.5764457055102 | | 152 | 371.1 | 362.451954544012 | 8.64804545598793 | | 153 | 331.5 | 353.362568993653 | -21.8625689936526 | | 154 | 353.7 | 314.055525322435 | 39.6444746775654 | | 155 | 396.7 | 366.573273416466 | 30.1267265835342 | | 156 | 447 | 387.633049996948 | 59.3669500030517 | | 157 | 533.5 | 505.446568820139 | 28.0534311798609 | | 158 | 565.4 | 543.805181842573 | 21.5948181574265 | | 159 | 542.3 | 566.284677040684 | -23.9846770406839 | | 160 | 488.7 | 518.608917065626 | -29.908917065626 | | 161 | 467.1 | 494.375879818437 | -27.2758798184374 | | 162 | 531.3 | 526.697013795197 | 4.60298620480307 | | 163 | 496.1 | 518.307088803149 | -22.2070888031488 | | 164 | 444 | 478.743728919878 | -34.7437289198785 | | 165 | 403.4 | 429.564768896736 | -26.1647688967365 | | 166 | 386.3 | 396.442496697389 | -10.142496697389 | | 167 | 394.1 | 402.898223963434 | -8.79822396343422 | | 168 | 404.1 | 390.215762980853 | 13.8842370191471 | | 169 | 462.1 | 457.23099268672 | 4.86900731328035 | | 170 | 448.1 | 465.976857378014 | -17.8768573780137 | | 171 | 432.3 | 436.831062875644 | -4.53106287564430 | | 172 | 386.3 | 394.975926168384 | -8.67592616838436 | | 173 | 395.2 | 380.646983570677 | 14.5530164293227 | | 174 | 421.9 | 447.344541882730 | -25.4445418827305 | | 175 | 382.9 | 401.403825092133 | -18.5038250921331 | | 176 | 384.2 | 355.531190126330 | 28.6688098736704 | | 177 | 345.5 | 358.342846127191 | -12.8428461271914 | | 178 | 323.4 | 336.074088928867 | -12.6740889288669 | | 179 | 372.6 | 337.534615886879 | 35.0653841131211 | | 180 | 376 | 365.508201147855 | 10.4917988521452 | | 181 | 462.7 | 427.900226617631 | 34.7997733823692 | | 182 | 487 | 460.617349070091 | 26.3826509299093 | | 183 | 444.2 | 475.650160482946 | -31.4501604829458 | | 184 | 399.3 | 412.649923436822 | -13.3499234368217 | | 185 | 394.9 | 399.846709607714 | -4.94670960771367 | | 186 | 455.4 | 445.185206713036 | 10.2147932869642 | | 187 | 414 | 434.151681288589 | -20.1516812885894 | | 188 | 375.5 | 396.700404236917 | -21.2004042369169 | | 189 | 347 | 350.842023269268 | -3.84202326926834 | | 190 | 339.4 | 336.922931677305 | 2.47706832269495 | | 191 | 385.8 | 359.682629003082 | 26.1173709969177 | | 192 | 378.8 | 377.49388064792 | 1.30611935207986 | | 193 | 451.8 | 435.823703111756 | 15.9762968882444 | | 194 | 446.1 | 450.391656203322 | -4.29165620332213 | | 195 | 422.5 | 428.182330339259 | -5.68233033925878 | | 196 | 383.1 | 388.765698048713 | -5.66569804871318 | | 197 | 352.8 | 383.132449695987 | -30.3324496959868 | | 198 | 445.3 | 406.570294496037 | 38.7297055039631 | | 199 | 367.5 | 415.337928552713 | -47.8379285527133 | | 200 | 355.1 | 351.778118991755 | 3.32188100824504 | | 201 | 326.2 | 328.814772864798 | -2.61477286479806 | | 202 | 319.8 | 316.300613326789 | 3.49938667321084 | | 203 | 331.8 | 342.794875426611 | -10.9948754266111 | | 204 | 340.9 | 322.394464234047 | 18.5055357659534 | | 205 | 394.1 | 395.827304834317 | -1.72730483431701 | | 206 | 417.2 | 389.465527626702 | 27.7344723732983 | | 207 | 369.9 | 393.743527649005 | -23.8435276490048 | | 208 | 349.2 | 336.743250834798 | 12.4567491652016 | | 209 | 321.4 | 342.370518648668 | -20.9705186486678 | | 210 | 405.7 | 383.344972566581 | 22.3550274334191 | | 211 | 342.9 | 364.568979412128 | -21.6689794121277 | | 212 | 316.5 | 331.084163280832 | -14.5841632808317 | | 213 | 284.2 | 291.148314350786 | -6.94831435078623 | | 214 | 270.9 | 274.744405521449 | -3.84440552144861 | | 215 | 288.8 | 291.392324176541 | -2.59232417654061 | | 216 | 278.8 | 281.406239980988 | -2.60623998098799 | | 217 | 324.4 | 331.548709542247 | -7.14870954224693 | | 218 | 310.9 | 322.03403410479 | -11.1340341047900 | | 219 | 299 | 280.536263762386 | 18.4637362376139 | | 220 | 273 | 262.568392994379 | 10.4316070056209 | | 221 | 279.3 | 259.188560635149 | 20.1114393648514 | | 222 | 359.2 | 341.614145144379 | 17.5858548556214 | | 223 | 305 | 312.287595026467 | -7.28759502646739 | | 224 | 282.1 | 292.819733659708 | -10.7197336597077 | | 225 | 250.3 | 258.189000392346 | -7.88900039234625 | | 226 | 246.5 | 242.263819140545 | 4.23618085945469 | | 227 | 257.9 | 267.392999763603 | -9.49299976360294 | | 228 | 266.5 | 252.401108266266 | 14.0988917337345 | | 229 | 315.9 | 318.240504504690 | -2.34050450469039 | | 230 | 318.4 | 314.586220079017 | 3.81377992098322 | | 231 | 295.4 | 293.341572567023 | 2.05842743297711 | | 232 | 266.4 | 262.346943102054 | 4.05305689794619 | | 233 | 245.8 | 256.644778866016 | -10.8447788660155 | | 234 | 362.8 | 311.946964229095 | 50.8530357709055 | | 235 | 324.9 | 309.635238925732 | 15.264761074268 | | 236 | 294.2 | 312.431349656668 | -18.2313496566681 | | 237 | 289.5 | 274.642196131005 | 14.8578038689951 | | 238 | 295.2 | 284.308174910184 | 10.891825089816 | | 239 | 290.3 | 317.984481049331 | -27.6844810493308 | | 240 | 272 | 294.296944379872 | -22.2969443798723 | | 241 | 307.4 | 327.848325620151 | -20.4483256201514 | | 242 | 328.7 | 309.650289181224 | 19.0497108187762 | | 243 | 292.9 | 302.360618874707 | -9.4606188747066 | | 244 | 249.1 | 262.132597556559 | -13.0325975565586 | | 245 | 230.4 | 238.948982446017 | -8.548982446017 | | 246 | 361.5 | 304.359094641057 | 57.1409053589425 | | 247 | 321.7 | 302.275735370039 | 19.4242646299612 | | 248 | 277.2 | 304.030832271001 | -26.8308322710011 | | 249 | 260.7 | 263.075734057070 | -2.37573405706956 | | 250 | 251 | 255.841975116547 | -4.84197511654668 | | 251 | 257.6 | 268.030371034543 | -10.4303710345427 | | 252 | 241.8 | 258.485679976229 | -16.6856799762290 | | 253 | 287.5 | 296.035494145975 | -8.53549414597478 | | 254 | 292.3 | 293.311561388790 | -1.01156138878952 | | 255 | 274.7 | 263.169720141407 | 11.5302798585933 | | 256 | 254.2 | 240.204734992584 | 13.9952650074159 | | 257 | 230 | 242.322756684355 | -12.3227566843547 | | 258 | 339 | 314.957960267801 | 24.0420397321986 | | 259 | 318.2 | 278.232862392812 | 39.9671376071882 | | 260 | 287 | 291.531307526183 | -4.53130752618301 | | 261 | 295.8 | 275.009248754181 | 20.7907512458190 | | 262 | 284 | 290.631696408165 | -6.631696408165 | | 263 | 271 | 303.683025011475 | -32.6830250114747 | | 264 | 262.7 | 275.913992861356 | -13.2139928613565 | | 265 | 340.6 | 319.589436458078 | 21.010563541922 | | 266 | 379.4 | 347.180295443733 | 32.2197045562672 | | 267 | 373.3 | 353.337564206285 | 19.9624357937149 | | 268 | 355.2 | 344.482824624507 | 10.7171753754927 | | 269 | 338.4 | 346.386849258154 | -7.986849258154 | | 270 | 466.9 | 434.457290558637 | 32.4427094413634 | | 271 | 451 | 414.312992794001 | 36.6870072059986 | | 272 | 422 | 425.434687129450 | -3.43468712944951 | | 273 | 429.2 | 420.40399481374 | 8.7960051862596 | | 274 | 425.9 | 428.076834263778 | -2.17683426377778 | | 275 | 460.7 | 447.786485345991 | 12.9135146540092 | | 276 | 463.6 | 471.33139000913 | -7.73139000913011 | | 277 | 541.4 | 534.286833737744 | 7.11316626225619 | | 278 | 544.2 | 560.382466783197 | -16.1824667831972 | | 279 | 517.5 | 529.019964978043 | -11.5199649780434 | | 280 | 