| workshop 8, ES | | *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: Thu, 09 Dec 2010 16:49:10 +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/09/t1291913228osoe1cbaemi6j9t.htm/, Retrieved Thu, 09 Dec 2010 17:47:12 +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/09/t1291913228osoe1cbaemi6j9t.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 | 0.859090117482425 | | beta | 0.0739570283340592 | | gamma | 1 |
| Interpolation Forecasts of Exponential Smoothing | | t | Observed | Fitted | Residuals | | 13 | 299.5 | 239.394497863248 | 60.105502136752 | | 14 | 347.4 | 339.492687410771 | 7.9073125892287 | | 15 | 338.3 | 339.929491887132 | -1.62949188713173 | | 16 | 327.7 | 329.223957559468 | -1.52395755946770 | | 17 | 351.6 | 353.166427606621 | -1.56642760662055 | | 18 | 396.6 | 400.389554566451 | -3.78955456645105 | | 19 | 438.8 | 384.599542925451 | 54.200457074549 | | 20 | 395.6 | 427.763510672247 | -32.1635106722474 | | 21 | 363.5 | 393.902014378528 | -30.4020143785276 | | 22 | 378.8 | 345.076353958667 | 33.7236460413326 | | 23 | 357 | 410.295571899362 | -53.295571899362 | | 24 | 369 | 383.104598762058 | -14.1045987620581 | | 25 | 464.8 | 456.976349628349 | 7.82365037165056 | | 26 | 479.1 | 502.592157461915 | -23.4921574619154 | | 27 | 431.3 | 470.50284979556 | -39.2028497955599 | | 28 | 366.5 | 420.938726552717 | -54.4387265527173 | | 29 | 326.3 | 389.460118106052 | -63.1601181060516 | | 30 | 355.1 | 369.585513312119 | -14.4855133121194 | | 31 | 331.6 | 338.228558771563 | -6.62855877156301 | | 32 | 261.3 | 298.551050153206 | -37.2510501532062 | | 33 | 249 | 241.829537110705 | 7.17046288929504 | | 34 | 205.5 | 217.967581386629 | -12.4675813866291 | | 35 | 235.6 | 211.957331684488 | 23.6426683155119 | | 36 | 240.9 | 241.988791886433 | -1.08879188643309 | | 37 | 264.9 | 316.56232599333 | -51.6623259933298 | | 38 | 253.8 | 289.312251522296 | -35.512251522296 | | 39 | 232.3 | 226.569741231411 | 5.73025876858878 | | 40 | 193.8 | 198.202113954364 | -4.40211395436415 | | 41 | 177 | 196.401440515527 | -19.4014405155267 | | 42 | 213.2 | 211.679362402521 | 1.52063759747909 | | 43 | 207.2 | 186.898365671523 | 20.3016343284766 | | 44 | 180.6 | 159.470447421685 | 21.1295525783147 | | 45 | 188.6 | 156.300958206048 | 32.2990417939525 | | 46 | 175.4 | 149.994479718443 | 25.4055202815573 | | 47 | 199 | 182.750182367081 | 16.2498176329190 | | 48 | 179.6 | 203.617154073341 | -24.0171540733411 | | 49 | 225.8 | 250.581620945858 | -24.7816209458582 | | 50 | 234 | 249.622858322169 | -15.6228583221695 | | 51 | 200.2 | 211.964952702772 | -11.7649527027719 | | 52 | 183.6 | 168.214385528082 | 15.3856144719179 | | 53 | 178.2 | 183.631603723902 | -5.43160372390227 | | 54 | 203.2 | 217.078589038250 | -13.8785890382498 | | 55 | 208.5 | 183.955882611467 | 24.5441173885333 | | 56 | 191.8 | 162.800036528590 | 28.9999634714103 | | 57 | 172.8 | 170.976618453956 | 1.82338154604352 | | 58 | 148 | 138.591929629812 | 9.40807037018797 | | 59 | 159.4 | 156.372335669959 | 3.02766433004098 | | 60 | 154.5 | 159.424275934008 | -4.92427593400774 | | 61 | 213.2 | 