| Workshop 8: ES Triple | | *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: Fri, 10 Dec 2010 15:32:01 +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/10/t1291995003um0xol8unhnpi3x.htm/, Retrieved Fri, 10 Dec 2010 16:30:04 +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/10/t1291995003um0xol8unhnpi3x.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 | 0.859090117482455 | | beta | 0.0739570283338065 | | gamma | 1 |
| Interpolation Forecasts of Exponential Smoothing | | t | Observed | Fitted | Residuals | | 13 | 299.5 | 239.394497863248 | 60.105502136752 | | 14 | 347.4 | 339.49268741076 | 7.90731258923984 | | 15 | 338.3 | 339.929491887117 | -1.62949188711656 | | 16 | 327.7 | 329.223957559453 | -1.52395755945292 | | 17 | 351.6 | 353.166427606607 | -1.56642760660714 | | 18 | 396.6 | 400.389554566439 | -3.78955456643905 | | 19 | 438.8 | 384.599542925441 | 54.2004570745594 | | 20 | 395.6 | 427.763510672228 | -32.163510672228 | | 21 | 363.5 | 393.902014378512 | -30.4020143785124 | | 22 | 378.8 | 345.07635395866 | 33.7236460413396 | | 23 | 357 | 410.295571899351 | -53.2955718993513 | | 24 | 369 | 383.104598762056 | -14.1045987620564 | | 25 | 464.8 | 456.976349628352 | 7.8236503716484 | | 26 | 479.1 | 502.592157461922 | -23.4921574619219 | | 27 | 431.3 | 470.502849795568 | -39.2028497955684 | | 28 | 366.5 | 420.938726552733 | -54.4387265527326 | | 29 | 326.3 | 389.460118106078 | -63.1601181060779 | | 30 | 355.1 | 369.585513312159 | -14.4855133121591 | | 31 | 331.6 | 338.228558771605 | -6.62855877160479 | | 32 | 261.3 | 298.551050153253 | -37.2510501532529 | | 33 | 249 | 241.829537110752 | 7.1704628892478 | | 34 | 205.5 | 217.967581386671 | -12.4675813866706 | | 35 | 235.6 | 211.957331684534 | 23.6426683154655 | | 36 | 240.9 | 241.988791886468 | -1.08879188646765 | | 37 | 264.9 | 316.562325993359 | -51.6623259933595 | | 38 | 253.8 | 289.312251522339 | -35.5122515223391 | | 39 | 232.3 | 226.569741231459 | 5.73025876854075 | | 40 | 193.8 | 198.202113954408 | -4.40211395440818 | | 41 | 177 | 196.401440515567 | -19.4014405155671 | | 42 | 213.2 | 211.67936240256 | 1.52063759743996 | | 43 | 207.2 | 186.898365671561 | 20.3016343284389 | | 44 | 180.6 | 159.470447421723 | 21.129552578277 | | 45 | 188.6 | 156.300958206072 | 32.2990417939276 | | 46 | 175.4 | 149.994479718458 | 25.4055202815422 | | 47 | 199 | 182.750182367091 | 16.2498176329088 | | 48 | 179.6 | 203.617154073345 | -24.0171540733448 | | 49 | 225.8 | 250.581620945864 | -24.781620945864 | | 50 | 234 | 249.622858322182 | -15.6228583221823 | | 51 | 200.2 | 211.964952702787 | -11.7649527027866 | | 52 | 183.6 | 168.2143855281 | 15.3856144719 | | 53 | 178.2 | 183.631603723916 | -5.43160372391608 | | 54 | 203.2 | 217.078589038259 | -13.8785890382595 | | 55 | 208.5 | 183.955882611479 | 24.544117388521 | | 56 | 191.8 | 162.800036528604 | 28.9999634713959 | | 57 | 172.8 | 170.97661845396 | 1.82338154604028 | | 58 | 148 | 138.591929629813 | 9.40807037018729 | | 59 | 159.4 | 156.37233566996 | 3.0276643300401 | | 60 | 154.5 | 159.424275934007 | -4.92427593400748 | | 61 | 213.2 | 