| | | *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: Mon, 27 Dec 2010 17:55:32 +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/27/t1293475174n14x48fu7jo3wie.htm/, Retrieved Mon, 27 Dec 2010 19:39:36 +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/27/t1293475174n14x48fu7jo3wie.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 | 1 | | beta | 0.0439627190836867 | | gamma | FALSE |
| Interpolation Forecasts of Exponential Smoothing | | t | Observed | Fitted | Residuals | | 3 | 264.6 | 326.3 | -61.6999999999999 | | 4 | 240.7 | 307.487500232537 | -66.7875002325366 | | 5 | 201.4 | 280.651340121512 | -79.2513401215118 | | 6 | 240.8 | 237.867235718744 | 2.93276428125586 | | 7 | 241.1 | 277.39616801098 | -36.2961680109797 | | 8 | 223.8 | 276.100489772899 | -52.3004897728986 | | 9 | 206.1 | 256.501218033073 | -50.4012180330735 | | 10 | 174.7 | 236.58544344321 | -61.8854434432099 | | 11 | 203.3 | 202.464791077747 | 0.8352089222534 | | 12 | 220.5 | 231.101509132972 | -10.6015091329718 | | 13 | 299.5 | 247.835437965096 | 51.6645620349041 | | 14 | 347.4 | 329.106752592418 | 18.2932474075819 | | 15 | 338.3 | 377.810973489326 | -39.5109734893259 | | 16 | 327.7 | 366.973963661092 | -39.2739636610917 | | 17 | 351.6 | 354.647373429356 | -3.04737342935618 | | 18 | 396.6 | 378.413402607338 | 18.1865973926617 | | 19 | 438.8 | 424.2129348796 | 14.5870651203999 | | 20 | 395.6 | 467.054221925744 | -71.4542219257436 | | 21 | 363.5 | 420.712900039879 | -57.2129000398788 | | 22 | 378.8 | 386.097665387463 | -7.29766538746253 | | 23 | 357 | 401.076840174067 | -44.0768401740668 | | 24 | 369 | 377.339102431398 | -8.3391024313977 | | 25 | 464.8 | 388.972492813796 | 75.827507186204 | | 26 | 479.1 | 488.106076211039 | -9.00607621103939 | | 27 | 431.3 | 502.010144612527 | -70.7101446125272 | | 28 | 366.5 | 451.10153438856 | -84.6015343885598 | | 29 | 326.3 | 382.582220898187 | -56.2822208981867 | | 30 | 355.1 | 339.907901431434 | 15.1920985685663 | | 31 | 331.6 | 369.375787393095 | -37.7757873930953 | | 32 | 261.3 | 344.215061063768 | -82.9150610637676 | | 33 | 249 | 270.269889526414 | -21.2698895264144 | | 34 | 205.5 | 257.034807348224 | -51.5348073482236 | | 35 | 235.6 | 211.269197089742 | 24.3308029102583 | | 36 | 240.9 | 242.438845343166 | -1.53884534316597 | | 37 | 264.9 | 247.671193517631 | 17.2288064823688 | | 38 | 253.8 | 272.428618697163 | -18.6286186971627 | | 39 | 232.3 | 260.509653966462 | -28.2096539664622 | | 40 | 193.8 | 237.769480873687 | -43.9694808736866 | | 41 | 177 | 197.336462937781 | -20.3364629377812 | | 42 | 213.2 | 179.642416730492 | 33.5575832695082 | | 43 | 207.2 | 217.317699336897 | -10.1176993368965 | | 44 | 180.6 | 210.872897763175 | -30.2728977631754 | | 45 | 188.6 | 182.942018862964 | 5.65798113703627 | | 46 | 175.4 | 191.190759098272 | -15.790759098272 | | 47 | 199 | 177.296554391917 | 21.7034456080835 | | 48 | 179.6 | 201.850696874333 | -22.2506968743328 | | 49 | 225.8 | 181.47249573823 | 44.3275042617698 | | 50 | 234 | 229.621253355771 | 4.37874664422864 | | 51 | 200.2 | 238.01375496443 | -37.8137549644302 | | 52 | 183.6 | 202.55135947743 | -18.9513594774296 | | 53 | 178.2 | 185.118206184469 | -6.9182061844694 | | 54 | 203.2 | 179.414063029419 | 23.7859369705814 | | 55 | 208.5 | 205.459757494598 | 3.04024250540152 | | 56 | 191.8 | 210.89341482181 | -19.0934148218097 | | 57 | 172.8 | 193.35401638965 | -20.5540163896502 | | 58 | 148 | 173.450405941071 | -25.4504059410706 | | 59 | 159.4 | 147.531536894117 | 11.8684631058825 | | 60 | 154.5 | 159.453306803596 | -4.95330680359649 | | 61 | 213.2 | 154.335545968055 | 58.8644540319453 | | 62 | 196.4 | 215.623387424676 | -19.2233874246756 | | 63 | 182.8 | 197.978275043488 | -15.1782750434878 | | 64 | 176.4 | 183.710996801576 | -7.31099680157598 | | 65 | 153.6 | 176.989585502967 | -23.3895855029666 | | 66 | 173.2 | 153.161315726016 | 20.0386842739842 | | 67 | 171 | 173.64227077356 | -2.64227077355963 | | 68 | 151.2 | 171.326109365799 | -20.1261093657986 | | 69 | 161.9 | 150.641310873502 | 11.2586891264976 | | 70 | 157.2 | 161.836273460821 | -4.63627346082123 | | 71 | 201.7 | 156.932450273068 | 44.767549726932 | | 72 | 236.4 | 203.400553485778 | 32.999446514222 | | 73 | 356.1 | 239.5512988828 | 116.5487011172 | | 74 | 398.3 | 364.375096689584 | 33.924903310416 | | 75 | 403.7 | 408.066527683761 | -4.36652768376103 | | 76 | 384.6 | 413.274563253829 | -28.6745632538286 | | 77 | 365.8 | 392.913951484653 | -27.1139514846532 | | 78 | 368.1 | 372.921948452285 | -4.82194845228469 | | 79 | 367.9 | 375.009962487041 | -7.10996248704095 | | 80 | 347 | 374.497389203528 | -27.4973892035275 | | 81 | 343.3 | 352.388529206438 | -9.08852920643807 | | 82 | 292.9 | 348.288972750052 | -55.3889727500516 | | 83 | 311.5 | 295.453922900707 | 16.046077099293 | | 84 | 300.9 | 314.759352080618 | -13.8593520806185 | | 85 | 366.9 | 303.550057278416 | 63.3499427215837 | | 86 | 356.9 | 372.335093014253 | -15.435093014253 | | 87 | 329.7 | 361.656524356037 | -31.9565243560368 | | 88 | 316.2 | 333.051628652881 | -16.8516286528813 | | 89 | 269 | 318.810785236312 | -49.8107852363121 | | 90 | 289.3 | 269.42096767763 | 19.8790323223698 | | 91 | 266.2 | 290.594903991274 | -24.3949039912741 | | 92 | 253.6 | 266.422437680032 | -12.8224376800323 | | 93 | 233.8 | 253.258728454337 | -19.4587284543369 | | 94 | 228.4 | 232.603269841573 | -4.20326984157316 | | 95 | 253.6 | 227.018482670295 | 26.5815173297048 | | 96 | 260.1 | 253.387078449479 | 6.71292155052092 | | 97 | 306.6 | 260.182196733835 | 46.4178032661645 | | 98 | 309.2 | 308.722849579308 | 0.477150420692283 | | 99 | 309.5 | 311.343826409213 | -1.84382640921325 | | 100 | 271 | 311.562766786746 | -40.562766786746 | | 101 | 279.9 | 271.279517265243 | 8.62048273475682 | | 102 | 317.9 | 280.558497126077 | 37.341502873923 | | 103 | 298.4 | 320.200131127086 | -21.800131127086 | | 104 | 246.7 | 299.741738086358 | -53.0417380863584 | | 105 | 227.3 | 245.709879055157 | -18.4098790551573 | | 106 | 209.1 | 225.500530713891 | -16.4005307138908 | | 107 | 259.9 | 206.579518789293 | 53.3204812107074 | | 108 | 266 | 259.723632126166 | 6.27636787383409 | | 109 | 320.6 | 266.099558323869 | 54.5004416761308 | | 110 | 308.5 | 323.095545931214 | -14.5955459312138 | | 111 | 282.2 | 310.353886045567 | -28.1538860455668 | | 112 | 262.7 | 282.816164662231 | -20.1161646622314 | | 113 | 263.5 | 262.431803366145 | 1.06819663385545 | | 114 | 313.1 | 263.278764194685 | 49.8212358053152 | | 115 | 284.3 | 315.069041188796 | -30.7690411887961 | | 116 | 252.6 | 284.916350474539 | -32.3163504745386 | | 117 | 250.3 | 251.795635836817 | -1.49563583681649 | | 118 | 246.5 | 249.429883618671 | -2.92988361867106 | | 119 | 312.7 | 245.501077968196 | 67.1989220318045 | | 120 | 333.2 | 314.655325300206 | 18.5446746997937 | | 121 | 446.4 | 335.970599624532 | 110.429400375468 | | 122 | 511.6 | 454.025376331818 | 57.5746236681817 | | 123 | 515.5 | 521.756513338492 | -6.25651333849169 | | 124 | 506.4 | 525.381460000148 | -18.9814600001482 | | 125 | 483.2 | 515.446983406363 | -32.2469834063634 | | 126 | 522.3 | 490.829318333573 | 31.4706816664268 | | 127 | 509.8 | 531.312855071046 | -21.5128550710463 | | 128 | 460.7 | 517.86709146687 | -57.16709146687 | | 129 | 405.8 | 466.253870683881 | -60.4538706838805 | | 130 | 375 | 408.696154149484 | -33.6961541494836 | | 131 | 378.5 | 376.414779590409 | 2.08522040959082 | | 132 | 406.8 | 380.006451549504 | 26.7935484504964 | | 133 | 467.8 | 409.484368793288 | 58.315631206712 | | 134 | 469.8 | 473.048082506216 | -3.24808250621646 | | 135 | 429.8 | 474.905287967435 | -45.1052879674351 | | 136 | 355.8 | 432.922336863334 | -77.122336863334 | | 137 | 332.7 | 355.531829232734 | -22.8318292327338 | | 138 | 378 | 331.428079938008 | 46.5719200619917 | | 139 | 360.5 | 378.775508176882 | -18.2755081768816 | | 140 | 334.7 | 360.47206714479 | -25.7720671447897 | | 141 | 319.5 | 333.539056996697 | -14.0390569966974 | | 142 | 323.1 | 317.721861877752 | 5.37813812224829 | | 143 | 363.6 | 321.558299453213 | 42.0417005467866 | | 144 | 352.1 | 363.906566924152 | -11.8065669241523 | | 145 | 411.9 | 351.887518139123 | 60.012481860877 | | 146 | 388.6 | 414.325830020688 | -25.7258300206876 | | 147 | 416.4 | 389.894852582293 | 26.5051474177066 | | 148 | 360.7 | 418.86009093249 | -58.1600909324898 | | 149 | 338 | 360.603215192943 | -22.603215192943 | | 150 | 417.2 | 336.909516393028 | 80.2904836069724 | | 151 | 388.4 | 419.639304368934 | -31.2393043689343 | | 152 | 371.1 | 389.465939606593 | -18.365939606593 | | 153 | 331.5 | 371.35852296296 | -39.8585229629604 | | 154 | 353.7 | 330.006233914849 | 23.6937660851509 | | 155 | 396.7 | 353.247876297285 | 43.4521237027148 | | 156 | 447 | 398.158149805217 | 48.8418501947828 | | 157 | 533.5 | 450.605370344858 | 82.894629655142 | | 158 | 565.4 | 540.749643661933 | 24.6503563380668 | | 159 | 542.3 | 573.733340352936 | -31.4333403529364 | | 160 | 488.7 | 549.251445241138 | -60.5514452411383 | | 161 | 467.1 | 492.989439063891 | -25.889439063891 | | 162 | 531.3 | 470.251268927091 | 61.048731072909 | | 163 | 496.1 | 537.135137141665 | -41.0351371416647 | | 164 | 444 | 500.131120934945 | -56.1311209349452 | | 165 | 403.4 | 445.56344423343 | -42.1634442334297 | | 166 | 386.3 | 403.109824578995 | -16.8098245789947 | | 167 | 394.1 | 385.270818983182 | 8.82918101681764 | | 168 | 404.1 | 393.458973787964 | 10.6410262120363 | | 169 | 462.1 | 403.926782234086 | 58.1732177659143 | | 170 | 448.1 | 464.484235064923 | -16.3842350649227 | | 171 | 432.3 | 449.763939541362 | -17.4639395413624 | | 172 | 386.3 | 433.196177273211 | -46.896177273211 | | 173 | 395.2 | 385.13449380565 | 10.06550619435 | | 174 | 421.9 | 394.477000826907 | 27.4229991730926 | | 175 | 382.9 | 422.382590435986 | -39.4825904359862 | | 176 | 384.2 | 381.646828403953 | 2.55317159604732 | | 177 | 345.5 | 383.059072769602 | -37.5590727696022 | | 178 | 323.4 | 342.707873804388 | -19.3078738043884 | | 179 | 372.6 | 319.759047172223 | 52.8409528277772 | | 180 | 376 | 371.282079137505 | 4.71792086249525 | | 181 | 462.7 | 374.889491767042 | 87.8105082329583 | | 182 | 487 | 465.449880473083 | 21.5501195269171 | | 183 | 444.2 | 490.697282324065 | -46.4972823240647 | | 184 | 399.3 | 445.853135363097 | -46.5531353630969 | | 185 | 394.9 | 398.906532950664 | -4.00653295066434 | | 186 | 455.4 | 394.330394868055 | 61.0696051319453 | | 187 | 414 | 457.515180763022 | -43.515180763022 | | 188 | 375.5 | 414.202135095261 | -38.7021350952615 | | 189 | 347 | 374.00068400213 | -27.0006840021296 | | 190 | 339.4 | 344.313660516277 | -4.91366051627665 | | 191 | 385.8 | 336.497642639327 | 49.3023573606731 | | 192 | 378.8 | 385.065108326138 | -6.26510832613775 | | 193 | 451.8 | 377.789677128767 | 74.0103228712331 | | 194 | 446.1 | 454.043372162448 | -7.94337216244782 | | 195 | 422.5 | 447.994159923493 | -25.494159923493 | | 196 | 383.1 | 423.273367332502 | -40.1733673325019 | | 197 | 352.8 | 382.107236869817 | -29.3072368698174 | | 198 | 445.3 | 350.518811048191 | 94.7811889518095 | | 199 | 367.5 | 447.185649832497 | -79.6856498324967 | | 200 | 355.1 | 365.88245199391 | -10.7824519939096 | | 201 | 326.2 | 353.008426085868 | -26.8084260858681 | | 202 | 319.8 | 322.929854780779 | -3.12985478077923 | | 203 | 331.8 | 316.392257854279 | 15.4077421457209 | | 204 | 340.9 | 329.069624093945 | 11.8303759060547 | | 205 | 394.1 | 338.689719586558 | 55.4102804134424 | | 206 | 417.2 | 394.325706178722 | 22.8742938212779 | | 207 | 369.9 | 418.431322332225 | -48.5313223322246 | | 208 | 349.2 | 368.997753441773 | -19.7977534417732 | | 209 | 321.4 | 347.427390368724 | -26.0273903687245 | | 210 | 405.7 | 318.483155517463 | 87.2168444825372 | | 211 | 342.9 | 406.617445150814 | -63.7174451508141 | | 212 | 316.5 | 341.016253008919 | -24.5162530089186 | | 213 | 284.2 | 313.538451864903 | -29.338451864903 | | 214 | 270.9 | 279.948653747216 | -9.04865374721601 | | 215 | 288.8 | 266.250850324442 | 22.5491496755585 | | 216 | 278.8 | 285.142172257204 | -6.3421722572042 | | 217 | 324.4 | 274.86335311988 | 49.5366468801196 | | 218 | 310.9 | 322.641118811019 | -11.7411188110189 | | 219 | 299 | 308.624947303002 | -9.62494730300182 | | 220 | 273 | 296.301808448525 | -23.3018084485247 | | 221 | 279.3 | 269.27739758956 | 10.0226024104397 | | 222 | 359.2 | 276.018018443818 | 83.181981556182 | | 223 | 305 | 359.574924531797 | -54.5749245317968 | | 224 | 282.1 | 302.975662455592 | -20.875662455592 | | 225 | 250.3 | 279.157911571371 | -28.8579115713709 | | 226 | 246.5 | 246.089239311617 | 0.410760688383107 | | 227 | 257.9 | 242.307297468371 | 15.5927025316291 | | 228 | 266.5 | 254.392795069524 | 12.1072049304756 | | 229 | 315.9 | 263.525060718772 | 52.3749392812284 | | 230 | 318.4 | 315.227605461417 | 3.17239453858269 | | 231 | 295.4 | 