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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_arimaforecasting.wasp
Title produced by softwareARIMA Forecasting
Date of computationThu, 10 Dec 2009 08:24:18 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Dec/10/t1260458745clkbdz1peg3q7v0.htm/, Retrieved Thu, 28 Mar 2024 19:56:25 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=65469, Retrieved Thu, 28 Mar 2024 19:56:25 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordssdws10
Estimated Impact120
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [ARIMA Forecasting] [] [2009-12-07 09:54:52] [b98453cac15ba1066b407e146608df68]
-   PD    [ARIMA Forecasting] [forecasting] [2009-12-10 15:24:18] [2d672adbf8ae6977476cb9852ecac1a3] [Current]
- R         [ARIMA Forecasting] [Testing period = 12] [2009-12-18 13:03:23] [8733f8ed033058987ec00f5e71b74854]
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Dataseries X:
593530.00
610943.00
612613.00
611324.00
594167.00
595454.00
590865.00
589379.00
584428.00
573100.00
567456.00
569028.00
620735.00
628884.00
628232.00
612117.00
595404.00
597141.00
593408.00
590072.00
579799.00
574205.00
572775.00
572942.00
619567.00
625809.00
619916.00
587625.00
565742.00
557274.00
560576.00
548854.00
531673.00
525919.00
511038.00
498662.00
555362.00
564591.00
541657.00
527070.00
509846.00
514258.00
516922.00
507561.00
492622.00
490243.00
469357.00
477580.00
528379.00
533590.00
517945.00
506174.00
501866.00
516141.00
528222.00
532638.00
536322.00
536535.00
523597.00
536214.00
586570.00
596594.00
580523.00




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=65469&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=65469&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=65469&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Univariate ARIMA Extrapolation Forecast
timeY[t]F[t]95% LB95% UBp-value(H0: Y[t] = F[t])P(F[t]>Y[t-1])P(F[t]>Y[t-s])P(F[t]>Y[35])
23572775-------
24572942-------
25619567-------
26625809-------
27619916-------
28587625-------
29565742-------
30557274-------
31560576-------
32548854-------
33531673-------
34525919-------
35511038-------
36498662512130.2152501214.7536523045.67690.00780.577700.5777
37555362549465.7592533408.0408565523.47770.2359101
38564591555090.6579531776.2661578405.04960.21220.490900.9999
39541657546133.7926519239.7878573027.79730.37210.089300.9947
40527070508801.9867478001.2313539602.74210.12250.018300.4434
41509846484641.0185449763.91519518.1270.07830.008600.069
42514258472528.1681434347.4486510708.88760.01610.027700.024
43516922472042.061430408.3015513675.82050.01730.023400.0332
44507561457282.9456412278.8699502287.02130.01430.004700.0096
45492622436513.2664388350.9362484675.59660.01120.00191e-040.0012
46490243427281.9954375929.8554478634.13530.00810.00631e-047e-04
47469357409088.4787354619.1752463557.78220.01510.00171e-041e-04
48477580406683.1556344594.4641468771.8470.01260.02390.00185e-04
49528379440600.3053371190.1245510010.48610.00660.14826e-040.0233
50533590442829.1652364384.1708521274.15950.01170.01630.00120.0442
51517945430423.6774345188.6284515658.72640.02210.00880.00530.0319
52506174389678.7213297415.1482481942.29430.00670.00320.00180.005
53501866362101.936262687.1985461516.67350.00290.00230.00180.0017
54516141346561.4801240655.7555452467.20488e-040.0020.0010.0012
55528222342661.0971230169.1137455153.08066e-040.00130.00120.0017
56532638324484.5044205507.416443461.59273e-044e-040.00130.0011
57536322300296.2099175049.5262425542.89351e-041e-040.00135e-04
58536535287651.1047156133.2612419168.94821e-041e-040.00134e-04
59523597266042.6961128343.5945403741.79771e-041e-040.00192e-04
60536214260223.5134112602.4113407844.61551e-042e-040.0024e-04
61586570290728.8023133304.0188448153.58571e-040.00110.00150.003
62596594289546.0375120848.208458243.86712e-043e-040.00230.005