223.114609211206 | -9.91460921120594 | | 62 | 196.4 | 237.594180801579 | -41.1941808015789 | | 63 | 182.8 | 178.262799760322 | 4.53720023967833 | | 64 | 176.4 | 153.129781835642 | 23.2702181643578 | | 65 | 153.6 | 173.674935132261 | -20.0749351322614 | | 66 | 173.2 | 193.709042121908 | -20.5090421219084 | | 67 | 171 | 160.240373884812 | 10.7596261151881 | | 68 | 151.2 | 126.930528161028 | 24.2694718389715 | | 69 | 161.9 | 125.973435002333 | 35.9265649976671 | | 70 | 157.2 | 124.881675573488 | 32.3183244265116 | | 71 | 201.7 | 163.827076326725 | 37.8729236732753 | | 72 | 236.4 | 200.289731456666 | 36.110268543334 | | 73 | 356.1 | 305.732413633239 | 50.3675863667614 | | 74 | 398.3 | 378.625462123997 | 19.6745378760027 | | 75 | 403.7 | 392.930378293759 | 10.7696217062409 | | 76 | 384.6 | 391.087800001011 | -6.48780000101078 | | 77 | 365.8 | 393.366236037297 | -27.5662360372971 | | 78 | 368.1 | 419.833367569902 | -51.7333675699016 | | 79 | 367.9 | 374.892290362595 | -6.99229036259482 | | 80 | 347 | 338.053774113893 | 8.94622588610662 | | 81 | 343.3 | 334.41981217343 | 8.88018782656985 | | 82 | 292.9 | 316.710509488053 | -23.8105094880528 | | 83 | 311.5 | 311.77886280598 | -0.278862805980452 | | 84 | 300.9 | 316.353298389022 | -15.4532983890225 | | 85 | 366.9 | 377.367075471289 | -10.4670754712892 | | 86 | 356.9 | 387.667386022289 | -30.7673860222894 | | 87 | 329.7 | 348.17316030028 | -18.4731603002799 | | 88 | 316.2 | 307.708500690041 | 8.4914993099589 | | 89 | 269 | 309.768910811548 | -40.7689108115476 | | 90 | 289.3 | 310.533091409789 | -21.2330914097892 | | 91 | 266.2 | 289.081542105605 | -22.8815421056054 | | 92 | 253.6 | 230.811667742145 | 22.7883322578549 | | 93 | 233.8 | 229.912532395132 | 3.8874676048685 | | 94 | 228.4 | 193.842889774857 | 34.5571102251435 | | 95 | 253.6 | 236.613859543985 | 16.9861404560152 | | 96 | 260.1 | 249.222935445932 | 10.8770645540677 | | 97 | 306.6 | 330.573069195611 | -23.9730691956107 | | 98 | 309.2 | 322.565480154246 | -13.3654801542456 | | 99 | 309.5 | 297.014561387098 | 12.4854386129019 | | 100 | 271 | 286.173816735981 | -15.1738167359812 | | 101 | 279.9 | 258.686817021153 | 21.2131829788474 | | 102 | 317.9 | 317.114578730618 | 0.785421269381686 | | 103 | 298.4 | 317.408182699643 | -19.0081826996427 | | 104 | 246.7 | 272.208856180446 | -25.5088561804462 | | 105 | 227.3 | 227.393813157527 | -0.0938131575273076 | | 106 | 209.1 | 192.211641881394 | 16.8883581186062 | | 107 | 259.9 | 216.191135150406 | 43.7088648495944 | | 108 | 266 | 251.457955826303 | 14.5420441736967 | | 109 | 320.6 | 331.840111835229 | -11.2401118352288 | | 110 | 308.5 | 337.869195516856 | -29.369195516856 | | 111 | 282.2 | 302.79868563497 | -20.5986856349696 | | 112 | 262.7 | 258.122602326402 | 4.57739767359834 | | 113 | 263.5 | 252.470239788878 | 11.0297602111219 | | 114 | 313.1 | 298.363314923534 | 14.7366850764665 | | 115 | 284.3 | 307.831866174972 | -23.5318661749717 | | 116 | 252.6 | 257.521531948129 | -4.9215319481286 | | 117 | 250.3 | 234.973370772292 | 15.3266292277083 | | 118 | 246.5 | 217.410738648673 | 29.0892613513275 | | 119 | 