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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 computationWed, 07 Dec 2011 09:04:58 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Dec/07/t1323266720xviu9epk1oy93vd.htm/, Retrieved Thu, 31 Oct 2024 23:11:23 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=152400, Retrieved Thu, 31 Oct 2024 23:11:23 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact126
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [] [2008-12-08 19:22:39] [d2d412c7f4d35ffbf5ee5ee89db327d4]
- RMP   [Spectral Analysis] [] [2011-12-07 13:16:39] [272f2f17453c7186d6073ebf31ee4b1c]
- RMP       [ARIMA Forecasting] [] [2011-12-07 14:04:58] [722cc7f94b3c1568a723b3c5e98a2726] [Current]
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Dataseries X:
655362
873127
1107897
1555964
1671159
1493308
2957796
2638691
1305669
1280496
921900
867888
652586
913831
1108544
1555827
1699283
1509458
3268975
2425016
1312703
1365498
934453
775019
651142
843192
1146766
1652601
1465906
1652734
2922334
2702805
1458956
1410363
1019279
936574
708917
885295
1099663
1576220
1487870
1488635
2882530
2677026
1404398
1344370
936865
872705
628151
953712
1160384
1400618
1661511
1495347
2918786
2775677
1407026
1370199
964526
850851
683118
847224
1073256
1514326
1503734
1507712
2865698
2788128
1391596
1366378
946295
859626




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time6 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net

\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 & 6 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=152400&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]6 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=152400&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=152400&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 time6 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







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[48])
36936574-------
37708917-------
38885295-------
391099663-------
401576220-------
411487870-------
421488635-------
432882530-------
442677026-------
451404398-------
461344370-------
47936865-------
48872705-------
49628151620716.2913564682.5277676750.0550.397400.0010
50953712880347.7514824048.6969936646.80590.005310.43160.6049
5111603841089720.27221032968.80121146471.74320.007310.36571
5214006181543706.80741486932.93481600480.68010.13081
5316615111779338.17341722512.79571836163.55110111
5414953471517686.01971460672.99851574699.04080.221300.8411
5529187863259508.84353202403.18393316614.50310111
5627756772442434.82732385337.2392499532.41570001
5714070261253946.21541196794.01391311098.4170001
5813701991297116.99211239769.44911354464.53510.00621e-040.05321
59964526898654.8446841268.7972956040.89210.012200.09590.8123
60850851779230.2479722058.0117836402.4840.00707e-047e-04
61683118667867.194607558.6488728175.73920.310100.90160
62847224892078.4332831978.0223952178.84410.071810.02220.7362
6310732561170677.02931110218.08491231135.97388e-0410.63071
6415143261634142.28131573731.42061694553.1421e-04111
6515037341512134.49011451686.31011572582.67010.39270.471701