63580523273730.170295468.4555451991.88494e-042e-040.00360.0045

\begin{tabular}{lllllllll}
\hline
Univariate ARIMA Extrapolation Forecast \tabularnewline
time & Y[t] & F[t] & 95% LB & 95% UB & p-value(H0: Y[t] = F[t]) & P(F[t]>Y[t-1]) & P(F[t]>Y[t-s]) & P(F[t]>Y[35]) \tabularnewline
23 & 572775 & - & - & - & - & - & - & - \tabularnewline
24 & 572942 & - & - & - & - & - & - & - \tabularnewline
25 & 619567 & - & - & - & - & - & - & - \tabularnewline
26 & 625809 & - & - & - & - & - & - & - \tabularnewline
27 & 619916 & - & - & - & - & - & - & - \tabularnewline
28 & 587625 & - & - & - & - & - & - & - \tabularnewline
29 & 565742 & - & - & - & - & - & - & - \tabularnewline
30 & 557274 & - & - & - & - & - & - & - \tabularnewline
31 & 560576 & - & - & - & - & - & - & - \tabularnewline
32 & 548854 & - & - & - & - & - & - & - \tabularnewline
33 & 531673 & - & - & - & - & - & - & - \tabularnewline
34 & 525919 & - & - & - & - & - & - & - \tabularnewline
35 & 511038 & - & - & - & - & - & - & - \tabularnewline
36 & 498662 & 512130.2152 & 501214.7536 & 523045.6769 & 0.0078 & 0.5777 & 0 & 0.5777 \tabularnewline
37 & 555362 & 549465.7592 & 533408.0408 & 565523.4777 & 0.2359 & 1 & 0 & 1 \tabularnewline
38 & 564591 & 555090.6579 & 531776.2661 & 578405.0496 & 0.2122 & 0.4909 & 0 & 0.9999 \tabularnewline
39 & 541657 & 546133.7926 & 519239.7878 & 573027.7973 & 0.3721 & 0.0893 & 0 & 0.9947 \tabularnewline
40 & 527070 & 508801.9867 & 478001.2313 & 539602.7421 & 0.1225 & 0.0183 & 0 & 0.4434 \tabularnewline
41 & 509846 & 484641.0185 & 449763.91 & 519518.127 & 0.0783 & 0.0086 & 0 & 0.069 \tabularnewline
42 & 514258 & 472528.1681 & 434347.4486 & 510708.8876 & 0.0161 & 0.0277 & 0 & 0.024 \tabularnewline
43 & 516922 & 472042.061 & 430408.3015 & 513675.8205 & 0.0173 & 0.0234 & 0 & 0.0332 \tabularnewline
44 & 507561 & 457282.9456 & 412278.8699 & 502287.0213 & 0.0143 & 0.0047 & 0 & 0.0096 \tabularnewline
45 & 492622 & 436513.2664 & 388350.9362 & 484675.5966 & 0.0112 & 0.0019 & 1e-04 & 0.0012 \tabularnewline
46 & 490243 & 427281.9954 & 375929.8554 & 478634.1353 & 0.0081 & 0.0063 & 1e-04 & 7e-04 \tabularnewline
47 & 469357 & 409088.4787 & 354619.1752 & 463557.7822 & 0.0151 & 0.0017 & 1e-04 & 1e-04 \tabularnewline
48 & 477580 & 406683.1556 & 344594.4641 & 468771.847 & 0.0126 & 0.0239 & 0.0018 & 5e-04 \tabularnewline
49 & 528379 & 440600.3053 & 371190.1245 & 510010.4861 & 0.0066 & 0.1482 & 6e-04 & 0.0233 \tabularnewline
50 & 533590 & 442829.1652 & 364384.1708 & 521274.1595 & 0.0117 & 0.0163 & 0.0012 & 0.0442 \tabularnewline
51 & 517945 & 430423.6774 & 345188.6284 & 515658.7264 & 0.0221 & 0.0088 & 0.0053 & 0.0319 \tabularnewline
52 & 506174 & 389678.7213 & 297415.1482 & 481942.2943 & 0.0067 & 0.0032 & 0.0018 & 0.005 \tabularnewline
53 & 501866 & 362101.936 & 262687.1985 & 461516.6735 & 0.0029 & 0.0023 & 0.0018 & 0.0017 \tabularnewline
54 & 516141 & 346561.4801 & 240655.7555 & 452467.2048 & 8e-04 & 0.002 & 0.001 & 0.0012 \tabularnewline
55 & 528222 & 342661.0971 & 230169.1137 & 455153.0806 & 6e-04 & 0.0013 & 0.0012 & 0.0017 \tabularnewline
56 & 532638 & 324484.5044 & 205507.416 & 443461.5927 & 3e-04 & 4e-04 & 0.0013 & 0.0011 \tabularnewline
57 & 536322 & 300296.2099 & 175049.5262 & 425542.8935 & 1e-04 & 1e-04 & 0.0013 & 5e-04 \tabularnewline
58 & 536535 & 287651.1047 & 156133.2612 & 419168.9482 & 1e-04 & 1e-04 & 0.0013 & 4e-04 \tabularnewline
59 & 523597 & 266042.6961 & 128343.5945 & 403741.7977 & 1e-04 & 1e-04 & 0.0019 & 2e-04 \tabularnewline
60 & 536214 & 260223.5134 & 112602.4113 & 407844.6155 & 1e-04 & 2e-04 & 0.002 & 4e-04 \tabularnewline
61 & 586570 & 290728.8023 & 133304.0188 & 448153.5857 & 1e-04 & 0.0011 & 0.0015 & 0.003 \tabularnewline
62 & 596594 & 289546.0375 & 120848.208 & 458243.8671 & 2e-04 & 3e-04 & 0.0023 & 0.005 \tabularnewline