312.7 | 258.405409058459 | 54.2945909415409 | | 120 | 333.2 | 302.083228497544 | 31.1167715024562 | | 121 | 446.4 | 397.551495514056 | 48.8485044859444 | | 122 | 511.6 | 460.945211166634 | 50.654788833366 | | 123 | 515.5 | 509.240413523162 | 6.25958647683836 | | 124 | 506.4 | 506.274072424597 | 0.125927575402955 | | 125 | 483.2 | 512.512377188494 | -29.3123771884942 | | 126 | 522.3 | 536.512774692799 | -14.2127746927988 | | 127 | 509.8 | 526.121899968486 | -16.3218999684856 | | 128 | 460.7 | 495.489232971948 | -34.789232971948 | | 129 | 405.8 | 459.098800682688 | -53.2988006826882 | | 130 | 375 | 389.123472139655 | -14.1234721396549 | | 131 | 378.5 | 398.404078112993 | -19.9040781129926 | | 132 | 406.8 | 372.21618999884 | 34.5838100011602 | | 133 | 467.8 | 470.525432412876 | -2.72543241287559 | | 134 | 469.8 | 483.954123473307 | -14.1541234733069 | | 135 | 429.8 | 460.286335606016 | -30.486335606016 | | 136 | 355.8 | 412.522391646774 | -56.7223916467743 | | 137 | 332.7 | 349.797567198493 | -17.0975671984926 | | 138 | 378 | 371.218195698947 | 6.78180430105317 | | 139 | 360.5 | 364.699191314884 | -4.19919131488405 | | 140 | 334.7 | 328.781850809106 | 5.91814919089416 | | 141 | 319.5 | 314.243978390394 | 5.25602160960568 | | 142 | 323.1 | 293.30246578657 | 29.7975342134303 | | 143 | 363.6 | 335.500939767781 | 28.0990602322186 | | 144 | 352.1 | 357.280180836375 | -5.18018083637537 | | 145 | 411.9 | 412.695121167536 | -0.79512116753557 | | 146 | 388.6 | 422.818142247419 | -34.2181422474189 | | 147 | 416.4 | 374.98383573684 | 41.4161642631602 | | 148 | 360.7 | 385.233730369838 | -24.5337303698377 | | 149 | 338 | 357.730557989374 | -19.7305579893737 | | 150 | 417.2 | 382.07192241625 | 35.1280775837498 | | 151 | 388.4 | 401.976465130286 | -13.5764651302858 | | 152 | 371.1 | 362.451917133401 | 8.64808286659905 | | 153 | 331.5 | 353.362534337185 | -21.8625343371847 | | 154 | 353.7 | 314.05541302732 | 39.6445869726801 | | 155 | 396.7 | 366.573233905232 | 30.126766094768 | | 156 | 447 | 387.633087863443 | 59.3669121365568 | | 157 | 533.5 | 505.446748995601 | 28.0532510043992 | | 158 | 565.4 | 543.805443437597 | 21.5945565624032 | | 159 | 542.3 | 566.284953845716 | -23.9849538457161 | | 160 | 488.7 | 518.6091507996 | -29.9091507996002 | | 161 | 467.1 | 494.376039391581 | -27.2760393915808 | | 162 | 531.3 | 526.697088456681 | 4.60291154331867 | | 163 | 496.1 | 518.307181163606 | -22.2071811636062 | | 164 | 444 | 478.743739592729 | -34.7437395927293 | | 165 | 403.4 | 429.564702208668 | -26.164702208668 | | 166 | 386.3 | 396.442329515034 | -10.1423295150339 | | 167 | 394.1 | 402.898035530533 | -8.7980355305329 | | 168 | 404.1 | 390.215574175923 | 13.8844258240767 | | 169 | 462.1 | 457.2308840541 | 4.8691159459002 | | 170 | 448.1 | 465.976809417731 | -17.876809417731 | | 171 | 432.3 | 436.830999113449 | -4.53099911344901 | | 172 | 386.3 | 394.975883254873 | -8.67588325487282 | | 173 | 395.2 | 380.646930027697 | 14.5530699723026 | | 174 | 421.9 | 447.344493179185 | -25.4444931791852 | | 175 | 382.9 | 401.403746337658 | -18.5037463376585 | | 176 | 384.2 | 