317.86707255134 | -22.4670725513396 | | 232 | 266.4 | 293.879358952132 | -27.4793589521323 | | 233 | 245.8 | 263.67129161392 | -17.8712916139199 | | 234 | 362.8 | 242.285621041035 | 120.514378958965 | | 235 | 324.9 | 364.583760828752 | -39.6837608287525 | | 236 | 294.2 | 324.939154799254 | -30.7391547992538 | | 237 | 289.5 | 292.887777971944 | -3.38777797194427 | | 238 | 295.2 | 288.038842040646 | 7.16115795935423 | | 239 | 290.3 | 294.053666016327 | -3.75366601632675 | | 240 | 272 | 288.988644651717 | -16.988644651717 | | 241 | 307.4 | 269.941777639281 | 37.458222360719 | | 242 | 328.7 | 306.9885429463 | 21.7114570537004 | | 243 | 292.9 | 329.243037633649 | -36.3430376336489 | | 244 | 249.1 | 291.845298879513 | -42.7452988795129 | | 245 | 230.4 | 246.166099312725 | -15.7660993127247 | | 246 | 361.5 | 226.772978717594 | 134.727021282406 | | 247 | 321.7 | 363.795944907214 | -42.0959449072142 | | 248 | 277.2 | 322.145292706696 | -44.945292706696 | | 249 | 260.7 | 275.669375429297 | -14.9693754292974 | | 250 | 251 | 258.511280982441 | -7.51128098244095 | | 251 | 257.6 | 248.481064646651 | 9.11893535334872 | | 252 | 241.8 | 255.481957839933 | -13.6819578399329 | | 253 | 287.5 | 239.080461770901 | 48.4195382290989 | | 254 | 292.3 | 286.909116328229 | 5.39088367177123 | | 255 | 274.7 | 291.946114232704 | -17.2461142327037 | | 256 | 254.2 | 273.587928157406 | -19.3879281574061 | | 257 | 230 | 252.235582118207 | -22.2355821182074 | | 258 | 339 | 227.058045467882 | 111.941954532118 | | 259 | 318.2 | 340.979318168657 | -22.7793181686567 | | 260 | 287 | 319.17787740309 | -32.1778774030901 | | 261 | 295.8 | 286.563250418109 | 9.23674958189122 | | 262 | 284 | 295.769323045224 | -11.7693230452238 | | 263 | 271 | 283.451911602381 | -12.4519116023815 | | 264 | 262.7 | 269.904491710551 | -7.20449171055111 | | 265 | 340.6 | 261.287762665339 | 79.3122373346607 | | 266 | 379.4 | 342.674544275182 | 36.7254557248182 | | 267 | 373.3 | 383.089095168432 | -9.78909516843225 | | 268 | 355.2 | 376.558739927459 | -21.3587399274591 | | 269 | 338.4 | 357.519751644047 | -19.1197516440466 | | 270 | 466.9 | 339.87919537357 | 127.02080462643 | | 271 | 451 | 473.963375325145 | -22.9633753251451 | | 272 | 422 | 457.053842906513 | -35.0538429065126 | | 273 | 429.2 | 426.51278065801 | 2.6872193419901 | | 274 | 425.9 | 433.830918127058 | -7.93091812705802 | | 275 | 460.7 | 430.182253401362 | 30.5177465986376 | | 276 | 463.6 | 466.323896522146 | -2.72389652214548 | | 277 | 541.4 | 469.104146624529 | 72.2958533754706 | | 278 | 544.2 | 550.082468917391 | -5.8824689173905 | | 279 | 517.5 | 552.623859588857 | -35.1238595888569 | | 280 | 469.4 | 524.379719216617 | -54.9797192166171 | | 281 | 439.4 | 473.862661265397 | -34.4626612653969 | | 282 | 549 | 442.34758896931 | 106.65241103069 | | 283 | 533 | 556.63631895505 | -23.6363189550501 | | 284 | 506.1 | 539.597202104657 | -33.4972021046568 | | 285 | 484 | 511.22457401844 | -27.2245740184404 | | 286 | 457 | 487.927707718695 | -30.9277077186946 | | 287 | 481.5 | 459.568041592355 | 21.9319584076447 | | 288 | 469.5 | 485.032230118786 | -15.5322301187857 | | 289 | 544.7 | 472.34939104933 | 72.3506089506697 | | 290 | 541.2 | 550.730120546162 | -9.53012054616227 | | 291 | 521.5 | 546.811150533758 | -25.3111505337578 | | 292 | 469.7 | 525.998403533157 | -56.2984035331572 | | 293 | 434.4 | 471.723372633769 | -37.323372633769 | | 294 | 542.6 | 434.782535687415 | 107.817464312585 | | 295 | 517.3 | 547.722484583304 | -30.4224845833045 | | 296 | 485.7 | 521.085029439741 | -35.3850294397408 | | 297 | 465.8 | 487.929407330714 | -22.1294073307135 | | 298 | 447 | 467.056538412745 | -20.0565384127449 | | 299 | 426.6 | 447.374798448714 | -20.7747984487142 | | 300 | 411.6 | 426.061481820493 | -14.4614818204932 | | 301 | 467.5 | 410.425715757685 | 57.074284242315 | | 302 | 484.5 | 468.834856482732 | 15.6651435172676 | | 303 | 451.2 | 486.523538786588 | -35.3235387865877 | | 304 | 417.4 | 451.670619973871 | -34.2706199738712 | | 305 | 379.9 | 416.363990335136 | -36.4639903351361 | | 306 | 484.7 | 377.260934171362 | 107.439065828638 | | 307 | 455 | 486.784247641 | -31.7842476410004 | | 308 | 420.8 | 455.686925690673 | -34.8869256906727 | | 309 | 416.5 | 419.95320157684 | -3.45320157684023 | | 310 | 376.3 | 415.501389445978 | -39.2013894459782 | | 311 | 405.6 | 373.577989774075 | 32.0220102259255 | | 312 | 405.8 | 404.285764414132 | 1.51423558586816 | | 313 | 500.8 | 404.55233432782 | 96.2476656721801 | | 314 | 514 | 503.783643416227 | 10.2163565837735 | | 315 | 475.5 | 517.432782230778 | -41.9327822307778 | | 316 | 430.1 | 477.089303105169 | -46.9893031051686 | | 317 | 414.4 | 429.623525572818 | -15.2235255728179 | | 318 | 538 | 413.254257994597 | 124.745742005403 | | 319 | 526 | 542.338420007266 | -16.3384200072663 | | 320 | 488.5 | 529.620138638216 | -41.1201386382156 | | 321 | 520.2 | 490.312385534581 | 29.8876144654186 | | 322 | 504.4 | 523.326326333406 | -18.9263263334063 | | 323 | 568.5 | 506.694273565524 | 61.8057264344755 | | 324 | 610.6 | 573.511421354527 | 37.0885786454735 | | 325 | 818 | 617.241936118731 | 200.758063881269 | | 326 | 830.9 | 833.467806484928 | -2.56780648492781 | | 327 | 835.9 | 846.25491872977 | -10.3549187297697 | | 328 | 782 | 850.799688346518 | -68.7996883465183 | | 329 | 762.3 | 793.875066974695 | -31.5750669746952 | | 330 | 856.9 | 772.786941175238 | 84.113058824762 | | 331 | 820.9 | 871.08477995162 | -50.1847799516207 | | 332 | 769.6 | 832.878520568331 | -63.2785205683309 | | 333 | 752.2 | 778.796624744554 | -26.5966247445541 | | 334 | 724.4 | 760.227364802335 | -35.8273648023352 | | 335 | 723.1 | 730.852296428021 | -7.75229642802117 | | 336 | 719.5 | 729.211484397903 | -9.71148439790272 | | 337 | 817.4 | 725.184541137432 | 92.2154588625679 | | 338 | 803.3 | 827.13858345058 | -23.8385834505805 | | 339 | 752.5 | 811.99057450299 | -59.4905745029895 | | 340 | 689 | 758.575207087987 | -69.5752070879875 | | 341 | 630.4 | 692.016491803589 | -61.6164918035889 | | 342 | 765.5 | 630.707663283505 | 134.792336716495 | | 343 | 757.7 | 771.733500917206 | -14.0335009172064 | | 344 | 732.2 | 763.316550058623 | -31.1165500586227 | | 345 | 702.6 | 736.448581909542 | -33.848581909542 | | 346 | 683.3 | 705.360506211672 | -22.0605062116716 | | 347 | 709.5 | 685.090666374244 | 24.4093336257561 | | 348 | 702.2 | 712.363767051453 | -10.163767051453 | | 349 | 784.8 | 