63 & 580523 & 273730.1702 & 95468.4555 & 451991.8849 & 4e-04 & 2e-04 & 0.0036 & 0.0045 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=65469&T=1

[TABLE]
[ROW][C]Univariate ARIMA Extrapolation Forecast[/C][/ROW]
[ROW][C]time[/C][C]Y[t][/C][C]F[t][/C][C]95% LB[/C][C]95% UB[/C][C]p-value(H0: Y[t] = F[t])[/C][C]P(F[t]>Y[t-1])[/C][C]P(F[t]>Y[t-s])[/C][C]P(F[t]>Y[35])[/C][/ROW]
[ROW][C]23[/C][C]572775[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]24[/C][C]572942[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]25[/C][C]619567[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]26[/C][C]625809[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]27[/C][C]619916[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]28[/C][C]587625[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]29[/C][C]565742[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]30[/C][C]557274[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]31[/C][C]560576[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]32[/C][C]548854[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]33[/C][C]531673[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]34[/C][C]525919[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]35[/C][C]511038[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]36[/C][C]498662[/C][C]512130.2152[/C][C]501214.7536[/C][C]523045.6769[/C][C]0.0078[/C][C]0.5777[/C][C]0[/C][C]0.5777[/C][/ROW]
[ROW][C]37[/C][C]555362[/C][C]549465.7592[/C][C]533408.0408[/C][C]565523.4777[/C][C]0.2359[/C][C]1[/C][C]0[/C][C]1[/C][/ROW]
[ROW][C]38[/C][C]564591[/C][C]555090.6579[/C][C]531776.2661[/C][C]578405.0496[/C][C]0.2122[/C][C]0.4909[/C][C]0[/C][C]0.9999[/C][/ROW]
[ROW][C]39[/C][C]541657[/C][C]546133.7926[/C][C]519239.7878[/C][C]573027.7973[/C][C]0.3721[/C][C]0.0893[/C][C]0[/C][C]0.9947[/C][/ROW]
[ROW][C]40[/C][C]527070[/C][C]508801.9867[/C][C]478001.2313[/C][C]539602.7421[/C][C]0.1225[/C][C]0.0183[/C][C]0[/C][C]0.4434[/C][/ROW]
[ROW][C]41[/C][C]509846[/C][C]484641.0185[/C][C]449763.91[/C][C]519518.127[/C][C]0.0783[/C][C]0.0086[/C][C]0[/C][C]0.069[/C][/ROW]
[ROW][C]42[/C][C]514258[/C][C]472528.1681[/C][C]434347.4486[/C][C]510708.8876[/C][C]0.0161[/C][C]0.0277[/C][C]0[/C][C]0.024[/C][/ROW]
[ROW][C]43[/C][C]516922[/C][C]472042.061[/C][C]430408.3015[/C][C]513675.8205[/C][C]0.0173[/C][C]0.0234[/C][C]0[/C][C]0.0332[/C][/ROW]
[ROW][C]44[/C][C]507561[/C][C]457282.9456[/C][C]412278.8699[/C][C]502287.0213[/C][C]0.0143[/C][C]0.0047[/C][C]0[/C][C]0.0096[/C][/ROW]
[ROW][C]45[/C][C]492622[/C][C]436513.2664[/C][C]388350.9362[/C][C]484675.5966[/C][C]0.0112[/C][C]0.0019[/C][C]1e-04[/C][C]0.0012[/C][/ROW]
[ROW][C]46[/C][C]490243[/C][C]427281.9954[/C][C]375929.8554[/C][C]478634.1353[/C][C]0.0081[/C][C]0.0063[/C][C]1e-04[/C][C]7e-04[/C][/ROW]
[ROW][C]47[/C][C]469357[/C][C]409088.4787[/C][C]354619.1752[/C][C]463557.7822[/C][C]0.0151[/C][C]0.0017[/C][C]1e-04[/C][C]1e-04[/C][/ROW]
[ROW][C]48[/C][C]477580[/C][C]406683.1556[/C][C]344594.4641[/C][C]468771.847[/C][C]0.0126[/C][C]0.0239[/C][C]0.0018[/C][C]5e-04[/C][/ROW]
[ROW][C]49[/C][C]528379[/C][C]440600.3053[/C][C]371190.1245[/C][C]510010.4861[/C][C]0.0066[/C][C]0.1482[/C][C]6e-04[/C][C]0.0233[/C][/ROW]
[ROW][C]50[/C][C]533590[/C][C]442829.1652[/C][C]364384.1708[/C][C]521274.1595[/C][C]0.0117[/C][C]0.0163[/C][C]0.0012[/C][C]0.0442[/C][/ROW]
[ROW][C]51[/C][C]517945[/C][C]430423.6774[/C][C]345188.6284[/C][C]515658.7264[/C][C]0.0221[/C][C]0.0088[/C][C]0.0053[/C][C]0.0319[/C][/ROW]
[ROW][C]52[/C][C]506174[/C][C]389678.7213[/C][C]297415.1482[/C][C]481942.2943[/C][C]0.0067[/C][C]0.0032[/C][C]0.0018[/C][C]0.005[/C][/ROW]
[ROW][C]53[/C][C]501866[/C][C]362101.936[/C][C]262687.1985[/C][C]461516.6735[/C][C]0.0029[/C][C]0.0023[/C][C]0.0018[/C][C]0.0017[/C][/ROW]
[ROW][C]54[/C][C]516141[/C][C]346561.4801[/C][C]240655.7555[/C][C]452467.2048[/C][C]8e-04[/C][C]0.002[/C][C]0.001[/C][C]0.0012[/C][/ROW]
