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Description of Statistical Computation

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, 31 Dec 2009 08:08:41 -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/31/t12622721838al3drnwu09gemq.htm/, Retrieved Thu, 02 May 2024 05:44:05 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=71474, Retrieved Thu, 02 May 2024 05:44:05 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact143

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Standard Deviation-Mean Plot] [deel1 st dev mean...] [2009-12-16 19:13:20] [95cead3ebb75668735f848316249436a]
- RMP   [(Partial) Autocorrelation Function] [deel1 acf D=d=0] [2009-12-16 19:17:58] [95cead3ebb75668735f848316249436a]
-         [(Partial) Autocorrelation Function] [deel1 acf D=d=1] [2009-12-16 19:21:27] [95cead3ebb75668735f848316249436a]
- RM        [Variance Reduction Matrix] [deel1 vrm] [2009-12-16 19:23:09] [95cead3ebb75668735f848316249436a]
- RM          [Spectral Analysis] [deel1 spectrum D=d=1] [2009-12-16 19:31:03] [95cead3ebb75668735f848316249436a]
- RMP           [ARIMA Forecasting] [deel1 arima forca...] [2009-12-18 14:46:40] [95cead3ebb75668735f848316249436a]
-   PD            [ARIMA Forecasting] [arima forecasting...] [2009-12-30 19:35:17] [acdebb2ecda2ddb208f4e14f4a68b9e7]
-   P                 [ARIMA Forecasting] [forecasting (verk...] [2009-12-31 15:08:41] [b243db81ea3e1f02fb3382887fb0f701] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
2072.65
2020.13
2032.76
2050.31
2128.98
2122.14
2122.89
2091.95
2002.97
1923.21
1834.44
1819.15
1792.00
1822.40
1900.70
1903.00
1958.80
1820.50
1719.80
1661.10
1664.40
1703.40
1774.90
1795.00
1816.30
1867.40
1900.00
1961.10
2065.70
2073.50
2080.80
2118.00
2099.00
2085.20
1937.70
1749.50
1750.30
1675.60
1697.50
1699.80
1655.90
1636.00
1614.20
1602.30
1548.70
1556.10
1526.90
1509.20
1566.30
1596.00
1654.50
1664.20
1687.70
1691.00
1664.60
1697.50
1685.10
1643.00
1559.60
1560.20
1590.16
1604.93
1661.80
1670.73
1692.40
1688.17
1658.04
1613.46
1595.11
1558.83
1526.65
1475.19

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=71474&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]2 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=71474&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=71474&T=0

As an alternative you can also use a QR Code:  
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 time2 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[48])
361749.5-------
371750.3-------
381675.6-------
391697.5-------
401699.8-------
411655.9-------
421636-------
431614.2-------
441602.3-------
451548.7-------
461556.1-------
471526.9-------
481509.2-------
491566.31514.10741449.55881587.05410.08040.552500.5525
5015961510.60511404.54071641.49850.10050.20210.00670.5084
511654.51533.70731388.76361728.38420.1120.26530.04960.5974
521664.21545.50641369.18751800.52170.18080.20110.11780.6099
531687.71566.57991359.86661888.16490.23020.27590.29310.6367
5416911542.16271322.95271898.60480.20660.21180.30290.5719
