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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 computationWed, 30 Dec 2009 12:35:17 -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/30/t1262201781rogo5o8rghi7sea.htm/, Retrieved Mon, 06 May 2024 00:24:52 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=71359, Retrieved Mon, 06 May 2024 00:24:52 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact142

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] [b243db81ea3e1f02fb3382887fb0f701] [Current]
-   P                 [ARIMA Forecasting] [forecasting (verk...] [2009-12-31 15:08:41] [acdebb2ecda2ddb208f4e14f4a68b9e7]
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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 time1 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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=71359&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]1 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=71359&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=71359&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 time1 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-------
491566.31503.35781446.26411566.97590.02620.428600.4286
5015961498.81351403.08031614.50870.04980.12650.00140.4302
511654.51498.26111371.41891662.73260.03130.12210.00880.4481
521664.21497.78411345.68841707.44380.05990.07150.02950.4575
531687.71496.30021323.45361747.70710.06780.09530.10670.4599
5416911495.62321304.89621786.87290.09430.09810.17240.4636
551664.61494.92491288.61581824.34020.15640.12170.2390.4662
561697.51494.51981274.28521861.12410.13890.18160.28220.4687
571685.11492.79321260.49531894.57970.17410.1590.39250.4681
5816431493.04681249.08291931.19390.25120.19510.38890.4712
591559.61492.14251237.87071965.16330.38990.2660.44270.4718
601560.21491.66161227.6941999.78820.39570.39660.4730.473
611590.161491.44941217.95892036.47860.36130.40240.39390.4746
621604.931491.35571208.74512074.26570.35130.36990.36250.4761
631661.81491.31441200.04242112.77550.29540.360.30340.4775
641670.731491.29611191.8122151.89720.29720.30650.3040.4788
651692.41491.28811184.00912191.63420.28680.30780.29130.48
661688.171491.28451176.59152232.03970.30120.29730.29860.4811
671658.041491.2831169.52172273.18750.3380.31080.3320.4821
681613.461491.28231162.76682315.16110.38570.34580.31190.483
691595.111491.2821156.29852358.04880.40720.39120.33060.4838
701558.831491.28181150.0922401.94230.44220.41160.3720.4846
711526.651491.28181144.12572446.93670.47110.44490.44430.4853
721475.191491.28171138.38082493.13110.48740.47240.44640.486

\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 & 1503.3578 & 1446.2641 & 1566.9759 & 0.0262 & 0.4286 & 0 & 0.4286 \tabularnewline
50 & 1596 & 1498.8135 & 1403.0803 & 1614.5087 & 0.0498 & 0.1265 & 0.0014 & 0.4302 \tabularnewline
51 & 1654.5 & 1498.2611 & 1371.4189 & 1662.7326 & 0.0313 & 0.1221 & 0.0088 & 0.4481 \tabularnewline
52 & 1664.2 & 1497.7841 & 1345.6884 & 1707.4438 & 0.0599 & 0.0715 & 0.0295 & 0.4575 \tabularnewline
53 & 1687.7 & 1496.3002 & 1323.4536 & 1747.7071 & 0.0678 & 0.0953 & 0.1067 & 0.4599 \tabularnewline