223.114609211209 | -9.91460921120859 | | 62 | 196.4 | 237.594180801579 | -41.1941808015789 | | 63 | 182.8 | 178.262799760314 | 4.53720023968557 | | 64 | 176.4 | 153.129781835634 | 23.2702181643663 | | 65 | 153.6 | 173.674935132256 | -20.0749351322562 | | 66 | 173.2 | 193.709042121904 | -20.5090421219044 | | 67 | 171 | 160.240373884805 | 10.7596261151946 | | 68 | 151.2 | 126.930528161016 | 24.2694718389843 | | 69 | 161.9 | 125.973435002326 | 35.9265649976736 | | 70 | 157.2 | 124.881675573492 | 32.3183244265076 | | 71 | 201.7 | 163.827076326735 | 37.8729236732654 | | 72 | 236.4 | 200.289731456684 | 36.1102685433159 | | 73 | 356.1 | 305.732413633267 | 50.3675863667326 | | 74 | 398.3 | 378.625462124035 | 19.6745378759645 | | 75 | 403.7 | 392.930378293805 | 10.7696217061948 | | 76 | 384.6 | 391.087800001056 | -6.48780000105558 | | 77 | 365.8 | 393.366236037334 | -27.566236037334 | | 78 | 368.1 | 419.833367569935 | -51.7333675699348 | | 79 | 367.9 | 374.892290362618 | -6.9922903626179 | | 80 | 347 | 338.053774113903 | 8.94622588609707 | | 81 | 343.3 | 334.419812173438 | 8.88018782656167 | | 82 | 292.9 | 316.710509488063 | -23.8105094880632 | | 83 | 311.5 | 311.778862805985 | -0.278862805984659 | | 84 | 300.9 | 316.353298389024 | -15.4532983890244 | | 85 | 366.9 | 377.367075471291 | -10.4670754712908 | | 86 | 356.9 | 387.667386022286 | -30.7673860222865 | | 87 | 329.7 | 348.173160300275 | -18.4731603002754 | | 88 | 316.2 | 307.708500690031 | 8.49149930996879 | | 89 | 269 | 309.768910811536 | -40.7689108115355 | | 90 | 289.3 | 310.533091409775 | -21.2330914097747 | | 91 | 266.2 | 289.081542105592 | -22.8815421055921 | | 92 | 253.6 | 230.811667742120 | 22.7883322578801 | | 93 | 233.8 | 229.912532395107 | 3.88746760489278 | | 94 | 228.4 | 193.842889774835 | 34.5571102251653 | | 95 | 253.6 | 236.613859543972 | 16.9861404560275 | | 96 | 260.1 | 249.222935445924 | 10.8770645540759 | | 97 | 306.6 | 330.573069195610 | -23.9730691956096 | | 98 | 309.2 | 322.565480154239 | -13.3654801542392 | | 99 | 309.5 | 297.014561387094 | 12.4854386129063 | | 100 | 271 | 286.173816735979 | -15.1738167359792 | | 101 | 279.9 | 258.686817021143 | 21.2131829788573 | | 102 | 317.9 | 317.114578730618 | 0.785421269382084 | | 103 | 298.4 | 317.408182699649 | -19.0081826996491 | | 104 | 246.7 | 272.208856180445 | -25.5088561804449 | | 105 | 227.3 | 227.393813157513 | -0.0938131575134094 | | 106 | 209.1 | 192.211641881379 | 16.8883581186212 | | 107 | 259.9 | 216.191135150394 | 43.7088648496064 | | 108 | 266 | 251.4579558263 | 14.5420441737002 | | 109 | 320.6 | 331.840111835233 | -11.2401118352329 | | 110 | 308.5 | 337.86919551686 | -29.3691955168601 | | 111 | 282.2 | 302.798685634973 | -20.5986856349726 | | 112 | 262.7 | 258.122602326398 | 4.57739767360204 | | 113 | 263.5 | 252.470239788871 | 11.0297602111286 | | 114 | 313.1 | 298.363314923531 | 14.7366850764687 | | 115 | 284.3 | 307.831866174978 | -23.5318661749784 | | 116 | 252.6 | 257.52153194813 | -4.92153194812991 | | 117 | 250.3 | 234.973370772286 | 15.3266292277141 | | 118 | 246.5 | 217.410738648667 | 29.0892613513326 | | 119 | 