551664.61521.38051292.0461909.09740.23450.19560.31950.5245
561697.51508.60061268.85851929.86020.18970.2340.33140.4989
571685.11486.03191241.5761927.46270.18840.17390.39040.459
5816431483.71381228.28151963.19010.25750.20520.38370.4585
591559.61460.92761203.95791952.79720.34710.23410.39630.4237
601560.21432.57921177.66561925.83920.3060.30690.38040.3804
611590.161431.37141165.80411966.99230.28060.31870.31070.3879
621604.931426.00051152.15191999.16940.27030.28730.28050.388
631661.81444.66731152.15242096.54430.25690.3150.26410.4231
641670.731454.22171147.31552176.76020.27850.28670.28450.4407
651692.41471.85391146.92212289.48460.29850.31680.30240.4643
661688.171451.08721127.40082279.14020.28730.28390.28510.4453
671658.041433.3851110.19912274.82550.30040.27640.29510.4299
681613.461422.4761097.0452290.99720.33320.29750.26740.4224
691595.111403.17561080.30572273.59640.33280.31790.26280.4057
701558.831401.18671072.58242318.23480.36810.33930.30260.4087
711526.651381.62421056.75712292.7180.37750.35150.35090.3919
721475.191357.18311039.07182244.04370.39710.3540.32680.3684

\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 & 1749.5 & - & - & - & - & - & - & - \tabularnewline
37 & 1750.3 & - & - & - & - & - & - & - \tabularnewline
38 & 1675.6 & - & - & - & - & - & - & - \tabularnewline
39 & 1697.5 & - & - & - & - & - & - & - \tabularnewline
40 & 1699.8 & - & - & - & - & - & - & - \tabularnewline
41 & 1655.9 & - & - & - & - & - & - & - \tabularnewline
42 & 1636 & - & - & - & - & - & - & - \tabularnewline
43 & 1614.2 & - & - & - & - & - & - & - \tabularnewline
44 & 1602.3 & - & - & - & - & - & - & - \tabularnewline
45 & 1548.7 & - & - & - & - & - & - & - \tabularnewline
46 & 1556.1 & - & - & - & - & - & - & - \tabularnewline
47 & 1526.9 & - & - & - & - & - & - & - \tabularnewline
48 & 1509.2 & - & - & - & - & - & - & - \tabularnewline
49 & 1566.3 & 1514.1074 & 1449.5588 & 1587.0541 & 0.0804 & 0.5525 & 0 & 0.5525 \tabularnewline
50 & 1596 & 1510.6051 & 1404.5407 & 1641.4985 & 0.1005 & 0.2021 & 0.0067 & 0.5084 \tabularnewline
51 & 1654.5 & 1533.7073 & 1388.7636 & 1728.3842 & 0.112 & 0.2653 & 0.0496 & 0.5974 \tabularnewline
52 & 1664.2 & 1545.5064 & 1369.1875 & 1800.5217 & 0.1808 & 0.2011 & 0.1178 & 0.6099 \tabularnewline
53 & 1687.7 & 1566.5799 & 1359.8666 & 1888.1649 & 0.2302 & 0.2759 & 0.2931 & 0.6367 \tabularnewline
54 & 1691 & 1542.1627 & 1322.9527 & 1898.6048 & 0.2066 & 0.2118 & 0.3029 & 0.5719 \tabularnewline
55 & 1664.6 & 1521.3805 & 1292.046 & 1909.0974 & 0.2345 & 0.1956 & 0.3195 & 0.5245 \tabularnewline
56 & 1697.5 & 1508.6006 & 1268.8585 & 1929.8602 & 0.1897 & 0.234 & 0.3314 & 0.4989 \tabularnewline
57 & 1685.1 & 1486.0319 & 1241.576 & 1927.4627 & 0.1884 & 0.1739 & 0.3904 & 0.459 \tabularnewline
58 & 1643 & 1483.7138 & 1228.2815 & 1963.1901 & 0.2575 & 0.2052 & 0.3837 & 0.4585 \tabularnewline
59 & 1559.6 & 1460.9276 & 1203.9579 & 1952.7972 & 0.3471 & 0.2341 & 0.3963 & 0.4237 \tabularnewline
60 & 1560.2 & 1432.5792 & 1177.6656 & 1925.8392 & 0.306 & 0.3069 & 0.3804 & 0.3804 \tabularnewline