6615077121605164.51861544393.30111665935.73628e-040.99950.99981
6728656982994656.54792933657.08643055656.0095010.99261
6827881282636613.81092575654.80352697572.81830001
6913915961447636.9521386655.3481508618.5560.035800.90411
7013663781441296.23111380037.43571502555.02650.00830.94410.98851
719462951039360.3192977829.42091100891.21740.001500.99141
72859626910160.5732848628.2408971692.90560.05370.12490.97060.8836

\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[48]) \tabularnewline
36 & 936574 & - & - & - & - & - & - & - \tabularnewline
37 & 708917 & - & - & - & - & - & - & - \tabularnewline
38 & 885295 & - & - & - & - & - & - & - \tabularnewline
39 & 1099663 & - & - & - & - & - & - & - \tabularnewline
40 & 1576220 & - & - & - & - & - & - & - \tabularnewline
41 & 1487870 & - & - & - & - & - & - & - \tabularnewline
42 & 1488635 & - & - & - & - & - & - & - \tabularnewline
43 & 2882530 & - & - & - & - & - & - & - \tabularnewline
44 & 2677026 & - & - & - & - & - & - & - \tabularnewline
45 & 1404398 & - & - & - & - & - & - & - \tabularnewline
46 & 1344370 & - & - & - & - & - & - & - \tabularnewline
47 & 936865 & - & - & - & - & - & - & - \tabularnewline
48 & 872705 & - & - & - & - & - & - & - \tabularnewline
49 & 628151 & 620716.2913 & 564682.5277 & 676750.055 & 0.3974 & 0 & 0.001 & 0 \tabularnewline
50 & 953712 & 880347.7514 & 824048.6969 & 936646.8059 & 0.0053 & 1 & 0.4316 & 0.6049 \tabularnewline
51 & 1160384 & 1089720.2722 & 1032968.8012 & 1146471.7432 & 0.0073 & 1 & 0.3657 & 1 \tabularnewline
52 & 1400618 & 1543706.8074 & 1486932.9348 & 1600480.68 & 0 & 1 & 0.1308 & 1 \tabularnewline
53 & 1661511 & 1779338.1734 & 1722512.7957 & 1836163.5511 & 0 & 1 & 1 & 1 \tabularnewline
54 & 1495347 & 1517686.0197 & 1460672.9985 & 1574699.0408 & 0.2213 & 0 & 0.841 & 1 \tabularnewline
55 & 2918786 & 3259508.8435 & 3202403.1839 & 3316614.5031 & 0 & 1 & 1 & 1 \tabularnewline
56 & 2775677 & 2442434.8273 & 2385337.239 & 2499532.4157 & 0 & 0 & 0 & 1 \tabularnewline
57 & 1407026 & 1253946.2154 & 1196794.0139 & 1311098.417 & 0 & 0 & 0 & 1 \tabularnewline
58 & 1370199 & 1297116.9921 & 1239769.4491 & 1354464.5351 & 0.0062 & 1e-04 & 0.0532 & 1 \tabularnewline
59 & 964526 & 898654.8446 & 841268.7972 & 956040.8921 & 0.0122 & 0 & 0.0959 & 0.8123 \tabularnewline
60 & 850851 & 779230.2479 & 722058.0117 & 836402.484 & 0.007 & 0 & 7e-04 & 7e-04 \tabularnewline
61 & 683118 & 667867.194 & 607558.6488 & 728175.7392 & 0.3101 & 0 & 0.9016 & 0 \tabularnewline
62 & 847224 & 892078.4332 & 831978.0223 & 952178.8441 & 0.0718 & 1 & 0.0222 & 0.7362 \tabularnewline
63 & 1073256 & 1170677.0293 & 1110218.0849 & 1231135.9738 & 8e-04 & 1 & 0.6307 & 1 \tabularnewline
64 & 1514326 & 1634142.2813 & 1573731.4206 & 1694553.142 & 1e-04 & 1 & 1 & 1 \tabularnewline
65 & 1503734 & 1512134.4901 & 1451686.3101 & 1572582.6701 & 0.3927 & 0.4717 & 0 & 1 \tabularnewline
66 & 1507712 & 1605164.5186 & 1544393.3011 & 1665935.7362 & 8e-04 & 0.9995 & 0.9998 & 1 \tabularnewline
67 & 2865698 & 2994656.5479 & 2933657.0864 & 3055656.0095 & 0 & 1 & 0.9926 & 1 \tabularnewline
68 & 2788128 & 2636613.8109 & 2575654.8035 & 2697572.8183 & 0 & 0 & 0 & 1 \tabularnewline