312.7 | 258.405409058459 | 54.2945909415409 | | 120 | 333.2 | 302.083228497552 | 31.1167715024483 | | 121 | 446.4 | 397.551495514074 | 48.8485044859261 | | 122 | 511.6 | 460.945211166665 | 50.6547888333353 | | 123 | 515.5 | 509.240413523209 | 6.25958647679107 | | 124 | 506.4 | 506.274072424646 | 0.125927575354126 | | 125 | 483.2 | 512.512377188537 | -29.3123771885368 | | 126 | 522.3 | 536.512774692833 | -14.2127746928335 | | 127 | 509.8 | 526.121899968517 | -16.3218999685168 | | 128 | 460.7 | 495.489232971975 | -34.7892329719745 | | 129 | 405.8 | 459.098800682701 | -53.2988006827012 | | 130 | 375 | 389.123472139652 | -14.1234721396516 | | 131 | 378.5 | 398.404078112982 | -19.9040781129816 | | 132 | 406.8 | 372.216189998819 | 34.5838100011813 | | 133 | 467.8 | 470.525432412864 | -2.7254324128636 | | 134 | 469.8 | 483.954123473299 | -14.1541234732989 | | 135 | 429.8 | 460.286335606010 | -30.4863356060103 | | 136 | 355.8 | 412.522391646766 | -56.7223916467659 | | 137 | 332.7 | 349.797567198470 | -17.0975671984697 | | 138 | 378 | 371.218195698921 | 6.7818043010787 | | 139 | 360.5 | 364.699191314863 | -4.19919131486256 | | 140 | 334.7 | 328.781850809087 | 5.91814919091331 | | 141 | 319.5 | 314.243978390375 | 5.25602160962535 | | 142 | 323.1 | 293.302465786552 | 29.7975342134482 | | 143 | 363.6 | 335.500939767767 | 28.0990602322334 | | 144 | 352.1 | 357.280180836365 | -5.18018083636463 | | 145 | 411.9 | 412.695121167524 | -0.79512116752386 | | 146 | 388.6 | 422.81814224741 | -34.2181422474104 | | 147 | 416.4 | 374.98383573683 | 41.41616426317 | | 148 | 360.7 | 385.233730369838 | -24.5337303698381 | | 149 | 338 | 357.730557989373 | -19.7305579893726 | | 150 | 417.2 | 382.071922416245 | 35.1280775837548 | | 151 | 388.4 | 401.976465130287 | -13.5764651302866 | | 152 | 371.1 | 362.451917133403 | 8.64808286659706 | | 153 | 331.5 | 353.362534337185 | -21.8625343371849 | | 154 | 353.7 | 314.055413027316 | 39.6445869726841 | | 155 | 396.7 | 366.573233905229 | 30.1267660947705 | | 156 | 447 | 387.633087863443 | 59.3669121365567 | | 157 | 533.5 | 505.446748995613 | 28.0532510043871 | | 158 | 565.4 | 543.805443437618 | 21.5945565623821 | | 159 | 542.3 | 566.28495384575 | -23.9849538457499 | | 160 | 488.7 | 518.609150799627 | -29.9091507996273 | | 161 | 467.1 | 494.376039391603 | -27.276039391603 | | 162 | 531.3 | 526.697088456698 | 4.60291154330207 | | 163 | 496.1 | 518.307181163617 | -22.2071811636166 | | 164 | 444 | 478.743739592739 | -34.7437395927390 | | 165 | 403.4 | 429.564702208665 | -26.1647022086655 | | 166 | 386.3 | 396.442329515027 | -10.1423295150270 | | 167 | 394.1 | 402.898035530515 | -8.79803553051534 | | 168 | 404.1 | 390.2155741759 | 13.8844258241000 | | 169 | 462.1 | 457.230884054076 | 4.86911594592397 | | 170 | 448.1 | 465.976809417712 | -17.8768094177124 | | 171 | 432.3 | 436.830999113435 | -4.53099911343531 | | 172 | 386.3 | 394.975883254861 | -8.67588325486065 | | 173 | 395.2 | 380.646930027689 | 14.5530699723114 | | 174 | 421.9 | 447.344493179183 | -25.4444931791832 | | 175 | 382.9 | 401.403746337647 | -18.5037463376473 | | 176 | 384.2 | 355.531060486566 | 28.6689395134337 | | 177 | 345.5 | 358.342768894584 | -12.8427688945837 | | 178 | 323.4 | 336.073935863074 | -12.6739358630738 | | 179 | 372.6 | 337.534428429857 | 35.0655715701430 | | 180 | 376 | 365.508088925666 | 10.4919110743336 | | 181 | 462.7 | 427.9001781852 | 34.7998218148004 | | 182 | 487 | 460.617422941469 | 26.3825770585309 | | 183 | 444.2 | 475.650295578912 | -31.4502955789123 | | 184 | 399.3 | 412.65001012336 | -13.3500101233601 | | 185 | 394.9 | 399.846762703077 | -4.94676270307656 | | 186 | 455.4 | 445.185236787119 | 10.2147632128815 | | 187 | 414 | 434.151738608345 | -20.1517386083446 | | 188 | 375.5 | 396.700384154204 | -21.2003841542037 | | 189 | 347 | 350.841962139071 | -3.84196213907143 | | 190 | 339.4 | 336.922819170614 | 2.47718082938633 | | 191 | 385.8 | 359.682488023083 | 26.1175119769171 | | 192 | 378.8 | 377.493798924096 | 1.30620107590363 | | 193 | 451.8 | 435.82365094061 | 15.9763490593901 | | 194 | 446.1 | 450.391690398502 | -4.29169039850217 | | 195 | 422.5 | 428.182394150978 | -5.68239415097798 | | 196 | 383.1 | 388.765764693693 | -5.66576469369301 | | 197 | 352.8 | 383.132498938452 | -30.3324989384524 | | 198 | 445.3 | 406.570266636767 | 38.7297333632334 | | 199 | 367.5 | 415.337997290189 | -47.837997290189 | | 200 | 355.1 | 351.778059801714 | 3.32194019828631 | | 201 | 326.2 | 328.814714534768 | -2.61471453476753 | | 202 | 319.8 | 316.300508680215 | 3.49949131978502 | | 203 | 331.8 | 342.794735054655 | -10.9947350546549 | | 204 | 340.9 | 322.394312257600 | 18.5056877423995 | | 205 | 394.1 | 395.827214314555 | -1.72721431455511 | | 206 | 417.2 | 389.465493350531 | 27.7345066494692 | | 207 | 369.9 | 393.743594079094 | -23.8435940790945 | | 208 | 349.2 | 336.743286493260 | 12.4567135067405 | | 209 | 321.4 | 342.370587319696 | -20.9705873196964 | | 210 | 405.7 | 383.34495918673 | 22.3550408132700 | | 211 | 342.9 | 364.569053506196 | -21.6690535061960 | | 212 | 316.5 | 331.08415028388 | -14.5841502838796 | | 213 | 284.2 | 291.148261888214 | -6.94826188821418 | | 214 | 270.9 | 274.744300734941 | -3.8443007349415 | | 215 | 288.8 | 291.392175220424 | -2.59217522042428 | | 216 | 278.8 | 281.406079633912 | -2.60607963391226 | | 217 | 324.4 | 331.548573088619 | -7.14857308861878 | | 218 | 310.9 | 322.033931876 | -11.1339318760000 | | 219 | 299 | 280.536209451936 | 18.4637905480643 | | 220 | 273 | 262.568393858026 | 10.4316061419743 | | 221 | 279.3 | 259.188605093526 | 20.1113949064741 | | 222 | 359.2 | 341.614182874145 | 17.5858171258547 | | 223 | 305 | 312.287709889269 | -7.28770988926874 | | 224 | 282.1 | 292.819794800931 | -10.7197948009313 | | 225 | 250.3 | 258.189017955932 | -7.88901795593245 | | 226 | 246.5 | 242.263779527083 | 4.23622047291747 | | 227 | 257.9 | 267.392926941994 | -9.49292694199391 | | 228 | 266.5 | 252.401000184412 | 14.0989998155881 | | 229 | 315.9 | 318.240445580024 | -2.34044558002398 | | 230 | 318.4 | 314.586196245975 | 3.81380375402478 | | 231 | 295.4 | 293.341606487174 | 2.05839351282617 | | 232 | 266.4 | 262.347002142980 | 4.05299785702027 | | 233 | 245.8 | 256.644862137151 | -10.8448621371514 | | 234 | 362.8 | 311.946987675627 | 50.8530123243732 | | 235 | 324.9 | 309.635404948491 | 15.2645950515093 | | 236 | 294.2 | 312.431512532724 | -18.2315125327239 | | 237 | 289.5 | 274.642290068773 | 14.8577099312266 | | 238 | 295.2 | 284.30824957793 | 10.8917504220698 | | 239 | 290.3 | 317.984531433389 | -27.6845314333885 | | 240 | 272 | 294.296902373437 | -22.2969023734373 | | 241 | 307.4 | 327.848256250686 | -20.4482562506863 | | 242 | 328.7 | 309.650215588375 | 19.0497844116255 | | 243 | 292.9 | 302.360636400293 | -9.46063640029325 | | 244 | 249.1 | 262.132621337357 | -13.0326213373573 | | 245 | 230.4 | 238.949005941186 | -8.54900594118638 | | 246 | 361.5 | 304.359054953153 | 57.1409450468469 | | 247 | 321.7 | 302.275857787857 | 19.4241422121430 | | 248 | 277.2 | 304.030983001473 | -26.8309830014731 | | 249 | 260.7 | 263.075789422791 | -2.37578942279106 | | 250 | 251 | 255.841984245517 | -4.84198424551727 | | 251 | 257.6 | 268.030343313101 | -10.4303433131005 | | 252 | 241.8 | 258.485597270850 | -16.6855972708498 | | 253 | 287.5 | 296.035389246669 | -8.5353892466693 | | 254 | 292.3 | 293.311460964061 | -1.01146096406137 | | 255 | 274.7 | 263.169679564259 | 11.5303204357407 | | 256 | 254.2 | 240.204751811019 | 13.9952481889812 | | 257 | 230 | 242.322825473095 | -12.3228254730953 | | 258 | 339 | 314.957941966707 | 24.0420580332934 | | 259 | 318.2 | 278.232940400313 | 39.9670595996868 | | 260 | 287 | 291.531480962212 | -4.53148096221179 | | 261 | 295.8 | 275.009365595288 | 20.7906344047116 | | 262 | 284 | 290.631809056571 | -6.63180905657066 | | 263 | 271 | 303.683088525344 | -32.6830885253437 | | 264 | 262.7 | 275.913953207478 | -13.2139532074780 | | 265 | 340.6 | 319.589369984918 | 21.0106300150820 | | 266 | 379.4 | 347.180284108713 | 32.219715891287 | | 267 | 373.3 | 353.337660495244 | 19.9623395047556 | | 268 | 355.2 | 344.482985562506 | 10.7170144374941 | | 269 | 338.4 | 346.387055178677 | -7.9870551786774 | | 270 | 466.9 | 434.457407814004 | 32.4425921859960 | | 271 | 451 | 414.313193742979 | 36.6868062570209 | | 272 | 422 | 425.434985112567 | -3.4349851125674 | | 273 | 429.2 | 420.404229643925 | 8.79577035607525 | | 274 | 425.9 | 428.077042793156 | -2.17704279315626 | | 275 | 460.7 | 447.786654269541 | 12.9133457304588 | | 276 | 463.6 | 471.331531394291 | -7.73153139429104 | | 277 | 541.4 | 534.286927176634 | 7.11307282336645 | | 278 | 544.2 | 560.382569088679 | -16.1825690886793 | | 279 | 517.5 | 529.020070591136 | -11.5200705911363 | | 280 | 469.4 | 495.605387268549 | -26.2053872685491 | | 281 | 439.4 | 464.5972823163 | -25.1972823162999 | | 282 | 549 | 543.929055135587 | 5.07094486441315 | | 283 | 533 | 499.478722234201 | 33.5212777657994 | | 284 | 506.1 | 500.636899395111 | 5.46310060488884 | | 285 | 484 | 503.948599258902 | -19.9485992589015 | | 286 | 457 | 482.529699094909 | -25.529699094909 | | 287 | 481.5 | 479.968398984442 | 1.53160101555784 | | 288 | 469.5 | 485.767856568259 | -16.2678565682589 | | 289 | 544.7 | 537.880761423332 | 6.81923857666834 | | 290 | 541.2 | 554.821948325962 | -13.6219483259616 | | 291 | 521.5 | 520.859498155071 | 0.640501844928622 | | 292 | 469.7 | 491.138419523167 | -21.4384195231671 | | 293 | 434.4 | 459.986377618624 | -25.5863776186239 | | 294 | 542.6 | 538.843009599184 | 3.75699040081633 | | 295 | 517.3 | 492.78335613908 | 24.5166438609202 | | 296 | 485.7 | 477.190502334347 | 8.5094976656531 | | 297 | 465.8 | 474.67056277421 | -8.87056277420947 | | 298 | 447 | 457.818104143248 | -10.8181041432483 | | 299 | 426.6 | 468.479148728359 | -41.8791487283589 | | 300 | 411.6 | 428.489160341709 | -16.8891603417085 | | 301 | 467.5 | 477.29445373108 | -9.79445373108047 | | 302 | 484.5 | 469.999997676811 | 14.5000023231894 | | 303 | 451.2 | 456.910688022182 | -5.71068802218218 | | 304 | 417.4 | 412.922829551031 | 4.47717044896865 | | 305 | 379.9 | 399.397295919848 | -19.4972959198481 | | 306 | 484.7 | 483.953812065845 | 0.746187934154989 | | 307 | 455 | 434.375598404971 | 20.6244015950293 | | 308 | 420.8 | 409.078846218855 | 11.7211537811448 | | 309 | 416.5 | 402.968494974445 | 13.5315050255546 | | 310 | 376.3 | 402.60984436441 | -26.3098443644103 | | 311 | 405.6 | 392.12384130082 | 13.4761586991799 | | 312 | 405.8 | 403.265989317779 | 2.53401068222070 | | 313 | 500.8 | 471.046919554052 | 29.7530804459482 | | 314 | 514 | 504.95303885559 | 9.04696114440986 | | 315 | 475.5 | 487.787076964117 | -12.2870769641169 | | 316 | 430.1 | 442.623129418816 | -12.5231294188159 | | 317 | 414.4 | 413.072491832793 | 1.32750816720716 | | 318 | 538 | 521.652942786623 | 16.3470572133773 | | 319 | 526 | 492.550575949806 | 33.4494240501936 | | 320 | 488.5 | 482.104223106623 | 6.39577689337688 | | 321 | 520.2 | 476.422742659817 | 43.7772573401832 | | 322 | 504.4 | 503.104318792768 | 1.29568120723246 | | 323 | 568.5 | 530.364568479738 | 38.1354315202620 | | 324 | 610.6 | 571.140520262962 | 39.4594797370384 | | 325 | 818 | 686.81640239347 | 131.183597606530 | | 326 | 830.9 | 823.724454383606 | 7.17554561639349 | | 327 | 835.9 | 820.607373932622 | 15.2926260673780 | | 328 | 782 | 819.518684587387 | -37.5186845873873 | | 329 | 762.3 | 789.27326289807 | -26.9732628980706 | | 330 | 856.9 | 892.686051835778 | -35.7860518357785 | | 331 | 820.9 | 834.923070258689 | -14.0230702586894 | | 332 | 769.6 | 790.581771362873 | -20.9817713628735 | | 333 | 752.2 | 775.608807568464 | -23.4088075684635 | | 334 | 724.4 | 743.277586017302 | -18.8775860173021 | | 335 | 723.1 | 761.808702989784 | -38.7087029897843 | | 336 | 719.5 | 735.283276729274 | -15.7832767292742 | | 337 | 817.4 | 811.443684328279 | 5.95631567172086 | | 338 | 803.3 | 810.358043321348 | -7.05804332134812 | | 339 | 752.5 | 782.314249740754 | -29.8142497407543 | | 340 | 689 | 718.324599906597 | -29.3245999065972 | | 341 | 630.4 | 680.416753181473 | -50.0167531814726 | | 342 | 765.5 | 745.139376464763 | 20.3606235352371 | | 343 | 757.7 | 724.593467430877 | 33.1065325691234 | | 344 | 732.2 | 708.670009000125 | 23.5299909998747 | | 345 | 702.6 | 723.332569468259 | -20.7325694682588 | | 346 | 683.3 | 685.84691080968 | -2.54691080968041 | | 347 | 709.5 | 708.558670126892 | 0.94132987310752 | | 348 | 