[ROW][C]55[/C][C]528222[/C][C]342661.0971[/C][C]230169.1137[/C][C]455153.0806[/C][C]6e-04[/C][C]0.0013[/C][C]0.0012[/C][C]0.0017[/C][/ROW]
[ROW][C]56[/C][C]532638[/C][C]324484.5044[/C][C]205507.416[/C][C]443461.5927[/C][C]3e-04[/C][C]4e-04[/C][C]0.0013[/C][C]0.0011[/C][/ROW]
[ROW][C]57[/C][C]536322[/C][C]300296.2099[/C][C]175049.5262[/C][C]425542.8935[/C][C]1e-04[/C][C]1e-04[/C][C]0.0013[/C][C]5e-04[/C][/ROW]
[ROW][C]58[/C][C]536535[/C][C]287651.1047[/C][C]156133.2612[/C][C]419168.9482[/C][C]1e-04[/C][C]1e-04[/C][C]0.0013[/C][C]4e-04[/C][/ROW]
[ROW][C]59[/C][C]523597[/C][C]266042.6961[/C][C]128343.5945[/C][C]403741.7977[/C][C]1e-04[/C][C]1e-04[/C][C]0.0019[/C][C]2e-04[/C][/ROW]
[ROW][C]60[/C][C]536214[/C][C]260223.5134[/C][C]112602.4113[/C][C]407844.6155[/C][C]1e-04[/C][C]2e-04[/C][C]0.002[/C][C]4e-04[/C][/ROW]
[ROW][C]61[/C][C]586570[/C][C]290728.8023[/C][C]133304.0188[/C][C]448153.5857[/C][C]1e-04[/C][C]0.0011[/C][C]0.0015[/C][C]0.003[/C][/ROW]
[ROW][C]62[/C][C]596594[/C][C]289546.0375[/C][C]120848.208[/C][C]458243.8671[/C][C]2e-04[/C][C]3e-04[/C][C]0.0023[/C][C]0.005[/C][/ROW]
[ROW][C]63[/C][C]580523[/C][C]273730.1702[/C][C]95468.4555[/C][C]451991.8849[/C][C]4e-04[/C][C]2e-04[/C][C]0.0036[/C][C]0.0045[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=65469&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=65469&T=1

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Univariate ARIMA Extrapolation Forecast
timeY[t]F[t]95% LB95% UBp-value(H0: Y[t] = F[t])P(F[t]>Y[t-1])P(F[t]>Y[t-s])P(F[t]>Y[35])
23572775-------
24572942-------
25619567-------
26625809-------
27619916-------
28587625-------
29565742-------
30557274-------
31560576-------
32548854-------
33531673-------
34525919-------
35511038-------
36498662512130.2152501214.7536523045.67690.00780.577700.5777
37555362549465.7592533408.0408565523.47770.2359101
38564591555090.6579531776.2661578405.04960.21220.490900.9999
39541657546133.7926519239.7878573027.79730.37210.089300.9947
40527070508801.9867478001.2313539602.74210.12250.018300.4434
41509846484641.0185449763.91519518.1270.07830.008600.069
42514258472528.1681434347.4486510708.88760.01610.027700.024
43516922472042.061430408.3015513675.82050.01730.023400.0332
44507561457282.9456412278.8699502287.02130.01430.004700.0096
45492622436513.2664388350.9362484675.59660.01120.00191e-040.0012
46490243427281.9954375929.8554478634.13530.00810.00631e-047e-04
47469357409088.4787354619.1752463557.78220.01510.00171e-041e-04
48477580406683.1556344594.4641468771.8470.01260.02390.00185e-04
49528379440600.3053371190.1245510010.48610.00660.14826e-040.0233
50533590442829.1652364384.1708521274.15950.01170.01630.00120.0442
51517945430423.6774345188.6284515658.72640.02210.00880.00530.0319
52506174389678.7213297415.1482481942.29430.00670.00320.00180.005
53501866362101.936262687.1985461516.67350.00290.00230.00180.0017
54516141346561.4801240655.7555452467.20488e-040.0020.0010.0012
55528222342661.0971230169.1137455153.08066e-040.00130.00120.0017
56532638324484.5044205507.416443461.59273e-044e-040.00130.0011
57536322300296.2099175049.5262425542.89351e-041e-040.00135e-04
58536535287651.1047156133.2612419168.94821e-041e-040.00134e-04
59523597266042.6961128343.5945403741.79771e-041e-040.00192e-04
60536214260223.5134112602.4113407844.61551e-042e-040.0024e-04
61586570290728.8023133304.0188448153.58571e-040.00110.00150.003
62596594289546.0375120848.208458243.86712e-043e-040.00230.005
63580523273730.170295468.4555451991.88494e-042e-040.00360.0045







Univariate ARIMA Extrapolation Forecast Performance
time% S.E.PEMAPESq.EMSERMSE
360.0109-0.02630181392821.245100
370.01490.01070.018534765655.2056108079238.225410396.1165
380.02140.01710.01890256500.4155102138325.622110106.3508
390.0251-0.00820.015620041671.604281614162.11769034.0557