61 & 1590.16 & 1431.3714 & 1165.8041 & 1966.9923 & 0.2806 & 0.3187 & 0.3107 & 0.3879 \tabularnewline
62 & 1604.93 & 1426.0005 & 1152.1519 & 1999.1694 & 0.2703 & 0.2873 & 0.2805 & 0.388 \tabularnewline
63 & 1661.8 & 1444.6673 & 1152.1524 & 2096.5443 & 0.2569 & 0.315 & 0.2641 & 0.4231 \tabularnewline
64 & 1670.73 & 1454.2217 & 1147.3155 & 2176.7602 & 0.2785 & 0.2867 & 0.2845 & 0.4407 \tabularnewline
65 & 1692.4 & 1471.8539 & 1146.9221 & 2289.4846 & 0.2985 & 0.3168 & 0.3024 & 0.4643 \tabularnewline
66 & 1688.17 & 1451.0872 & 1127.4008 & 2279.1402 & 0.2873 & 0.2839 & 0.2851 & 0.4453 \tabularnewline
67 & 1658.04 & 1433.385 & 1110.1991 & 2274.8255 & 0.3004 & 0.2764 & 0.2951 & 0.4299 \tabularnewline
68 & 1613.46 & 1422.476 & 1097.045 & 2290.9972 & 0.3332 & 0.2975 & 0.2674 & 0.4224 \tabularnewline
69 & 1595.11 & 1403.1756 & 1080.3057 & 2273.5964 & 0.3328 & 0.3179 & 0.2628 & 0.4057 \tabularnewline
70 & 1558.83 & 1401.1867 & 1072.5824 & 2318.2348 & 0.3681 & 0.3393 & 0.3026 & 0.4087 \tabularnewline
71 & 1526.65 & 1381.6242 & 1056.7571 & 2292.718 & 0.3775 & 0.3515 & 0.3509 & 0.3919 \tabularnewline
72 & 1475.19 & 1357.1831 & 1039.0718 & 2244.0437 & 0.3971 & 0.354 & 0.3268 & 0.3684 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=71474&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]1749.5[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]37[/C][C]1750.3[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]38[/C][C]1675.6[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]39[/C][C]1697.5[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]40[/C][C]1699.8[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]41[/C][C]1655.9[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]42[/C][C]1636[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]43[/C][C]1614.2[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]44[/C][C]1602.3[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]45[/C][C]1548.7[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]46[/C][C]1556.1[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]47[/C][C]1526.9[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]48[/C][C]1509.2[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]49[/C][C]1566.3[/C][C]1514.1074[/C][C]1449.5588[/C][C]1587.0541[/C][C]0.0804[/C][C]0.5525[/C][C]0[/C][C]0.5525[/C][/ROW]
[ROW][C]50[/C][C]1596[/C][C]1510.6051[/C][C]1404.5407[/C][C]1641.4985[/C][C]0.1005[/C][C]0.2021[/C][C]0.0067[/C][C]0.5084[/C][/ROW]
[ROW][C]51[/C][C]1654.5[/C][C]1533.7073[/C][C]1388.7636[/C][C]1728.3842[/C][C]0.112[/C][C]0.2653[/C][C]0.0496[/C][C]0.5974[/C][/ROW]
[ROW][C]52[/C][C]1664.2[/C][C]1545.5064[/C][C]1369.1875[/C][C]1800.5217[/C][C]0.1808[/C][C]0.2011[/C][C]0.1178[/C][C]0.6099[/C][/ROW]
[ROW][C]53[/C][C]1687.7[/C][C]1566.5799[/C][C]1359.8666[/C][C]1888.1649[/C][C]0.2302[/C][C]0.2759[/C][C]0.2931[/C][C]0.6367[/C][/ROW]
[ROW][C]54[/C][C]1691[/C][C]1542.1627[/C][C]1322.9527[/C][C]1898.6048[/C][C]0.2066[/C][C]0.2118[/C][C]0.3029[/C][C]0.5719[/C][/ROW]