355.531060486578 | 28.6689395134222 | | 177 | 345.5 | 358.342768894592 | -12.8427688945918 | | 178 | 323.4 | 336.07393586308 | -12.6739358630805 | | 179 | 372.6 | 337.534428429873 | 35.065571570127 | | 180 | 376 | 365.50808892568 | 10.4919110743198 | | 181 | 462.7 | 427.900178185214 | 34.7998218147857 | | 182 | 487 | 460.617422941475 | 26.382577058525 | | 183 | 444.2 | 475.650295578904 | -31.4502955789035 | | 184 | 399.3 | 412.650010123354 | -13.3500101233535 | | 185 | 394.9 | 399.846762703069 | -4.9467627030694 | | 186 | 455.4 | 445.185236787112 | 10.2147632128879 | | 187 | 414 | 434.151738608339 | -20.1517386083392 | | 188 | 375.5 | 396.700384154198 | -21.2003841541979 | | 189 | 347 | 350.841962139076 | -3.84196213907563 | | 190 | 339.4 | 336.922819170617 | 2.4771808293832 | | 191 | 385.8 | 359.68248802309 | 26.1175119769102 | | 192 | 378.8 | 377.493798924106 | 1.30620107589419 | | 193 | 451.8 | 435.823650940621 | 15.9763490593787 | | 194 | 446.1 | 450.391690398511 | -4.29169039851109 | | 195 | 422.5 | 428.182394150982 | -5.68239415098157 | | 196 | 383.1 | 388.765764693691 | -5.66576469369073 | | 197 | 352.8 | 383.132498938447 | -30.3324989384468 | | 198 | 445.3 | 406.570266636765 | 38.7297333632347 | | 199 | 367.5 | 415.337997290186 | -47.8379972901856 | | 200 | 355.1 | 351.778059801713 | 3.32194019828705 | | 201 | 326.2 | 328.814714534771 | -2.61471453477117 | | 202 | 319.8 | 316.300508680218 | 3.49949131978224 | | 203 | 331.8 | 342.79473505466 | -10.99473505466 | | 204 | 340.9 | 322.394312257616 | 18.5056877423835 | | 205 | 394.1 | 395.827214314571 | -1.72721431457074 | | 206 | 417.2 | 389.465493350548 | 27.7345066494522 | | 207 | 369.9 | 393.7435940791 | -23.8435940791005 | | 208 | 349.2 | 336.743286493261 | 12.4567135067388 | | 209 | 321.4 | 342.370587319692 | -20.9705873196923 | | 210 | 405.7 | 383.344959186724 | 22.3550408132764 | | 211 | 342.9 | 364.569053506195 | -21.6690535061952 | | 212 | 316.5 | 331.084150283873 | -14.5841502838733 | | 213 | 284.2 | 291.148261888215 | -6.94826188821537 | | 214 | 270.9 | 274.744300734944 | -3.84430073494423 | | 215 | 288.8 | 291.392175220431 | -2.59217522043133 | | 216 | 278.8 | 281.406079633926 | -2.60607963392647 | | 217 | 324.4 | 331.548573088639 | -7.14857308863895 | | 218 | 310.9 | 322.033931876022 | -11.133931876022 | | 219 | 299 | 280.536209451958 | 18.4637905480419 | | 220 | 273 | 262.568393858034 | 10.431606141966 | | 221 | 279.3 | 259.188605093528 | 20.1113949064721 | | 222 | 359.2 | 341.614182874134 | 17.5858171258657 | | 223 | 305 | 312.287709889263 | -7.28770988926328 | | 224 | 282.1 | 292.819794800918 | -10.7197948009182 | | 225 | 250.3 | 258.189017955924 | -7.88901795592398 | | 226 | 246.5 | 242.263779527077 | 4.23622047292315 | | 227 | 257.9 | 267.392926941991 | -9.49292694199141 | | 228 | 266.5 | 252.401000184418 | 14.0989998155823 | | 229 | 315.9 | 318.240445580034 | -2.34044558003382 | | 230 | 318.4 | 314.586196245987 | 3.81380375401346 | | 231 | 295.4 | 293.341606487182 | 2.05839351281759 | | 232 | 266.4 | 262.34700214298 | 4.05299785701965 | | 233 | 245.8 | 256.644862137147 | -10.8448621371472 | | 234 | 362.8 | 311.946987675618 | 50.8530123243824 | | 235 | 324.9 | 309.635404948481 | 15.2645950515192 | | 236 | 294.2 | 312.431512532702 | -18.2315125327016 | | 237 | 289.5 | 274.642290068754 | 14.8577099312456 | | 238 | 295.2 | 284.308249577911 | 10.8917504220894 | | 239 | 290.3 | 317.984531433371 | -27.6845314333713 | | 240 | 272 | 294.296902373431 | -22.2969023734306 | | 241 | 307.4 | 327.848256250694 | -20.4482562506938 | | 242 | 328.7 | 309.650215588389 | 19.0497844116109 | | 243 | 292.9 | 302.360636400304 | -9.46063640030428 | | 244 | 249.1 | 262.132621337362 | -13.0326213373624 | | 245 | 230.4 | 238.94900594119 | -8.54900594119025 | | 246 | 361.5 | 304.35905495315 | 57.1409450468503 | | 247 | 321.7 | 302.275857787853 | 19.4241422121466 | | 248 | 277.2 | 304.030983001457 | -26.8309830014574 | | 249 | 260.7 | 263.075789422776 | -2.3757894227756 | | 250 | 251 | 255.841984245506 | -4.84198424550567 | | 251 | 257.6 | 268.030343313095 | -10.4303433130954 | | 252 | 241.8 | 258.48559727085 | -16.6855972708498 | | 253 | 287.5 | 296.03538924668 | -8.53538924668038 | | 254 | 292.3 | 293.311460964076 | -1.01146096407632 | | 255 | 274.7 | 263.169679564277 | 11.5303204357228 | | 256 | 254.2 | 240.204751811027 | 13.9952481889726 | | 257 | 230 | 242.322825473096 | -12.3228254730956 | | 258 | 339 | 314.957941966698 | 24.0420580333023 | | 259 | 318.2 | 278.232940400312 | 39.9670595996876 | | 260 | 287 | 291.531480962199 | -4.53148096219905 | | 261 | 295.8 | 275.009365595267 | 20.7906344047328 | | 262 | 284 | 290.631809056548 | -6.63180905654775 | | 263 | 271 | 303.683088525327 | -32.6830885253266 | | 264 | 262.7 | 275.913953207471 | -13.213953207471 | | 265 | 340.6 | 319.589369984922 | 21.010630015078 | | 266 | 379.4 | 347.180284108717 | 32.2197158912832 | | 267 | 373.3 | 353.337660495244 | 19.9623395047558 | | 268 | 355.2 | 344.482985562496 | 10.717014437504 | | 269 | 338.4 | 346.387055178661 | -7.98705517866148 | | 270 | 466.9 | 434.457407813978 | 32.4425921860222 | | 271 | 451 | 414.313193742959 | 36.6868062570415 | | 272 | 422 | 425.434985112541 | -3.43498511254069 | | 273 | 429.2 | 420.404229643889 | 8.79577035611146 | | 274 | 425.9 | 428.077042793122 | -2.17704279312193 | | 275 | 460.7 | 447.786654269512 | 12.9133457304876 | | 276 | 463.6 | 471.331531394263 | -7.73153139426262 | | 277 | 541.4 | 534.286927176613 | 7.11307282338691 | | 278 | 544.2 | 560.382569088665 | -16.1825690886645 | | 279 | 517.5 | 529.02007059113 | -11.5200705911302 | | 280 | 469.4 | 495.605387268543 | -26.2053872685433 | | 281 | 439.4 | 464.597282316297 | -25.1972823162968 | | 282 | 549 | 543.929055135577 | 5.07094486442315 | | 283 | 533 | 499.4787222342 | 33.5212777657998 | | 284 | 506.1 | 500.636899395108 | 5.46310060489179 | | 285 | 484 | 503.948599258886 | -19.9485992588855 | | 286 | 457 | 482.529699094897 | -25.5296990948971 | | 287 | 481.5 | 479.968398984439 | 1.53160101556125 | | 288 | 469.5 | 485.767856568259 | -16.2678565682593 | | 289 | 544.7 | 537.880761423339 | 6.81923857666152 | | 290 | 541.2 | 554.821948325974 | -13.6219483259738 | | 291 | 521.5 | 520.859498155089 | 0.640501844911341 | | 292 | 469.7 | 491.138419523182 | -21.4384195231822 | | 293 | 434.4 | 459.986377618638 | -25.586377618638 | | 294 | 542.6 | 538.84300959919 | 3.7569904008102 | | 295 | 517.3 | 492.783356139092 | 24.5166438609077 | | 296 | 485.7 | 477.190502334361 | 8.50949766563929 | | 297 | 465.8 | 474.670562774211 | -8.87056277421073 | | 298 | 447 | 457.818104143248 | -10.8181041432475 | | 299 | 426.6 | 468.47914872836 | -41.8791487283603 | | 300 | 411.6 | 428.489160341722 | -16.8891603417221 | | 301 | 467.5 | 477.294453731101 | -9.7944537311007 | | 302 | 484.5 | 469.99999767684 | 14.5000023231601 | | 303 | 451.2 | 456.91068802221 | -5.71068802221049 | | 304 | 417.4 | 412.922829551058 | 4.47717044894171 | | 305 | 379.9 | 399.397295919868 | -19.4972959198679 | | 306 | 484.7 | 483.953812065854 | 0.746187934146235 | | 307 | 455 | 434.375598404984 | 20.6244015950161 | | 308 | 420.8 | 409.078846218872 | 11.721153781128 | | 309 | 416.5 | 402.968494974451 | 13.5315050255488 | | 310 | 376.3 | 402.609844364408 | -26.3098443644078 | | 311 | 405.6 | 392.123841300822 | 13.4761586991783 | | 312 | 405.8 | 403.26598931778 | 2.53401068221967 | | 313 | 500.8 | 471.046919554055 | 29.7530804459454 | | 314 | 514 | 504.953038855594 | 9.04696114440645 | | 315 | 475.5 | 487.787076964122 | -12.2870769641224 | | 316 | 430.1 | 442.623129418822 | -12.5231294188225 | | 317 | 414.4 | 413.072491832799 | 1.32750816720085 | | 318 | 538 | 521.652942786616 | 16.3470572133843 | | 319 | 526 | 492.550575949799 | 33.4494240502012 | | 320 | 488.5 | 482.104223106618 | 6.3957768933821 | | 321 | 520.2 | 476.422742659804 | 43.7772573401958 | | 322 | 504.4 | 503.104318792744 | 1.29568120725634 | | 323 | 568.5 | 530.364568479709 | 38.135431520291 | | 324 | 610.6 | 571.14052026293 | 39.4594797370704 | | 325 | 818 | 686.816402393432 | 131.183597606568 | | 326 | 830.9 | 823.724454383553 | 7.17554561644727 | | 327 | 835.9 | 820.607373932569 | 15.2926260674313 | | 328 | 782 | 819.518684587333 | -37.518684587333 | | 329 | 762.3 | 789.273262898023 | -26.9732628980232 | | 330 | 856.9 | 892.68605183573 | -35.7860518357298 | | 331 | 820.9 | 834.923070258653 | -14.0230702586531 | | 332 | 769.6 | 790.581771362855 | -20.9817713628547 | | 333 | 752.2 | 775.608807568446 | -23.408807568446 | | 334 | 724.4 | 743.277586017291 | -18.8775860172912 | | 335 | 723.1 | 761.808702989773 | -38.7087029897725 | | 336 | 719.5 | 735.283276729274 | -15.7832767292745 | | 337 | 817.4 | 811.443684328284 | 5.95631567171586 | | 338 | 803.3 | 810.358043321368 | -7.05804332136836 | | 339 | 752.5 | 782.314249740775 | -29.8142497407749 | | 340 | 689 | 718.324599906623 | -29.324599906623 | | 341 | 630.4 | 680.416753181498 | -50.0167531814978 | | 342 | 765.5 | 745.139376464787 | 20.3606235352129 | | 343 | 757.7 | 724.593467430896 | 33.1065325691039 | | 344 | 732.2 | 708.670009000146 | 23.5299909998541 | | 345 | 702.6 | 723.332569468268 | -20.7325694682683 | | 346 | 683.3 | 685.84691080969 | -2.54691080969042 | | 347 | 709.5 | 708.558670126898 | 0.941329873102063 | | 348 | 702.2 | 