69 & 1391596 & 1447636.952 & 1386655.348 & 1508618.556 & 0.0358 & 0 & 0.9041 & 1 \tabularnewline
70 & 1366378 & 1441296.2311 & 1380037.4357 & 1502555.0265 & 0.0083 & 0.9441 & 0.9885 & 1 \tabularnewline
71 & 946295 & 1039360.3192 & 977829.4209 & 1100891.2174 & 0.0015 & 0 & 0.9914 & 1 \tabularnewline
72 & 859626 & 910160.5732 & 848628.2408 & 971692.9056 & 0.0537 & 0.1249 & 0.9706 & 0.8836 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=152400&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[48])[/C][/ROW]
[ROW][C]36[/C][C]936574[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]37[/C][C]708917[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]38[/C][C]885295[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]39[/C][C]1099663[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]40[/C][C]1576220[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]41[/C][C]1487870[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]42[/C][C]1488635[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]43[/C][C]2882530[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]44[/C][C]2677026[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]45[/C][C]1404398[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]46[/C][C]1344370[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]47[/C][C]936865[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]48[/C][C]872705[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]49[/C][C]628151[/C][C]620716.2913[/C][C]564682.5277[/C][C]676750.055[/C][C]0.3974[/C][C]0[/C][C]0.001[/C][C]0[/C][/ROW]
[ROW][C]50[/C][C]953712[/C][C]880347.7514[/C][C]824048.6969[/C][C]936646.8059[/C][C]0.0053[/C][C]1[/C][C]0.4316[/C][C]0.6049[/C][/ROW]
[ROW][C]51[/C][C]1160384[/C][C]1089720.2722[/C][C]1032968.8012[/C][C]1146471.7432[/C][C]0.0073[/C][C]1[/C][C]0.3657[/C][C]1[/C][/ROW]
[ROW][C]52[/C][C]1400618[/C][C]1543706.8074[/C][C]1486932.9348[/C][C]1600480.68[/C][C]0[/C][C]1[/C][C]0.1308[/C][C]1[/C][/ROW]
[ROW][C]53[/C][C]1661511[/C][C]1779338.1734[/C][C]1722512.7957[/C][C]1836163.5511[/C][C]0[/C][C]1[/C][C]1[/C][C]1[/C][/ROW]
[ROW][C]54[/C][C]1495347[/C][C]1517686.0197[/C][C]1460672.9985[/C][C]1574699.0408[/C][C]0.2213[/C][C]0[/C][C]0.841[/C][C]1[/C][/ROW]
[ROW][C]55[/C][C]2918786[/C][C]3259508.8435[/C][C]3202403.1839[/C][C]3316614.5031[/C][C]0[/C][C]1[/C][C]1[/C][C]1[/C][/ROW]
[ROW][C]56[/C][C]2775677[/C][C]2442434.8273[/C][C]2385337.239[/C][C]2499532.4157[/C][C]0[/C][C]0[/C][C]0[/C][C]1[/C][/ROW]
[ROW][C]57[/C][C]1407026[/C][C]1253946.2154[/C][C]1196794.0139[/C][C]1311098.417[/C][C]0[/C][C]0[/C][C]0[/C][C]1[/C][/ROW]
[ROW][C]58[/C][C]1370199[/C][C]1297116.9921[/C][C]1239769.4491[/C][C]1354464.5351[/C][C]0.0062[/C][C]1e-04[/C][C]0.0532[/C][C]1[/C][/ROW]
[ROW][C]59[/C][C]964526[/C][C]898654.8446[/C][C]841268.7972[/C][C]956040.8921[/C][C]0.0122[/C][C]0[/C][C]0.0959[/C][C]0.8123[/C][/ROW]
[ROW][C]60[/C][C]850851[/C][C]779230.2479[/C][C]722058.0117[/C][C]836402.484[/C][C]0.007[/C][C]0[/C][C]7e-04[/C][C]7e-04[/C][/ROW]
[ROW][C]61[/C][C]683118[/C][C]667867.194[/C][C]607558.6488[/C][C]728175.7392[/C][C]0.3101[/C][C]0[/C][C]0.9016[/C][C]0[/C][/ROW]