[ROW][C]55[/C][C]1664.6[/C][C]1521.3805[/C][C]1292.046[/C][C]1909.0974[/C][C]0.2345[/C][C]0.1956[/C][C]0.3195[/C][C]0.5245[/C][/ROW]
[ROW][C]56[/C][C]1697.5[/C][C]1508.6006[/C][C]1268.8585[/C][C]1929.8602[/C][C]0.1897[/C][C]0.234[/C][C]0.3314[/C][C]0.4989[/C][/ROW]
[ROW][C]57[/C][C]1685.1[/C][C]1486.0319[/C][C]1241.576[/C][C]1927.4627[/C][C]0.1884[/C][C]0.1739[/C][C]0.3904[/C][C]0.459[/C][/ROW]
[ROW][C]58[/C][C]1643[/C][C]1483.7138[/C][C]1228.2815[/C][C]1963.1901[/C][C]0.2575[/C][C]0.2052[/C][C]0.3837[/C][C]0.4585[/C][/ROW]
[ROW][C]59[/C][C]1559.6[/C][C]1460.9276[/C][C]1203.9579[/C][C]1952.7972[/C][C]0.3471[/C][C]0.2341[/C][C]0.3963[/C][C]0.4237[/C][/ROW]
[ROW][C]60[/C][C]1560.2[/C][C]1432.5792[/C][C]1177.6656[/C][C]1925.8392[/C][C]0.306[/C][C]0.3069[/C][C]0.3804[/C][C]0.3804[/C][/ROW]
[ROW][C]61[/C][C]1590.16[/C][C]1431.3714[/C][C]1165.8041[/C][C]1966.9923[/C][C]0.2806[/C][C]0.3187[/C][C]0.3107[/C][C]0.3879[/C][/ROW]
[ROW][C]62[/C][C]1604.93[/C][C]1426.0005[/C][C]1152.1519[/C][C]1999.1694[/C][C]0.2703[/C][C]0.2873[/C][C]0.2805[/C][C]0.388[/C][/ROW]
[ROW][C]63[/C][C]1661.8[/C][C]1444.6673[/C][C]1152.1524[/C][C]2096.5443[/C][C]0.2569[/C][C]0.315[/C][C]0.2641[/C][C]0.4231[/C][/ROW]
[ROW][C]64[/C][C]1670.73[/C][C]1454.2217[/C][C]1147.3155[/C][C]2176.7602[/C][C]0.2785[/C][C]0.2867[/C][C]0.2845[/C][C]0.4407[/C][/ROW]
[ROW][C]65[/C][C]1692.4[/C][C]1471.8539[/C][C]1146.9221[/C][C]2289.4846[/C][C]0.2985[/C][C]0.3168[/C][C]0.3024[/C][C]0.4643[/C][/ROW]
[ROW][C]66[/C][C]1688.17[/C][C]1451.0872[/C][C]1127.4008[/C][C]2279.1402[/C][C]0.2873[/C][C]0.2839[/C][C]0.2851[/C][C]0.4453[/C][/ROW]
[ROW][C]67[/C][C]1658.04[/C][C]1433.385[/C][C]1110.1991[/C][C]2274.8255[/C][C]0.3004[/C][C]0.2764[/C][C]0.2951[/C][C]0.4299[/C][/ROW]
[ROW][C]68[/C][C]1613.46[/C][C]1422.476[/C][C]1097.045[/C][C]2290.9972[/C][C]0.3332[/C][C]0.2975[/C][C]0.2674[/C][C]0.4224[/C][/ROW]
[ROW][C]69[/C][C]1595.11[/C][C]1403.1756[/C][C]1080.3057[/C][C]2273.5964[/C][C]0.3328[/C][C]0.3179[/C][C]0.2628[/C][C]0.4057[/C][/ROW]
[ROW][C]70[/C][C]1558.83[/C][C]1401.1867[/C][C]1072.5824[/C][C]2318.2348[/C][C]0.3681[/C][C]0.3393[/C][C]0.3026[/C][C]0.4087[/C][/ROW]
[ROW][C]71[/C][C]1526.65[/C][C]1381.6242[/C][C]1056.7571[/C][C]2292.718[/C][C]0.3775[/C][C]0.3515[/C][C]0.3509[/C][C]0.3919[/C][/ROW]
[ROW][C]72[/C][C]1475.19[/C][C]1357.1831[/C][C]1039.0718[/C][C]2244.0437[/C][C]0.3971[/C][C]0.354[/C][C]0.3268[/C][C]0.3684[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=71474&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=71474&T=1

As an alternative you can also use a QR Code:  
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])
361749.5-------
371750.3-------
381675.6-------
391697.5-------
401699.8-------
411655.9-------
421636-------
431614.2-------
441602.3-------
451548.7-------
461556.1-------
471526.9-------
481509.2-------
491566.31514.10741449.55881587.05410.08040.552500.5525
5015961510.60511404.54071641.49850.10050.20210.00670.5084
511654.51533.70731388.76361728.38420.1120.26530.04960.5974