469.4 | 495.60527322686 | -26.2052732268602 | | 281 | 439.4 | 464.597184716138 | -25.1971847161378 | | 282 | 549 | 543.929070700797 | 5.07092929920282 | | 283 | 533 | 499.478709552813 | 33.521290447187 | | 284 | 506.1 | 500.636769458459 | 5.46323054154055 | | 285 | 484 | 503.948495371552 | -19.9484953715518 | | 286 | 457 | 482.529665212826 | -25.5296652128258 | | 287 | 481.5 | 479.9684432083 | 1.53155679170021 | | 288 | 469.5 | 485.767924492514 | -16.2679244925141 | | 289 | 544.7 | 537.880885611893 | 6.81911438810675 | | 290 | 541.2 | 554.822043823008 | -13.6220438230080 | | 291 | 521.5 | 520.85957847172 | 0.64042152827983 | | 292 | 469.7 | 491.138448912611 | -21.4384489126114 | | 293 | 434.4 | 459.986404812567 | -25.5864048125666 | | 294 | 542.6 | 538.843138031383 | 3.75686196861693 | | 295 | 517.3 | 492.783469254944 | 24.5165307450561 | | 296 | 485.7 | 477.190502868034 | 8.5094971319661 | | 297 | 465.8 | 474.670553357688 | -8.87055335768804 | | 298 | 447 | 457.818133261494 | -10.8181332614943 | | 299 | 426.6 | 468.479232017238 | -41.8792320172377 | | 300 | 411.6 | 428.489344879765 | -16.8893448797654 | | 301 | 467.5 | 477.294693840822 | -9.79469384082205 | | 302 | 484.5 | 470.000231579893 | 14.4997684201068 | | 303 | 451.2 | 456.910849666036 | -5.71084966603627 | | 304 | 417.4 | 412.922941889743 | 4.47705811025679 | | 305 | 379.9 | 399.397346773819 | -19.4973467738193 | | 306 | 484.7 | 483.953947729368 | 0.746052270631992 | | 307 | 455 | 434.375737518072 | 20.6242624819278 | | 308 | 420.8 | 409.07888172303 | 11.7211182769699 | | 309 | 416.5 | 402.968496975434 | 13.5315030245664 | | 310 | 376.3 | 402.609835981495 | -26.3098359814953 | | 311 | 405.6 | 392.123908769078 | 13.4760912309223 | | 312 | 405.8 | 403.266059598942 | 2.53394040105781 | | 313 | 500.8 | 471.047019437011 | 29.7529805629895 | | 314 | 514 | 504.953080580885 | 9.04691941911528 | | 315 | 475.5 | 487.787069745690 | -12.2870697456895 | | 316 | 430.1 | 442.623105111373 | -12.5231051113732 | | 317 | 414.4 | 413.072440870974 | 1.32755912902644 | | 318 | 538 | 521.652935370207 | 16.3470646297931 | | 319 | 526 | 492.550562754175 | 33.4494372458245 | | 320 | 488.5 | 482.10409993225 | 6.39590006775046 | | 321 | 520.2 | 476.422603773408 | 43.7773962265922 | | 322 | 504.4 | 503.104102004112 | 1.29589799588808 | | 323 | 568.5 | 530.364401574544 | 38.1355984254559 | | 324 | 610.6 | 571.140321084605 | 39.4596789153952 | | 325 | 818 | 686.81618934528 | 131.183810654720 | | 326 | 830.9 | 823.724004843686 | 7.17599515631389 | | 327 | 835.9 | 820.606917966822 | 15.2930820331775 | | 328 | 782 | 819.518193452945 | -37.5181934529445 | | 329 | 762.3 | 789.272837104078 | -26.9728371040779 | | 330 | 856.9 | 892.685744440066 | -35.7857444400662 | | 331 | 820.9 | 834.922887967442 | -14.0228879674422 | | 332 | 769.6 | 790.581584409861 | -20.9815844098612 | | 333 | 752.2 | 775.608670422403 | -23.4086704224034 | | 334 | 724.4 | 743.27748562043 | -18.8774856204301 | | 335 | 723.1 | 761.808687252763 | -38.7086872527631 | | 336 | 719.5 | 735.283368875808 | -15.7833688758084 | | 337 | 817.4 | 811.443875160517 | 5.95612483948332 | | 338 | 803.3 | 810.35817559438 | -7.05817559438037 | | 339 | 752.5 | 782.314361775406 | -29.8143617754065 | | 340 | 689 | 718.3247066874 | -29.3247066873996 | | 341 | 630.4 | 680.416867311052 | -50.0168673110519 | | 342 | 765.5 | 745.139600878037 | 20.3603991219634 | | 343 | 757.7 | 724.593672493996 | 33.1063275060045 | | 344 | 732.2 | 708.670098704652 | 