[ROW][C]62[/C][C]847224[/C][C]892078.4332[/C][C]831978.0223[/C][C]952178.8441[/C][C]0.0718[/C][C]1[/C][C]0.0222[/C][C]0.7362[/C][/ROW]
[ROW][C]63[/C][C]1073256[/C][C]1170677.0293[/C][C]1110218.0849[/C][C]1231135.9738[/C][C]8e-04[/C][C]1[/C][C]0.6307[/C][C]1[/C][/ROW]
[ROW][C]64[/C][C]1514326[/C][C]1634142.2813[/C][C]1573731.4206[/C][C]1694553.142[/C][C]1e-04[/C][C]1[/C][C]1[/C][C]1[/C][/ROW]
[ROW][C]65[/C][C]1503734[/C][C]1512134.4901[/C][C]1451686.3101[/C][C]1572582.6701[/C][C]0.3927[/C][C]0.4717[/C][C]0[/C][C]1[/C][/ROW]
[ROW][C]66[/C][C]1507712[/C][C]1605164.5186[/C][C]1544393.3011[/C][C]1665935.7362[/C][C]8e-04[/C][C]0.9995[/C][C]0.9998[/C][C]1[/C][/ROW]
[ROW][C]67[/C][C]2865698[/C][C]2994656.5479[/C][C]2933657.0864[/C][C]3055656.0095[/C][C]0[/C][C]1[/C][C]0.9926[/C][C]1[/C][/ROW]
[ROW][C]68[/C][C]2788128[/C][C]2636613.8109[/C][C]2575654.8035[/C][C]2697572.8183[/C][C]0[/C][C]0[/C][C]0[/C][C]1[/C][/ROW]
[ROW][C]69[/C][C]1391596[/C][C]1447636.952[/C][C]1386655.348[/C][C]1508618.556[/C][C]0.0358[/C][C]0[/C][C]0.9041[/C][C]1[/C][/ROW]
[ROW][C]70[/C][C]1366378[/C][C]1441296.2311[/C][C]1380037.4357[/C][C]1502555.0265[/C][C]0.0083[/C][C]0.9441[/C][C]0.9885[/C][C]1[/C][/ROW]
[ROW][C]71[/C][C]946295[/C][C]1039360.3192[/C][C]977829.4209[/C][C]1100891.2174[/C][C]0.0015[/C][C]0[/C][C]0.9914[/C][C]1[/C][/ROW]
[ROW][C]72[/C][C]859626[/C][C]910160.5732[/C][C]848628.2408[/C][C]971692.9056[/C][C]0.0537[/C][C]0.1249[/C][C]0.9706[/C][C]0.8836[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=152400&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=152400&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[48])
36936574-------
37708917-------
38885295-------
391099663-------
401576220-------
411487870-------
421488635-------
432882530-------
442677026-------
451404398-------
461344370-------
47936865-------
48872705-------
49628151620716.2913564682.5277676750.0550.397400.0010
50953712880347.7514824048.6969936646.80590.005310.43160.6049
5111603841089720.27221032968.80121146471.74320.007310.36571
5214006181543706.80741486932.93481600480.68010.13081
5316615111779338.17341722512.79571836163.55110111
5414953471517686.01971460672.99851574699.04080.221300.8411
5529187863259508.84353202403.18393316614.50310111
5627756772442434.82732385337.2392499532.41570001
5714070261253946.21541196794.01391311098.4170001
5813701991297116.99211239769.44911354464.53510.00621e-040.05321
59964526898654.8446841268.7972956040.89210.012200.09590.8123
60850851779230.2479722058.0117836402.4840.00707e-047e-04
61683118667867.194607558.6488728175.73920.310100.90160
62847224892078.4332831978.0223952178.84410.071810.02220.7362
6310732561170677.02931110218.08491231135.97388e-0410.63071
6415143261634142.28131573731.42061694553.1421e-04111
6515037341512134.49011451686.31011572582.67010.39270.471701
6615077121605164.51861544393.30111665935.73628e-040.99950.99981
6728656982994656.54792933657.08643055656.0095010.99261
6827881282636613.81092575654.80352697572.81830001
6913915961447636.9521386655.3481508618.5560.035800.90411
7013663781441296.23111380037.43571502555.02650.00830.94410.98851