521664.21545.50641369.18751800.52170.18080.20110.11780.6099
531687.71566.57991359.86661888.16490.23020.27590.29310.6367
5416911542.16271322.95271898.60480.20660.21180.30290.5719
551664.61521.38051292.0461909.09740.23450.19560.31950.5245
561697.51508.60061268.85851929.86020.18970.2340.33140.4989
571685.11486.03191241.5761927.46270.18840.17390.39040.459
5816431483.71381228.28151963.19010.25750.20520.38370.4585
591559.61460.92761203.95791952.79720.34710.23410.39630.4237
601560.21432.57921177.66561925.83920.3060.30690.38040.3804
611590.161431.37141165.80411966.99230.28060.31870.31070.3879
621604.931426.00051152.15191999.16940.27030.28730.28050.388
631661.81444.66731152.15242096.54430.25690.3150.26410.4231
641670.731454.22171147.31552176.76020.27850.28670.28450.4407
651692.41471.85391146.92212289.48460.29850.31680.30240.4643
661688.171451.08721127.40082279.14020.28730.28390.28510.4453
671658.041433.3851110.19912274.82550.30040.27640.29510.4299
681613.461422.4761097.0452290.99720.33320.29750.26740.4224
691595.111403.17561080.30572273.59640.33280.31790.26280.4057
701558.831401.18671072.58242318.23480.36810.33930.30260.4087
711526.651381.62421056.75712292.7180.37750.35150.35090.3919
721475.191357.18311039.07182244.04370.39710.3540.32680.3684






Univariate ARIMA Extrapolation Forecast Performance
time% S.E.PEMAPESq.EMSERMSE
490.02460.034502724.070400
500.04420.05650.04557292.29565008.18370.7685
510.06480.07880.056614590.87228202.412890.5672
520.08420.07680.061614088.16899673.851898.3557
530.10470.07730.064814670.083810673.0982103.3107
540.11790.09650.070122152.534312586.3375112.1888
550.130.09410.073520511.831713718.551117.1262
560.14250.12520.0835682.965616464.1028128.3125
570.15160.1340.08639628.107319037.8811137.9778
580.16490.10740.088125372.099219671.3029140.2544
590.17180.06750.08629736.237818768.1152136.9968
600.17570.08910.086516287.07418561.3618136.2401
610.19090.11090.088425213.82419073.0896138.1054
620.20510.12550.09132015.768219997.5667141.4128
630.23020.15030.09547146.606621807.5027147.6736
640.25350.14890.098346875.834523374.2734152.8865
650.28340.14980.101448640.572424860.5263157.6722
660.29110.16340.104856208.241826602.066163.1014
670.29950.15670.107550469.846727858.265166.908
680.31150.13430.108936474.901228289.0968168.1936
690.31650.13680.110236838.812828696.2261169.3996
700.33390.11250.110324851.396128521.4611168.883
710.33640.1050.110121032.488128195.8536167.9162
720.33340.08690.109113925.629227601.2609166.1363

\begin{tabular}{lllllllll}
\hline
Univariate ARIMA Extrapolation Forecast Performance \tabularnewline
time & % S.E. & PE & MAPE & Sq.E & MSE & RMSE \tabularnewline
49 & 0.0246 & 0.0345 & 0 & 2724.0704 & 0 & 0 \tabularnewline
50 & 0.0442 & 0.0565 & 0.0455 & 7292.2956 & 5008.183 & 70.7685 \tabularnewline
51 & 0.0648 & 0.0788 & 0.0566 & 14590.8722 & 8202.4128 & 90.5672 \tabularnewline
52 & 0.0842 & 0.0768 & 0.0616 & 14088.1689 & 9673.8518 & 98.3557 \tabularnewline
53 & 0.1047 & 0.0773 & 0.0648 & 14670.0838 & 10673.0982 & 103.3107 \tabularnewline