54 & 1691 & 1495.6232 & 1304.8962 & 1786.8729 & 0.0943 & 0.0981 & 0.1724 & 0.4636 \tabularnewline
55 & 1664.6 & 1494.9249 & 1288.6158 & 1824.3402 & 0.1564 & 0.1217 & 0.239 & 0.4662 \tabularnewline
56 & 1697.5 & 1494.5198 & 1274.2852 & 1861.1241 & 0.1389 & 0.1816 & 0.2822 & 0.4687 \tabularnewline
57 & 1685.1 & 1492.7932 & 1260.4953 & 1894.5797 & 0.1741 & 0.159 & 0.3925 & 0.4681 \tabularnewline
58 & 1643 & 1493.0468 & 1249.0829 & 1931.1939 & 0.2512 & 0.1951 & 0.3889 & 0.4712 \tabularnewline
59 & 1559.6 & 1492.1425 & 1237.8707 & 1965.1633 & 0.3899 & 0.266 & 0.4427 & 0.4718 \tabularnewline
60 & 1560.2 & 1491.6616 & 1227.694 & 1999.7882 & 0.3957 & 0.3966 & 0.473 & 0.473 \tabularnewline
61 & 1590.16 & 1491.4494 & 1217.9589 & 2036.4786 & 0.3613 & 0.4024 & 0.3939 & 0.4746 \tabularnewline
62 & 1604.93 & 1491.3557 & 1208.7451 & 2074.2657 & 0.3513 & 0.3699 & 0.3625 & 0.4761 \tabularnewline
63 & 1661.8 & 1491.3144 & 1200.0424 & 2112.7755 & 0.2954 & 0.36 & 0.3034 & 0.4775 \tabularnewline
64 & 1670.73 & 1491.2961 & 1191.812 & 2151.8972 & 0.2972 & 0.3065 & 0.304 & 0.4788 \tabularnewline
65 & 1692.4 & 1491.2881 & 1184.0091 & 2191.6342 & 0.2868 & 0.3078 & 0.2913 & 0.48 \tabularnewline
66 & 1688.17 & 1491.2845 & 1176.5915 & 2232.0397 & 0.3012 & 0.2973 & 0.2986 & 0.4811 \tabularnewline
67 & 1658.04 & 1491.283 & 1169.5217 & 2273.1875 & 0.338 & 0.3108 & 0.332 & 0.4821 \tabularnewline
68 & 1613.46 & 1491.2823 & 1162.7668 & 2315.1611 & 0.3857 & 0.3458 & 0.3119 & 0.483 \tabularnewline
69 & 1595.11 & 1491.282 & 1156.2985 & 2358.0488 & 0.4072 & 0.3912 & 0.3306 & 0.4838 \tabularnewline
70 & 1558.83 & 1491.2818 & 1150.092 & 2401.9423 & 0.4422 & 0.4116 & 0.372 & 0.4846 \tabularnewline
71 & 1526.65 & 1491.2818 & 1144.1257 & 2446.9367 & 0.4711 & 0.4449 & 0.4443 & 0.4853 \tabularnewline
72 & 1475.19 & 1491.2817 & 1138.3808 & 2493.1311 & 0.4874 & 0.4724 & 0.4464 & 0.486 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=71359&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]1503.3578[/C][C]1446.2641[/C][C]1566.9759[/C][C]0.0262[/C][C]0.4286[/C][C]0[/C][C]0.4286[/C][/ROW]
[ROW][C]50[/C][C]1596[/C][C]1498.8135[/C][C]1403.0803[/C][C]1614.5087[/C][C]0.0498[/C][C]0.1265[/C][C]0.0014[/C][C]0.4302[/C][/ROW]
[ROW][C]51[/C][C]1654.5[/C][C]1498.2611[/C][C]1371.4189[/C][C]1662.7326[/C][C]0.0313[/C][C]0.1221[/C][C]0.0088[/C][C]0.4481[/C][/ROW]
[ROW][C]52[/C][C]1664.2[/C][C]1497.7841[/C][C]1345.6884[/C][C]1707.4438[/C][C]0.0599[/C][C]0.0715[/C][C]0.0295[/C][C]0.4575[/C][/ROW]
[ROW][C]53[/C][C]1687.7[/C][C]1496.3002[/C][C]1323.4536[/C][C]1747.7071[/C][C]0.0678[/C][C]0.0953[/C][C]0.1067[/C][C]0.4599[/C][/ROW]
[ROW][C]54[/C][C]1691[/C][C]1495.6232[/C][C]1304.8962[/C][C]1786.8729[/C][C]0.0943[/C][C]0.0981[/C][C]0.1724[/C][C]0.4636[/C][/ROW]
[ROW][C]55[/C][C]1664.6[/C][C]1494.9249[/C][C]1288.6158[/C][C]1824.3402[/C][C]0.1564[/C][C]0.1217[/C][C]0.239[/C][C]0.4662[/C][/ROW]
[ROW][C]56[/C][C]1697.5[/C][C]1494.5198[/C][C]1274.2852[/C][C]1861.1241[/C][C]0.1389[/C][C]0.1816[/C][C]0.2822[/C][C]0.4687[/C][/ROW]
[ROW][C]57[/C][C]1685.1[/C][C]1492.7932[/C][C]1260.4953[/C][C]1894.5797[/C][C]0.1741[/C][C]0.159[/C][C]0.3925[/C][C]0.4681[/C][/ROW]