719462951039360.3192977829.42091100891.21740.001500.99141
72859626910160.5732848628.2408971692.90560.05370.12490.97060.8836







Univariate ARIMA Extrapolation Forecast Performance
time% S.E.PEMAPESq.EMSERMSE
490.04610.012055274892.927400
500.03260.08330.04775382312970.88972718793931.908652142.0553
510.02660.06480.05344993362427.48343476983430.433558965.9515
520.0188-0.09270.063220474406807.09567726339274.59987899.5977
530.0163-0.06620.063813883242793.31368957719978.34294645.2322
540.0192-0.01470.0556499031799.24367547938615.158986878.8732
550.0089-0.10450.0626116092056077.31723054241109.7529151836.2312
560.01190.13640.0718111050345642.98934053754176.4073184536.5931
570.02330.12210.077423433420442.119932873717094.8199181311.1058
580.02260.05630.07535340979880.687630120443373.4066173552.4226
590.03260.07330.07514339009110.08927776676622.1959166663.3632
600.03740.09190.07655129532136.058725889414581.6845160901.8787
610.04610.02280.0724232587082.729823915812466.3803154647.3811
620.0344-0.05030.07082011920177.502722351248731.4604149503.3402
630.0263-0.08320.07169490856957.125321493889279.8381146607.9441
640.0189-0.07330.071814355941256.14421047767528.3572145078.4875
650.0204-0.00560.067970568233.626219813814628.6672140761.5524
660.0193-0.06070.06759496993385.967919240657892.9617138710.6986
670.0104-0.04310.066216630307087.443919103271008.4607138214.5832
680.01180.05750.065722956549497.979219295934932.9366138909.8086
690.0215-0.03870.06453140588302.793218526632712.4536136112.5737
700.0217-0.0520.06395612741351.488617939637650.5916133938.9325
710.0302-0.08950.0658661153630.069617536225301.8732132424.4135
720.0345-0.05550.06462553743089.289616911955209.6822130045.9734

\begin{tabular}{lllllllll}
\hline
Univariate ARIMA Extrapolation Forecast Performance \tabularnewline
time & % S.E. & PE & MAPE & Sq.E & MSE & RMSE \tabularnewline
49 & 0.0461 & 0.012 & 0 & 55274892.9274 & 0 & 0 \tabularnewline
50 & 0.0326 & 0.0833 & 0.0477 & 5382312970.8897 & 2718793931.9086 & 52142.0553 \tabularnewline
51 & 0.0266 & 0.0648 & 0.0534 & 4993362427.4834 & 3476983430.4335 & 58965.9515 \tabularnewline
52 & 0.0188 & -0.0927 & 0.0632 & 20474406807.0956 & 7726339274.599 & 87899.5977 \tabularnewline
53 & 0.0163 & -0.0662 & 0.0638 & 13883242793.3136 & 8957719978.342 & 94645.2322 \tabularnewline
54 & 0.0192 & -0.0147 & 0.0556 & 499031799.2436 & 7547938615.1589 & 86878.8732 \tabularnewline
55 & 0.0089 & -0.1045 & 0.0626 & 116092056077.317 & 23054241109.7529 & 151836.2312 \tabularnewline
56 & 0.0119 & 0.1364 & 0.0718 & 111050345642.989 & 34053754176.4073 & 184536.5931 \tabularnewline
57 & 0.0233 & 0.1221 & 0.0774 & 23433420442.1199 & 32873717094.8199 & 181311.1058 \tabularnewline
58 & 0.0226 & 0.0563 & 0.0753 & 5340979880.6876 & 30120443373.4066 & 173552.4226 \tabularnewline
59 & 0.0326 & 0.0733 & 0.0751 & 4339009110.089 & 27776676622.1959 & 166663.3632 \tabularnewline
60 & 0.0374 & 0.0919 & 0.0765 & 5129532136.0587 & 25889414581.6845 & 160901.8787 \tabularnewline
61 & 0.0461 & 0.0228 & 0.0724 & 232587082.7298 & 23915812466.3803 & 154647.3811 \tabularnewline