54 & 0.1179 & 0.0965 & 0.0701 & 22152.5343 & 12586.3375 & 112.1888 \tabularnewline
55 & 0.13 & 0.0941 & 0.0735 & 20511.8317 & 13718.551 & 117.1262 \tabularnewline
56 & 0.1425 & 0.1252 & 0.08 & 35682.9656 & 16464.1028 & 128.3125 \tabularnewline
57 & 0.1516 & 0.134 & 0.086 & 39628.1073 & 19037.8811 & 137.9778 \tabularnewline
58 & 0.1649 & 0.1074 & 0.0881 & 25372.0992 & 19671.3029 & 140.2544 \tabularnewline
59 & 0.1718 & 0.0675 & 0.0862 & 9736.2378 & 18768.1152 & 136.9968 \tabularnewline
60 & 0.1757 & 0.0891 & 0.0865 & 16287.074 & 18561.3618 & 136.2401 \tabularnewline
61 & 0.1909 & 0.1109 & 0.0884 & 25213.824 & 19073.0896 & 138.1054 \tabularnewline
62 & 0.2051 & 0.1255 & 0.091 & 32015.7682 & 19997.5667 & 141.4128 \tabularnewline
63 & 0.2302 & 0.1503 & 0.095 & 47146.6066 & 21807.5027 & 147.6736 \tabularnewline
64 & 0.2535 & 0.1489 & 0.0983 & 46875.8345 & 23374.2734 & 152.8865 \tabularnewline
65 & 0.2834 & 0.1498 & 0.1014 & 48640.5724 & 24860.5263 & 157.6722 \tabularnewline
66 & 0.2911 & 0.1634 & 0.1048 & 56208.2418 & 26602.066 & 163.1014 \tabularnewline
67 & 0.2995 & 0.1567 & 0.1075 & 50469.8467 & 27858.265 & 166.908 \tabularnewline
68 & 0.3115 & 0.1343 & 0.1089 & 36474.9012 & 28289.0968 & 168.1936 \tabularnewline
69 & 0.3165 & 0.1368 & 0.1102 & 36838.8128 & 28696.2261 & 169.3996 \tabularnewline
70 & 0.3339 & 0.1125 & 0.1103 & 24851.3961 & 28521.4611 & 168.883 \tabularnewline
71 & 0.3364 & 0.105 & 0.1101 & 21032.4881 & 28195.8536 & 167.9162 \tabularnewline
72 & 0.3334 & 0.0869 & 0.1091 & 13925.6292 & 27601.2609 & 166.1363 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=71474&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]0.0246[/C][C]0.0345[/C][C]0[/C][C]2724.0704[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]50[/C][C]0.0442[/C][C]0.0565[/C][C]0.0455[/C][C]7292.2956[/C][C]5008.183[/C][C]70.7685[/C][/ROW]
[ROW][C]51[/C][C]0.0648[/C][C]0.0788[/C][C]0.0566[/C][C]14590.8722[/C][C]8202.4128[/C][C]90.5672[/C][/ROW]
[ROW][C]52[/C][C]0.0842[/C][C]0.0768[/C][C]0.0616[/C][C]14088.1689[/C][C]9673.8518[/C][C]98.3557[/C][/ROW]
[ROW][C]53[/C][C]0.1047[/C][C]0.0773[/C][C]0.0648[/C][C]14670.0838[/C][C]10673.0982[/C][C]103.3107[/C][/ROW]
[ROW][C]54[/C][C]0.1179[/C][C]0.0965[/C][C]0.0701[/C][C]22152.5343[/C][C]12586.3375[/C][C]112.1888[/C][/ROW]
[ROW][C]55[/C][C]0.13[/C][C]0.0941[/C][C]0.0735[/C][C]20511.8317[/C][C]13718.551[/C][C]117.1262[/C][/ROW]
[ROW][C]56[/C][C]0.1425[/C][C]0.1252[/C][C]0.08[/C][C]35682.9656[/C][C]16464.1028[/C][C]128.3125[/C][/ROW]
[ROW][C]57[/C][C]0.1516[/C][C]0.134[/C][C]0.086[/C][C]39628.1073[/C][C]19037.8811[/C][C]137.9778[/C][/ROW]
[ROW][C]58[/C][C]0.1649[/C][C]0.1074[/C][C]0.0881[/C][C]25372.0992[/C][C]19671.3029[/C][C]140.2544[/C][/ROW]
[ROW][C]59[/C][C]0.1718[/C][C]0.0675[/C][C]0.0862[/C][C]9736.2378[/C][C]18768.1152[/C][C]136.9968[/C][/ROW]
[ROW][C]60[/C][C]0.1757[/C][C]0.0891[/C][C]0.0865[/C][C]16287.074[/C][C]18561.3618[/C][C]136.2401[/C][/ROW]
[ROW][C]61[/C][C]0.1909[/C][C]0.1109[/C][C]0.0884[/C][C]25213.824[/C][C]19073.0896[/C][C]138.1054[/C][/ROW]