400.03090.03590.0196333720310.1956132035391.733211490.6654
410.03670.0520.025635291091.3917215911341.676314693.9219
420.04120.08830.03411741378870.9551433835274.430420828.7127
430.0450.09510.04172014208924.8599631381980.734125127.3154
440.05020.10990.04932527882750.9526842104288.536129019.0332
450.05630.12850.05723148189987.74641072712858.457232752.2955
460.06130.14740.06543964088104.73281335565153.573136545.3848
470.06790.14730.07223632294657.75451526959278.921639076.3263
480.07790.17430.08015026362549.69481796144145.904142380.9408
490.08040.19920.08867705099237.68122218212366.745447097.9019
500.09040.2050.09648237529141.94342619500151.758651181.0527
510.1010.20330.1037659981910.2582934530261.664854171.3048
520.12080.2990.114613571149966.03873560213773.686859667.527
530.14010.3860.129619533993585.64294447645985.462166690.6739
540.15590.48930.148628757213553.38625727096910.089775677.5853
550.16750.54150.168234432848669.887162384498.079284630.872
560.18710.64150.190843327877747.93068884550843.310294257.8954
570.21280.7860.217855708173610.739311012897332.7388104942.3524
580.23330.86520.24661943193337.0313227258028.5776115009.8171
590.26410.96810.276166334219461.48215440048088.2819124257.99
600.28941.06060.307476170748703.534317869276112.892133676.0117
610.27631.01760.334787522014269.460220548227580.4523143346.5297
620.29731.06040.361694278451249.137223278976605.2184152574.4953
630.33231.12080.388794121840418.439925809078884.2621160652.0429

\begin{tabular}{lllllllll}
\hline
Univariate ARIMA Extrapolation Forecast Performance \tabularnewline
time & % S.E. & PE & MAPE & Sq.E & MSE & RMSE \tabularnewline
36 & 0.0109 & -0.0263 & 0 & 181392821.2451 & 0 & 0 \tabularnewline
37 & 0.0149 & 0.0107 & 0.0185 & 34765655.2056 & 108079238.2254 & 10396.1165 \tabularnewline
38 & 0.0214 & 0.0171 & 0.018 & 90256500.4155 & 102138325.6221 & 10106.3508 \tabularnewline
39 & 0.0251 & -0.0082 & 0.0156 & 20041671.6042 & 81614162.1176 & 9034.0557 \tabularnewline
40 & 0.0309 & 0.0359 & 0.0196 & 333720310.1956 & 132035391.7332 & 11490.6654 \tabularnewline
41 & 0.0367 & 0.052 & 0.025 & 635291091.3917 & 215911341.6763 & 14693.9219 \tabularnewline
42 & 0.0412 & 0.0883 & 0.0341 & 1741378870.9551 & 433835274.4304 & 20828.7127 \tabularnewline
43 & 0.045 & 0.0951 & 0.0417 & 2014208924.8599 & 631381980.7341 & 25127.3154 \tabularnewline
44 & 0.0502 & 0.1099 & 0.0493 & 2527882750.9526 & 842104288.5361 & 29019.0332 \tabularnewline
45 & 0.0563 & 0.1285 & 0.0572 & 3148189987.7464 & 1072712858.4572 & 32752.2955 \tabularnewline
46 & 0.0613 & 0.1474 & 0.0654 & 3964088104.7328 & 1335565153.5731 & 36545.3848 \tabularnewline
47 & 0.0679 & 0.1473 & 0.0722 & 3632294657.7545 & 1526959278.9216 & 39076.3263 \tabularnewline
48 & 0.0779 & 0.1743 & 0.0801 & 5026362549.6948 & 1796144145.9041 & 42380.9408 \tabularnewline
49 & 0.0804 & 0.1992 & 0.0886 & 7705099237.6812 & 2218212366.7454 & 47097.9019 \tabularnewline
50 & 0.0904 & 0.205 & 0.0964 & 8237529141.9434 & 2619500151.7586 & 51181.0527 \tabularnewline
51 & 0.101 & 0.2033 & 0.103 & 7659981910.258 & 2934530261.6648 & 54171.3048 \tabularnewline
52 & 0.1208 & 0.299 & 0.1146 & 13571149966.0387 & 3560213773.6868 & 59667.527 \tabularnewline
53 & 0.1401 & 0.386 & 0.1296 & 19533993585.6429 & 4447645985.4621 & 66690.6739 \tabularnewline
54 & 0.1559 & 0.4893 & 0.1486 & 28757213553.3862 & 5727096910.0897 & 75677.5853 \tabularnewline
55 & 0.1675 & 0.5415 & 0.1682 & 34432848669.88 & 7162384498.0792 & 84630.872 \tabularnewline
56 & 0.1871 & 0.6415 & 0.1908 & 43327877747.9306 & 8884550843.3102 & 94257.8954 \tabularnewline
57 & 0.2128 & 0.786 & 0.2178 & 55708173610.7393 & 11012897332.7388 & 104942.3524 \tabularnewline
58 & 0.2333 & 0.8652 & 0.246 & 61943193337.03 & 13227258028.5776 & 115009.8171 \tabularnewline