704.616940215738 | 80.1830597842619 | | 350 | 810.9 | 790.742005548304 | 20.157994451696 | | 351 | 755.6 | 817.728205795674 | -62.1282057956744 | | 352 | 656.8 | 759.696880937106 | -102.896880937106 | | 353 | 615.1 | 656.37325426588 | -41.27325426588 | | 354 | 745.3 | 612.85876978292 | 132.44123021708 | | 355 | 694.1 | 748.881246382051 | -54.781246382051 | | 356 | 675.7 | 695.272913836303 | -19.5729138363027 | | 357 | 643.7 | 676.012435323668 | -32.3124353236682 | | 358 | 622.1 | 642.591892806624 | -20.4918928066239 | | 359 | 634.6 | 620.091013479673 | 14.5089865203267 | | 360 | 588 | 633.228867978255 | -45.2288679782555 | | 361 | 689.7 | 584.640483960854 | 105.059516039146 | | 362 | 673.9 | 690.959185951551 | -17.0591859515513 | | 363 | 647.9 | 674.409217751767 | -26.5092177517669 | | 364 | 568.8 | 647.243800458618 | -78.4438004586176 | | 365 | 545.7 | 564.695197695199 | -18.9951976951986 | | 366 | 632.6 | 540.760117154986 | 91.8398828450145 | | 367 | 643.8 | 631.69764812518 | 12.1023518748203 | | 368 | 593.1 | 643.429700420904 | -50.3297004209041 | | 369 | 579.7 | 590.517069939734 | -10.8170699397339 | | 370 | 546 | 576.641522132665 | -30.6415221326649 | | 371 | 562.9 | 541.59443750285 | 21.30556249715 | | 372 | 572.5 | 559.431087961832 | 13.0689120381679 |
| Extrapolation Forecasts of Exponential Smoothing | | t | Forecast | 95% Lower Bound | 95% Upper Bound | | 373 | 569.605632870495 | 482.369788627267 | 656.841477113724 | | 374 | 566.711265740991 | 440.600148292308 | 692.822383189674 | | 375 | 563.816898611486 | 405.984137005413 | 721.64966021756 | | 376 | 560.922531481982 | 374.747858222753 | 747.09720474121 | | 377 | 558.028164352477 | 345.465431750268 | 770.590896954686 | | 378 | 555.133797222973 | 317.423225336 | 792.844369109946 | | 379 | 552.239430093468 | 290.207700304992 | 814.271159881944 | | 380 | 549.345062963964 | 263.556214432631 | 835.133911495296 | | 381 | 546.450695834459 | 237.291112544819 | 855.610279124099 | | 382 | 543.556328704954 | 211.286574187579 | 875.82608322233 | | 383 | 540.66196157545 | 185.450323544369 | 895.873599606531 | | 384 | 537.767594445945 | 159.712812194612 | 915.82237669728 |
| | | | Charts produced by software: |  | | http://www.freestatistics.org/blog/date/2010/Dec/27/t1293475174n14x48fu7jo3wie/16p371293472525.png (open in new window) | | http://www.freestatistics.org/blog/date/2010/Dec/27/t1293475174n14x48fu7jo3wie/16p371293472525.ps (open in new window) |
 | | http://www.freestatistics.org/blog/date/2010/Dec/27/t1293475174n14x48fu7jo3wie/2hyka1293472525.png (open in new window) | | http://www.freestatistics.org/blog/date/2010/Dec/27/t1293475174n14x48fu7jo3wie/2hyka1293472525.ps (open in new window) |
 | | http://www.freestatistics.org/blog/date/2010/Dec/27/t1293475174n14x48fu7jo3wie/3hyka1293472525.png (open in new window) | | http://www.freestatistics.org/blog/date/2010/Dec/27/t1293475174n14x48fu7jo3wie/3hyka1293472525.ps (open in new window) |
| | | | Parameters (Session): | | par1 = 12 ; par2 = Double ; par3 = additive ; | | | | Parameters (R input): | | par1 = 12 ; par2 = Double ; 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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