62 & 0.0344 & -0.0503 & 0.0708 & 2011920177.5027 & 22351248731.4604 & 149503.3402 \tabularnewline
63 & 0.0263 & -0.0832 & 0.0716 & 9490856957.1253 & 21493889279.8381 & 146607.9441 \tabularnewline
64 & 0.0189 & -0.0733 & 0.0718 & 14355941256.144 & 21047767528.3572 & 145078.4875 \tabularnewline
65 & 0.0204 & -0.0056 & 0.0679 & 70568233.6262 & 19813814628.6672 & 140761.5524 \tabularnewline
66 & 0.0193 & -0.0607 & 0.0675 & 9496993385.9679 & 19240657892.9617 & 138710.6986 \tabularnewline
67 & 0.0104 & -0.0431 & 0.0662 & 16630307087.4439 & 19103271008.4607 & 138214.5832 \tabularnewline
68 & 0.0118 & 0.0575 & 0.0657 & 22956549497.9792 & 19295934932.9366 & 138909.8086 \tabularnewline
69 & 0.0215 & -0.0387 & 0.0645 & 3140588302.7932 & 18526632712.4536 & 136112.5737 \tabularnewline
70 & 0.0217 & -0.052 & 0.0639 & 5612741351.4886 & 17939637650.5916 & 133938.9325 \tabularnewline
71 & 0.0302 & -0.0895 & 0.065 & 8661153630.0696 & 17536225301.8732 & 132424.4135 \tabularnewline
72 & 0.0345 & -0.0555 & 0.0646 & 2553743089.2896 & 16911955209.6822 & 130045.9734 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=152400&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]49[/C][C]0.0461[/C][C]0.012[/C][C]0[/C][C]55274892.9274[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]50[/C][C]0.0326[/C][C]0.0833[/C][C]0.0477[/C][C]5382312970.8897[/C][C]2718793931.9086[/C][C]52142.0553[/C][/ROW]
[ROW][C]51[/C][C]0.0266[/C][C]0.0648[/C][C]0.0534[/C][C]4993362427.4834[/C][C]3476983430.4335[/C][C]58965.9515[/C][/ROW]
[ROW][C]52[/C][C]0.0188[/C][C]-0.0927[/C][C]0.0632[/C][C]20474406807.0956[/C][C]7726339274.599[/C][C]87899.5977[/C][/ROW]
[ROW][C]53[/C][C]0.0163[/C][C]-0.0662[/C][C]0.0638[/C][C]13883242793.3136[/C][C]8957719978.342[/C][C]94645.2322[/C][/ROW]
[ROW][C]54[/C][C]0.0192[/C][C]-0.0147[/C][C]0.0556[/C][C]499031799.2436[/C][C]7547938615.1589[/C][C]86878.8732[/C][/ROW]
[ROW][C]55[/C][C]0.0089[/C][C]-0.1045[/C][C]0.0626[/C][C]116092056077.317[/C][C]23054241109.7529[/C][C]151836.2312[/C][/ROW]
[ROW][C]56[/C][C]0.0119[/C][C]0.1364[/C][C]0.0718[/C][C]111050345642.989[/C][C]34053754176.4073[/C][C]184536.5931[/C][/ROW]
[ROW][C]57[/C][C]0.0233[/C][C]0.1221[/C][C]0.0774[/C][C]23433420442.1199[/C][C]32873717094.8199[/C][C]181311.1058[/C][/ROW]
[ROW][C]58[/C][C]0.0226[/C][C]0.0563[/C][C]0.0753[/C][C]5340979880.6876[/C][C]30120443373.4066[/C][C]173552.4226[/C][/ROW]
[ROW][C]59[/C][C]0.0326[/C][C]0.0733[/C][C]0.0751[/C][C]4339009110.089[/C][C]27776676622.1959[/C][C]166663.3632[/C][/ROW]
[ROW][C]60[/C][C]0.0374[/C][C]0.0919[/C][C]0.0765[/C][C]5129532136.0587[/C][C]25889414581.6845[/C][C]160901.8787[/C][/ROW]
[ROW][C]61[/C][C]0.0461[/C][C]0.0228[/C][C]0.0724[/C][C]232587082.7298[/C][C]23915812466.3803[/C][C]154647.3811[/C][/ROW]
[ROW][C]62[/C][C]0.0344[/C][C]-0.0503[/C][C]0.0708[/C][C]2011920177.5027[/C][C]22351248731.4604[/C][C]149503.3402[/C][/ROW]
[ROW][C]63[/C][C]0.0263[/C][C]-0.0832[/C][C]0.0716[/C][C]9490856957.1253[/C][C]21493889279.8381[/C][C]146607.9441[/C][/ROW]
[ROW][C]64[/C][C]0.0189[/C][C]-0.0733[/C][C]0.0718[/C][C]14355941256.144[/C][C]21047767528.3572[/C][C]145078.4875[/C][/ROW]