59 & 0.2641 & 0.9681 & 0.2761 & 66334219461.482 & 15440048088.2819 & 124257.99 \tabularnewline
60 & 0.2894 & 1.0606 & 0.3074 & 76170748703.5343 & 17869276112.892 & 133676.0117 \tabularnewline
61 & 0.2763 & 1.0176 & 0.3347 & 87522014269.4602 & 20548227580.4523 & 143346.5297 \tabularnewline
62 & 0.2973 & 1.0604 & 0.3616 & 94278451249.1372 & 23278976605.2184 & 152574.4953 \tabularnewline
63 & 0.3323 & 1.1208 & 0.3887 & 94121840418.4399 & 25809078884.2621 & 160652.0429 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=65469&T=2

[TABLE]
[ROW][C]Univariate ARIMA Extrapolation Forecast Performance[/C][/ROW]
[ROW][C]time[/C][C]% S.E.[/C][C]PE[/C][C]MAPE[/C][C]Sq.E[/C][C]MSE[/C][C]RMSE[/C][/ROW]
[ROW][C]36[/C][C]0.0109[/C][C]-0.0263[/C][C]0[/C][C]181392821.2451[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]37[/C][C]0.0149[/C][C]0.0107[/C][C]0.0185[/C][C]34765655.2056[/C][C]108079238.2254[/C][C]10396.1165[/C][/ROW]
[ROW][C]38[/C][C]0.0214[/C][C]0.0171[/C][C]0.018[/C][C]90256500.4155[/C][C]102138325.6221[/C][C]10106.3508[/C][/ROW]
[ROW][C]39[/C][C]0.0251[/C][C]-0.0082[/C][C]0.0156[/C][C]20041671.6042[/C][C]81614162.1176[/C][C]9034.0557[/C][/ROW]
[ROW][C]40[/C][C]0.0309[/C][C]0.0359[/C][C]0.0196[/C][C]333720310.1956[/C][C]132035391.7332[/C][C]11490.6654[/C][/ROW]
[ROW][C]41[/C][C]0.0367[/C][C]0.052[/C][C]0.025[/C][C]635291091.3917[/C][C]215911341.6763[/C][C]14693.9219[/C][/ROW]
[ROW][C]42[/C][C]0.0412[/C][C]0.0883[/C][C]0.0341[/C][C]1741378870.9551[/C][C]433835274.4304[/C][C]20828.7127[/C][/ROW]
[ROW][C]43[/C][C]0.045[/C][C]0.0951[/C][C]0.0417[/C][C]2014208924.8599[/C][C]631381980.7341[/C][C]25127.3154[/C][/ROW]
[ROW][C]44[/C][C]0.0502[/C][C]0.1099[/C][C]0.0493[/C][C]2527882750.9526[/C][C]842104288.5361[/C][C]29019.0332[/C][/ROW]
[ROW][C]45[/C][C]0.0563[/C][C]0.1285[/C][C]0.0572[/C][C]3148189987.7464[/C][C]1072712858.4572[/C][C]32752.2955[/C][/ROW]
[ROW][C]46[/C][C]0.0613[/C][C]0.1474[/C][C]0.0654[/C][C]3964088104.7328[/C][C]1335565153.5731[/C][C]36545.3848[/C][/ROW]
[ROW][C]47[/C][C]0.0679[/C][C]0.1473[/C][C]0.0722[/C][C]3632294657.7545[/C][C]1526959278.9216[/C][C]39076.3263[/C][/ROW]
[ROW][C]48[/C][C]0.0779[/C][C]0.1743[/C][C]0.0801[/C][C]5026362549.6948[/C][C]1796144145.9041[/C][C]42380.9408[/C][/ROW]
[ROW][C]49[/C][C]0.0804[/C][C]0.1992[/C][C]0.0886[/C][C]7705099237.6812[/C][C]2218212366.7454[/C][C]47097.9019[/C][/ROW]
[ROW][C]50[/C][C]0.0904[/C][C]0.205[/C][C]0.0964[/C][C]8237529141.9434[/C][C]2619500151.7586[/C][C]51181.0527[/C][/ROW]
[ROW][C]51[/C][C]0.101[/C][C]0.2033[/C][C]0.103[/C][C]7659981910.258[/C][C]2934530261.6648[/C][C]54171.3048[/C][/ROW]
[ROW][C]52[/C][C]0.1208[/C][C]0.299[/C][C]0.1146[/C][C]13571149966.0387[/C][C]3560213773.6868[/C][C]59667.527[/C][/ROW]
[ROW][C]53[/C][C]0.1401[/C][C]0.386[/C][C]0.1296[/C][C]19533993585.6429[/C][C]4447645985.4621[/C][C]66690.6739[/C][/ROW]
[ROW][C]54[/C][C]0.1559[/C][C]0.4893[/C][C]0.1486[/C][C]28757213553.3862[/C][C]5727096910.0897[/C][C]75677.5853[/C][/ROW]
[ROW][C]55[/C][C]0.1675[/C][C]0.5415[/C][C]0.1682[/C][C]34432848669.88[/C][C]7162384498.0792[/C][C]84630.872[/C][/ROW]
[ROW][C]56[/C][C]0.1871[/C][C]0.6415[/C][C]0.1908[/C][C]43327877747.9306[/C][C]8884550843.3102[/C][C]94257.8954[/C][/ROW]
[ROW][C]57[/C][C]0.2128[/C][C]0.786[/C][C]0.2178[/C][C]55708173610.7393[/C][C]11012897332.7388[/C][C]104942.3524[/C][/ROW]
[ROW][C]58[/C][C]0.2333[/C][C]0.8652[/C][C]0.246[/C][C]61943193337.03[/C][C]13227258028.5776[/C][C]115009.8171[/C][/ROW]
[ROW][C]59[/C][C]0.2641[/C][C]0.9681[/C][C]0.2761[/C][C]66334219461.482[/C][C]15440048088.2819[/C][C]124257.99[/C][/ROW]
[ROW][C]60[/C][C]0.2894[/C][C]1.0606[/C][C]0.3074[/C][C]76170748703.5343[/C][C]17869276112.892[/C][C]133676.0117[/C][/ROW]
[ROW][C]61[/C][C]0.2763[/C][C]1.0176[/C][C]0.3347[/C][C]87522014269.4602[/C][C]20548227580.4523[/C][C]143346.5297[/C][/ROW]