[ROW][C]62[/C][C]0.2051[/C][C]0.1255[/C][C]0.091[/C][C]32015.7682[/C][C]19997.5667[/C][C]141.4128[/C][/ROW]
[ROW][C]63[/C][C]0.2302[/C][C]0.1503[/C][C]0.095[/C][C]47146.6066[/C][C]21807.5027[/C][C]147.6736[/C][/ROW]
[ROW][C]64[/C][C]0.2535[/C][C]0.1489[/C][C]0.0983[/C][C]46875.8345[/C][C]23374.2734[/C][C]152.8865[/C][/ROW]
[ROW][C]65[/C][C]0.2834[/C][C]0.1498[/C][C]0.1014[/C][C]48640.5724[/C][C]24860.5263[/C][C]157.6722[/C][/ROW]
[ROW][C]66[/C][C]0.2911[/C][C]0.1634[/C][C]0.1048[/C][C]56208.2418[/C][C]26602.066[/C][C]163.1014[/C][/ROW]
[ROW][C]67[/C][C]0.2995[/C][C]0.1567[/C][C]0.1075[/C][C]50469.8467[/C][C]27858.265[/C][C]166.908[/C][/ROW]
[ROW][C]68[/C][C]0.3115[/C][C]0.1343[/C][C]0.1089[/C][C]36474.9012[/C][C]28289.0968[/C][C]168.1936[/C][/ROW]
[ROW][C]69[/C][C]0.3165[/C][C]0.1368[/C][C]0.1102[/C][C]36838.8128[/C][C]28696.2261[/C][C]169.3996[/C][/ROW]
[ROW][C]70[/C][C]0.3339[/C][C]0.1125[/C][C]0.1103[/C][C]24851.3961[/C][C]28521.4611[/C][C]168.883[/C][/ROW]
[ROW][C]71[/C][C]0.3364[/C][C]0.105[/C][C]0.1101[/C][C]21032.4881[/C][C]28195.8536[/C][C]167.9162[/C][/ROW]
[ROW][C]72[/C][C]0.3334[/C][C]0.0869[/C][C]0.1091[/C][C]13925.6292[/C][C]27601.2609[/C][C]166.1363[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=71474&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=71474&T=2

As an alternative you can also use a QR Code:  
QR Code


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

Univariate ARIMA Extrapolation Forecast Performance
time% S.E.PEMAPESq.EMSERMSE
490.02460.034502724.070400
500.04420.05650.04557292.29565008.18370.7685
510.06480.07880.056614590.87228202.412890.5672
520.08420.07680.061614088.16899673.851898.3557
530.10470.07730.064814670.083810673.0982103.3107
540.11790.09650.070122152.534312586.3375112.1888
550.130.09410.073520511.831713718.551117.1262
560.14250.12520.0835682.965616464.1028128.3125
570.15160.1340.08639628.107319037.8811137.9778
580.16490.10740.088125372.099219671.3029140.2544
590.17180.06750.08629736.237818768.1152136.9968
600.17570.08910.086516287.07418561.3618136.2401
610.19090.11090.088425213.82419073.0896138.1054
620.20510.12550.09132015.768219997.5667141.4128
630.23020.15030.09547146.606621807.5027147.6736
640.25350.14890.098346875.834523374.2734152.8865
650.28340.14980.101448640.572424860.5263157.6722
660.29110.16340.104856208.241826602.066163.1014
670.29950.15670.107550469.846727858.265166.908
680.31150.13430.108936474.901228289.0968168.1936
690.31650.13680.110236838.812828696.2261169.3996
700.33390.11250.110324851.396128521.4611168.883
710.33640.1050.110121032.488128195.8536167.9162
720.33340.08690.109113925.629227601.2609166.1363


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 24 ; par2 = -1.7 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = 1 ; par7 = 0 ; par8 = 0 ; par9 = 1 ; par10 = FALSE ;
Parameters (R input):
par1 = 24 ; par2 = -1.7 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = 1 ; par7 = 0 ; par8 = 0 ; 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')