702.2 | 714.79133006373 | -12.5913300637302 | | 349 | 784.8 | 792.42474932804 | -7.62474932803991 | | 350 | 810.9 | 772.642533036478 | 38.257466963522 | | 351 | 755.6 | 778.00606240596 | -22.4060624059607 | | 352 | 656.8 | 718.604184623424 | -61.8041846234242 | | 353 | 615.1 | 645.968578939544 | -30.8685789395437 | | 354 | 745.3 | 734.36553119831 | 10.9344688016899 | | 355 | 694.1 | 704.2262863319 | -10.1262863319005 | | 356 | 675.7 | 643.774237418427 | 31.9257625815733 | | 357 | 643.7 | 653.907648081456 | -10.2076480814559 | | 358 | 622.1 | 623.190251191292 | -1.0902511912916 | | 359 | 634.6 | 642.901356733145 | -8.30135673314498 | | 360 | 588 | 633.956006137348 | -45.9560061373481 | | 361 | 689.7 | 676.175328143507 | 13.5246718564929 | | 362 | 673.9 | 674.920698593769 | -1.02069859376888 | | 363 | 647.9 | 629.390155815864 | 18.5098441841363 | | 364 | 568.8 | 593.584269672429 | -24.7842696724288 | | 365 | 545.7 | 553.460453189621 | -7.76045318962144 | | 366 | 632.6 | 665.417236164421 | -32.8172361644212 | | 367 | 643.8 | 589.761273628342 | 54.0387263716575 | | 368 | 593.1 | 589.472682854466 | 3.62731714553377 | | 369 | 579.7 | 566.67458230676 | 13.0254176932401 | | 370 | 546 | 555.993761806171 | -9.99376180617082 | | 371 | 562.9 | 565.26668994843 | -2.36668994843046 | | 372 | 572.5 | 554.717760847406 | 17.7822391525937 |
| Extrapolation Forecasts of Exponential Smoothing | | t | Forecast | 95% Lower Bound | 95% Upper Bound | | 373 | 662.728972325128 | 615.085067232274 | 710.372877417982 | | 374 | 649.600121689966 | 584.775717000736 | 714.424526379197 | | 375 | 609.557625618123 | 529.496678783818 | 689.618572452427 | | 376 | 552.432638033007 | 458.034949763608 | 646.830326302405 | | 377 | 538.257345161054 | 429.979761907872 | 646.534928414236 | | 378 | 656.10115314916 | 534.169138379994 | 778.033167918327 | | 379 | 625.712929861622 | 490.216089728005 | 761.209769995239 | | 380 | 573.299258922809 | 424.241236727547 | 722.35728111807 | | 381 | 549.88130835719 | 387.208496635606 | 712.554120078773 | | 382 | 525.111327701728 | 348.730576688031 | 701.492078715426 | | 383 | 545.023966161218 | 354.814088633664 | 735.233843688772 | | 384 | 540.477228178168 | 336.296781562651 | 744.657674793684 |
| | | | Charts produced by software: |  | | http://www.freestatistics.org/blog/date/2010/Dec/09/t1291913228osoe1cbaemi6j9t/1748i1291913342.png (open in new window) | | http://www.freestatistics.org/blog/date/2010/Dec/09/t1291913228osoe1cbaemi6j9t/1748i1291913342.ps (open in new window) |
 | | http://www.freestatistics.org/blog/date/2010/Dec/09/t1291913228osoe1cbaemi6j9t/2ie731291913342.png (open in new window) | | http://www.freestatistics.org/blog/date/2010/Dec/09/t1291913228osoe1cbaemi6j9t/2ie731291913342.ps (open in new window) |
 | | http://www.freestatistics.org/blog/date/2010/Dec/09/t1291913228osoe1cbaemi6j9t/3ie731291913342.png (open in new window) | | http://www.freestatistics.org/blog/date/2010/Dec/09/t1291913228osoe1cbaemi6j9t/3ie731291913342.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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