[ROW][C]62[/C][C]0.2973[/C][C]1.0604[/C][C]0.3616[/C][C]94278451249.1372[/C][C]23278976605.2184[/C][C]152574.4953[/C][/ROW]
[ROW][C]63[/C][C]0.3323[/C][C]1.1208[/C][C]0.3887[/C][C]94121840418.4399[/C][C]25809078884.2621[/C][C]160652.0429[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=65469&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=65469&T=2

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Univariate ARIMA Extrapolation Forecast Performance
time% S.E.PEMAPESq.EMSERMSE
360.0109-0.02630181392821.245100
370.01490.01070.018534765655.2056108079238.225410396.1165
380.02140.01710.01890256500.4155102138325.622110106.3508
390.0251-0.00820.015620041671.604281614162.11769034.0557
400.03090.03590.0196333720310.1956132035391.733211490.6654
410.03670.0520.025635291091.3917215911341.676314693.9219
420.04120.08830.03411741378870.9551433835274.430420828.7127
430.0450.09510.04172014208924.8599631381980.734125127.3154
440.05020.10990.04932527882750.9526842104288.536129019.0332
450.05630.12850.05723148189987.74641072712858.457232752.2955
460.06130.14740.06543964088104.73281335565153.573136545.3848
470.06790.14730.07223632294657.75451526959278.921639076.3263
480.07790.17430.08015026362549.69481796144145.904142380.9408
490.08040.19920.08867705099237.68122218212366.745447097.9019
500.09040.2050.09648237529141.94342619500151.758651181.0527
510.1010.20330.1037659981910.2582934530261.664854171.3048
520.12080.2990.114613571149966.03873560213773.686859667.527
530.14010.3860.129619533993585.64294447645985.462166690.6739
540.15590.48930.148628757213553.38625727096910.089775677.5853
550.16750.54150.168234432848669.887162384498.079284630.872
560.18710.64150.190843327877747.93068884550843.310294257.8954
570.21280.7860.217855708173610.739311012897332.7388104942.3524
580.23330.86520.24661943193337.0313227258028.5776115009.8171
590.26410.96810.276166334219461.48215440048088.2819124257.99
600.28941.06060.307476170748703.534317869276112.892133676.0117
610.27631.01760.334787522014269.460220548227580.4523143346.5297
620.29731.06040.361694278451249.137223278976605.2184152574.4953
630.33231.12080.388794121840418.439925809078884.2621160652.0429



Parameters (Session):
par1 = 12 ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = 1 ; par7 = 1 ; par8 = 0 ; par9 = 0 ; par10 = FALSE ;
Parameters (R input):
par1 = 2 ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = 1 ; par7 = 1 ; par8 = 0 ; par9 = 0 ; par10 = FALSE ;
R code (references can be found in the software module):
par1 <- as.numeric(par1) #cut off periods
par1 <- 28
par2 <- as.numeric(par2) #lambda
par3 <- as.numeric(par3) #degree of non-seasonal differencing
par4 <- as.numeric(par4) #degree of seasonal differencing
par5 <- as.numeric(par5) #seasonal period
par6 <- as.numeric(par6) #p
par6 <- 3
par7 <- as.numeric(par7) #q
par7 <- 3
par8 <- as.numeric(par8) #P
par9 <- as.numeric(par9) #Q
if (par10 == 'TRUE') par10 <- TRUE
if (par10 == 'FALSE') par10 <- FALSE
if (par2 == 0) x <- log(x)
if (par2 != 0) x <- x^par2
lx <- length(x)
first <- lx - 2*par1
nx <- lx - par1
nx1 <- nx + 1
fx <- lx - nx
if (fx < 1) {
fx <- par5
nx1 <- lx + fx - 1
first <- lx - 2*fx
}
first <- 1
if (fx < 3) fx <- round(lx/10,0)
(arima.out <- arima(x[1:nx], order=c(par6,par3,par7), seasonal=list(order=c(par8,par4,par9), period=par5), include.mean=par10, method='ML'))
(forecast <- predict(arima.out,par1))
(lb <- forecast$pred - 1.96 * forecast$se)
(ub <- forecast$pred + 1.96 * forecast$se)
if (par2 == 0) {
x <- exp(x)
forecast$pred <- exp(forecast$pred)
lb <- exp(lb)
ub <- exp(ub)
}
if (par2 != 0) {
x <- x^(1/par2)
forecast$pred <- forecast$pred^(1/par2)
lb <- lb^(1/par2)
ub <- ub^(1/par2)
}
if (par2 < 0) {
olb <- lb
lb <- ub
ub <- olb
}
(actandfor <- c(x[1:nx], forecast$pred))
(perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
bitmap(file='test1.png')