714.791330063735 | -12.5913300637351 | | 349 | 784.8 | 792.424749328047 | -7.62474932804685 | | 350 | 810.9 | 772.642533036502 | 38.2574669634984 | | 351 | 755.6 | 778.006062405979 | -22.4060624059791 | | 352 | 656.8 | 718.604184623443 | -61.8041846234431 | | 353 | 615.1 | 645.968578939569 | -30.8685789395691 | | 354 | 745.3 | 734.36553119833 | 10.9344688016701 | | 355 | 694.1 | 704.226286331919 | -10.1262863319188 | | 356 | 675.7 | 643.774237418455 | 31.9257625815451 | | 357 | 643.7 | 653.907648081476 | -10.207648081476 | | 358 | 622.1 | 623.190251191307 | -1.09025119130649 | | 359 | 634.6 | 642.901356733155 | -8.30135673315465 | | 360 | 588 | 633.956006137359 | -45.9560061373586 | | 361 | 689.7 | 676.175328143525 | 13.524671856475 | | 362 | 673.9 | 674.920698593797 | -1.02069859379719 | | 363 | 647.9 | 629.390155815898 | 18.5098441841016 | | 364 | 568.8 | 593.584269672457 | -24.7842696724567 | | 365 | 545.7 | 553.460453189644 | -7.7604531896435 | | 366 | 632.6 | 665.417236164432 | -32.8172361644323 | | 367 | 643.8 | 589.76127362836 | 54.0387263716397 | | 368 | 593.1 | 589.472682854481 | 3.62731714551876 | | 369 | 579.7 | 566.674582306774 | 13.0254176932259 | | 370 | 546 | 555.993761806176 | -9.99376180617594 | | 371 | 562.9 | 565.266689948432 | -2.36668994843183 | | 372 | 572.5 | 554.717760847408 | 17.7822391525916 |
| Extrapolation Forecasts of Exponential Smoothing | | t | Forecast | 95% Lower Bound | 95% Upper Bound | | 373 | 662.728972325122 | 615.085067232269 | 710.372877417976 | | 374 | 649.600121689968 | 584.775717000743 | 714.424526379192 | | 375 | 609.557625618138 | 529.496678783849 | 689.618572452426 | | 376 | 552.432638033037 | 458.034949763668 | 646.830326302406 | | 377 | 538.25734516109 | 429.979761907953 | 646.534928414227 | | 378 | 656.101153149194 | 534.16913838009 | 778.033167918297 | | 379 | 625.712929861649 | 490.216089728115 | 761.209769995183 | | 380 | 573.299258922841 | 424.241236727684 | 722.357281117998 | | 381 | 549.881308357228 | 387.208496635773 | 712.554120078683 | | 382 | 525.11132770177 | 348.730576688226 | 701.492078715314 | | 383 | 545.023966161257 | 354.814088633884 | 735.233843688631 | | 384 | 540.477228178204 | 336.296781562896 | 744.657674793513 |
| | | | Charts produced by software: |  | | http://www.freestatistics.org/blog/date/2010/Dec/10/t1291995003um0xol8unhnpi3x/1811v1291995115.png (open in new window) | | http://www.freestatistics.org/blog/date/2010/Dec/10/t1291995003um0xol8unhnpi3x/1811v1291995115.ps (open in new window) |
 | | http://www.freestatistics.org/blog/date/2010/Dec/10/t1291995003um0xol8unhnpi3x/2811v1291995115.png (open in new window) | | http://www.freestatistics.org/blog/date/2010/Dec/10/t1291995003um0xol8unhnpi3x/2811v1291995115.ps (open in new window) |
 | | http://www.freestatistics.org/blog/date/2010/Dec/10/t1291995003um0xol8unhnpi3x/3811v1291995115.png (open in new window) | | http://www.freestatistics.org/blog/date/2010/Dec/10/t1291995003um0xol8unhnpi3x/3811v1291995115.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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