[ROW][C]65[/C][C]0.0204[/C][C]-0.0056[/C][C]0.0679[/C][C]70568233.6262[/C][C]19813814628.6672[/C][C]140761.5524[/C][/ROW]
[ROW][C]66[/C][C]0.0193[/C][C]-0.0607[/C][C]0.0675[/C][C]9496993385.9679[/C][C]19240657892.9617[/C][C]138710.6986[/C][/ROW]
[ROW][C]67[/C][C]0.0104[/C][C]-0.0431[/C][C]0.0662[/C][C]16630307087.4439[/C][C]19103271008.4607[/C][C]138214.5832[/C][/ROW]
[ROW][C]68[/C][C]0.0118[/C][C]0.0575[/C][C]0.0657[/C][C]22956549497.9792[/C][C]19295934932.9366[/C][C]138909.8086[/C][/ROW]
[ROW][C]69[/C][C]0.0215[/C][C]-0.0387[/C][C]0.0645[/C][C]3140588302.7932[/C][C]18526632712.4536[/C][C]136112.5737[/C][/ROW]
[ROW][C]70[/C][C]0.0217[/C][C]-0.052[/C][C]0.0639[/C][C]5612741351.4886[/C][C]17939637650.5916[/C][C]133938.9325[/C][/ROW]
[ROW][C]71[/C][C]0.0302[/C][C]-0.0895[/C][C]0.065[/C][C]8661153630.0696[/C][C]17536225301.8732[/C][C]132424.4135[/C][/ROW]
[ROW][C]72[/C][C]0.0345[/C][C]-0.0555[/C][C]0.0646[/C][C]2553743089.2896[/C][C]16911955209.6822[/C][C]130045.9734[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=152400&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=152400&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
490.04610.012055274892.927400
500.03260.08330.04775382312970.88972718793931.908652142.0553
510.02660.06480.05344993362427.48343476983430.433558965.9515
520.0188-0.09270.063220474406807.09567726339274.59987899.5977
530.0163-0.06620.063813883242793.31368957719978.34294645.2322
540.0192-0.01470.0556499031799.24367547938615.158986878.8732
550.0089-0.10450.0626116092056077.31723054241109.7529151836.2312
560.01190.13640.0718111050345642.98934053754176.4073184536.5931
570.02330.12210.077423433420442.119932873717094.8199181311.1058
580.02260.05630.07535340979880.687630120443373.4066173552.4226
590.03260.07330.07514339009110.08927776676622.1959166663.3632
600.03740.09190.07655129532136.058725889414581.6845160901.8787
610.04610.02280.0724232587082.729823915812466.3803154647.3811
620.0344-0.05030.07082011920177.502722351248731.4604149503.3402
630.0263-0.08320.07169490856957.125321493889279.8381146607.9441
640.0189-0.07330.071814355941256.14421047767528.3572145078.4875
650.0204-0.00560.067970568233.626219813814628.6672140761.5524
660.0193-0.06070.06759496993385.967919240657892.9617138710.6986
670.0104-0.04310.066216630307087.443919103271008.4607138214.5832
680.01180.05750.065722956549497.979219295934932.9366138909.8086
690.0215-0.03870.06453140588302.793218526632712.4536136112.5737
700.0217-0.0520.06395612741351.488617939637650.5916133938.9325
710.0302-0.08950.0658661153630.069617536225301.8732132424.4135
720.0345-0.05550.06462553743089.289616911955209.6822130045.9734



Parameters (Session):
par1 = FALSE ; par2 = 1 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = 3 ; par7 = 1 ; par8 = 2 ; par9 = 1 ;
Parameters (R input):
par1 = 24 ; par2 = 1 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = 3 ; par7 = 2 ; par8 = 2 ; par9 = 1 ; par10 = FALSE ;
R code (references can be found in the software module):
par1 <- as.numeric(par1) #cut off periods
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
par7 <- as.numeric(par7) #q
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')