23.5299012953485 | | 345 | 702.6 | 723.332597474981 | -20.7325974749814 | | 346 | 683.3 | 685.846963279467 | -2.54696327946715 | | 347 | 709.5 | 708.558749420682 | 0.94125057931842 | | 348 | 702.2 | 714.791441256038 | -12.5914412560384 | | 349 | 784.8 | 792.42495525268 | -7.6249552526806 | | 350 | 810.9 | 772.642717267078 | 38.2572827329222 | | 351 | 755.6 | 778.006125333704 | -22.4061253337040 | | 352 | 656.8 | 718.604237548373 | -61.8042375483727 | | 353 | 615.1 | 645.968699821164 | -30.8686998211639 | | 354 | 745.3 | 734.365737852872 | 10.9342621471280 | | 355 | 694.1 | 704.226495241626 | -10.126495241626 | | 356 | 675.7 | 643.77442214323 | 31.9255778567701 | | 357 | 643.7 | 653.907727436926 | -10.2077274369261 | | 358 | 622.1 | 623.190336538489 | -1.0903365384886 | | 359 | 634.6 | 642.901459588552 | -8.30145958855155 | | 360 | 588 | 633.956150404699 | -45.956150404699 | | 361 | 689.7 | 676.17562668597 | 13.5243733140298 | | 362 | 673.9 | 674.920955045504 | -1.02095504550380 | | 363 | 647.9 | 629.390346445731 | 18.509653554269 | | 364 | 568.8 | 593.584347262271 | -24.7843472622714 | | 365 | 545.7 | 553.460535954125 | -7.76053595412498 | | 366 | 632.6 | 665.417366198776 | -32.8173661987756 | | 367 | 643.8 | 589.761490297839 | 54.0385097021606 | | 368 | 593.1 | 589.472770007479 | 3.62722999252139 | | 369 | 579.7 | 566.67461613441 | 13.0253838655896 | | 370 | 546 | 555.993757927082 | -9.9937579270819 | | 371 | 562.9 | 565.266721418102 | -2.36672141810209 | | 372 | 572.5 | 554.717812381705 | 17.782187618295 |
| Extrapolation Forecasts of Exponential Smoothing | | t | Forecast | 95% Lower Bound | 95% Upper Bound | | 373 | 662.72907376386 | 615.085169490331 | 710.37297803739 | | 374 | 649.600323407577 | 584.775983773264 | 714.424663041891 | | 375 | 609.557892278852 | 529.497099827506 | 689.618684730198 | | 376 | 552.432900405948 | 458.035476354263 | 646.830324457633 | | 377 | 538.257577684042 | 429.980386344299 | 646.534769023785 | | 378 | 656.101380491767 | 534.16990139446 | 778.032859589073 | | 379 | 625.713210163436 | 490.217064183838 | 761.209356143034 | | 380 | 573.299566371783 | 424.242410480975 | 722.356722262591 | | 381 | 549.881611806264 | 387.209851343412 | 712.553372269115 | | 382 | 525.111610517392 | 348.732107793196 | 701.491113241588 | | 383 | 545.02424463445 | 354.815823879371 | 735.23266538953 | | 384 | 540.477524462648 | 336.298754010789 | 744.656294914508 |
| | | | Charts produced by software: |  | | http://www.freestatistics.org/blog/date/2010/Dec/08/t12918213179865yosk2e5j6ec/1bfv81291820345.png (open in new window) | | http://www.freestatistics.org/blog/date/2010/Dec/08/t12918213179865yosk2e5j6ec/1bfv81291820345.ps (open in new window) |
 | | http://www.freestatistics.org/blog/date/2010/Dec/08/t12918213179865yosk2e5j6ec/2bfv81291820345.png (open in new window) | | http://www.freestatistics.org/blog/date/2010/Dec/08/t12918213179865yosk2e5j6ec/2bfv81291820345.ps (open in new window) |
 | | http://www.freestatistics.org/blog/date/2010/Dec/08/t12918213179865yosk2e5j6ec/3bfv81291820345.png (open in new window) | | http://www.freestatistics.org/blog/date/2010/Dec/08/t12918213179865yosk2e5j6ec/3bfv81291820345.ps (open in new window) |
| | | | Parameters (Session): | | par1 = 12 ; par2 = Triple ; par3 = additive ; | | | | Parameters (R input): | | par1 = 12 ; par2 = Triple ; par3 = additive ; | | | | 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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