opar <- par(mar=c(4,4,2,2),las=1)
ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
plot(x,ylim=ylim,type='n',xlim=c(first,lx))
usr <- par('usr')
rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
abline(h= (-3:3)*2 , col ='gray', lty =3)
polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
lines(nx1:lx, lb , lty=2)
lines(nx1:lx, ub , lty=2)
lines(x, lwd=2)
lines(nx1:lx, forecast$pred , lwd=2 , col ='white')
box()
par(opar)
dev.off()
prob.dec <- array(NA, dim=fx)
prob.sdec <- array(NA, dim=fx)
prob.ldec <- array(NA, dim=fx)
prob.pval <- array(NA, dim=fx)
perf.pe <- array(0, dim=fx)
perf.mape <- array(0, dim=fx)
perf.mape1 <- array(0, dim=fx)
perf.se <- array(0, dim=fx)
perf.mse <- array(0, dim=fx)
perf.mse1 <- array(0, dim=fx)
perf.rmse <- array(0, dim=fx)
for (i in 1:fx) {
locSD <- (ub[i] - forecast$pred[i]) / 1.96
perf.pe[i] = (x[nx+i] - forecast$pred[i]) / forecast$pred[i]
perf.se[i] = (x[nx+i] - forecast$pred[i])^2
prob.dec[i] = pnorm((x[nx+i-1] - forecast$pred[i]) / locSD)
prob.sdec[i] = pnorm((x[nx+i-par5] - forecast$pred[i]) / locSD)
prob.ldec[i] = pnorm((x[nx] - forecast$pred[i]) / locSD)
prob.pval[i] = pnorm(abs(x[nx+i] - forecast$pred[i]) / locSD)
}
perf.mape[1] = abs(perf.pe[1])
perf.mse[1] = abs(perf.se[1])
for (i in 2:fx) {
perf.mape[i] = perf.mape[i-1] + abs(perf.pe[i])
perf.mape1[i] = perf.mape[i] / i
perf.mse[i] = perf.mse[i-1] + perf.se[i]
perf.mse1[i] = perf.mse[i] / i
}
perf.rmse = sqrt(perf.mse1)
bitmap(file='test2.png')
plot(forecast$pred, pch=19, type='b',main='ARIMA Extrapolation Forecast', ylab='Forecast and 95% CI', xlab='time',ylim=c(min(lb),max(ub)))
dum <- forecast$pred
dum[1:par1] <- x[(nx+1):lx]
lines(dum, lty=1)
lines(ub,lty=3)
lines(lb,lty=3)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Univariate ARIMA Extrapolation Forecast',9,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'time',1,header=TRUE)
a<-table.element(a,'Y[t]',1,header=TRUE)
a<-table.element(a,'F[t]',1,header=TRUE)
a<-table.element(a,'95% LB',1,header=TRUE)
a<-table.element(a,'95% UB',1,header=TRUE)
a<-table.element(a,'p-value
(H0: Y[t] = F[t])',1,header=TRUE)
a<-table.element(a,'P(F[t]>Y[t-1])',1,header=TRUE)
a<-table.element(a,'P(F[t]>Y[t-s])',1,header=TRUE)
mylab <- paste('P(F[t]>Y[',nx,sep='')
mylab <- paste(mylab,'])',sep='')
a<-table.element(a,mylab,1,header=TRUE)
a<-table.row.end(a)
for (i in (nx-par5):nx) {
a<-table.row.start(a)
a<-table.element(a,i,header=TRUE)
a<-table.element(a,x[i])
a<-table.element(a,'-')
a<-table.element(a,'-')
a<-table.element(a,'-')
a<-table.element(a,'-')
a<-table.element(a,'-')
a<-table.element(a,'-')
a<-table.element(a,'-')
a<-table.row.end(a)
}
for (i in 1:fx) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,round(x[nx+i],4))
a<-table.element(a,round(forecast$pred[i],4))
a<-table.element(a,round(lb[i],4))
a<-table.element(a,round(ub[i],4))
a<-table.element(a,round((1-prob.pval[i]),4))
a<-table.element(a,round((1-prob.dec[i]),4))
a<-table.element(a,round((1-prob.sdec[i]),4))
a<-table.element(a,round((1-prob.ldec[i]),4))
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,'Univariate ARIMA Extrapolation Forecast Performance',7,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'time',1,header=TRUE)
a<-table.element(a,'% S.E.',1,header=TRUE)
a<-table.element(a,'PE',1,header=TRUE)
a<-table.element(a,'MAPE',1,header=TRUE)
a<-table.element(a,'Sq.E',1,header=TRUE)
a<-table.element(a,'MSE',1,header=TRUE)
a<-table.element(a,'RMSE',1,header=TRUE)
a<-table.row.end(a)
for (i in 1:fx) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,round(perc.se[i],4))
a<-table.element(a,round(perf.pe[i],4))
a<-table.element(a,round(perf.mape1[i],4))
a<-table.element(a,round(perf.se[i],4))
a<-table.element(a,round(perf.mse1[i],4))
a<-table.element(a,round(perf.rmse[i],4))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')