[ROW][C]58[/C][C]1643[/C][C]1493.0468[/C][C]1249.0829[/C][C]1931.1939[/C][C]0.2512[/C][C]0.1951[/C][C]0.3889[/C][C]0.4712[/C][/ROW]
[ROW][C]59[/C][C]1559.6[/C][C]1492.1425[/C][C]1237.8707[/C][C]1965.1633[/C][C]0.3899[/C][C]0.266[/C][C]0.4427[/C][C]0.4718[/C][/ROW]
[ROW][C]60[/C][C]1560.2[/C][C]1491.6616[/C][C]1227.694[/C][C]1999.7882[/C][C]0.3957[/C][C]0.3966[/C][C]0.473[/C][C]0.473[/C][/ROW]
[ROW][C]61[/C][C]1590.16[/C][C]1491.4494[/C][C]1217.9589[/C][C]2036.4786[/C][C]0.3613[/C][C]0.4024[/C][C]0.3939[/C][C]0.4746[/C][/ROW]
[ROW][C]62[/C][C]1604.93[/C][C]1491.3557[/C][C]1208.7451[/C][C]2074.2657[/C][C]0.3513[/C][C]0.3699[/C][C]0.3625[/C][C]0.4761[/C][/ROW]
[ROW][C]63[/C][C]1661.8[/C][C]1491.3144[/C][C]1200.0424[/C][C]2112.7755[/C][C]0.2954[/C][C]0.36[/C][C]0.3034[/C][C]0.4775[/C][/ROW]
[ROW][C]64[/C][C]1670.73[/C][C]1491.2961[/C][C]1191.812[/C][C]2151.8972[/C][C]0.2972[/C][C]0.3065[/C][C]0.304[/C][C]0.4788[/C][/ROW]
[ROW][C]65[/C][C]1692.4[/C][C]1491.2881[/C][C]1184.0091[/C][C]2191.6342[/C][C]0.2868[/C][C]0.3078[/C][C]0.2913[/C][C]0.48[/C][/ROW]
[ROW][C]66[/C][C]1688.17[/C][C]1491.2845[/C][C]1176.5915[/C][C]2232.0397[/C][C]0.3012[/C][C]0.2973[/C][C]0.2986[/C][C]0.4811[/C][/ROW]
[ROW][C]67[/C][C]1658.04[/C][C]1491.283[/C][C]1169.5217[/C][C]2273.1875[/C][C]0.338[/C][C]0.3108[/C][C]0.332[/C][C]0.4821[/C][/ROW]
[ROW][C]68[/C][C]1613.46[/C][C]1491.2823[/C][C]1162.7668[/C][C]2315.1611[/C][C]0.3857[/C][C]0.3458[/C][C]0.3119[/C][C]0.483[/C][/ROW]
[ROW][C]69[/C][C]1595.11[/C][C]1491.282[/C][C]1156.2985[/C][C]2358.0488[/C][C]0.4072[/C][C]0.3912[/C][C]0.3306[/C][C]0.4838[/C][/ROW]
[ROW][C]70[/C][C]1558.83[/C][C]1491.2818[/C][C]1150.092[/C][C]2401.9423[/C][C]0.4422[/C][C]0.4116[/C][C]0.372[/C][C]0.4846[/C][/ROW]
[ROW][C]71[/C][C]1526.65[/C][C]1491.2818[/C][C]1144.1257[/C][C]2446.9367[/C][C]0.4711[/C][C]0.4449[/C][C]0.4443[/C][C]0.4853[/C][/ROW]
[ROW][C]72[/C][C]1475.19[/C][C]1491.2817[/C][C]1138.3808[/C][C]2493.1311[/C][C]0.4874[/C][C]0.4724[/C][C]0.4464[/C][C]0.486[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=71359&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=71359&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-------
491566.31503.35781446.26411566.97590.02620.428600.4286
5015961498.81351403.08031614.50870.04980.12650.00140.4302
511654.51498.26111371.41891662.73260.03130.12210.00880.4481
521664.21497.78411345.68841707.44380.05990.07150.02950.4575
531687.71496.30021323.45361747.70710.06780.09530.10670.4599
5416911495.62321304.89621786.87290.09430.09810.17240.4636
551664.61494.92491288.61581824.34020.15640.12170.2390.4662
561697.51494.51981274.28521861.12410.13890.18160.28220.4687
571685.11492.79321260.49531894.57970.17410.1590.39250.4681
5816431493.04681249.08291931.19390.25120.19510.38890.4712
591559.61492.14251237.87071965.16330.38990.2660.44270.4718
601560.21491.66161227.6941999.78820.39570.39660.4730.473
611590.161491.44941217.95892036.47860.36130.40240.39390.4746
621604.931491.35571208.74512074.26570.35130.36990.36250.4761
631661.81491.31441200.04242112.77550.29540.360.30340.4775
641670.731491.29611191.8122151.89720.29720.30650.3040.4788
651692.41491.28811184.00912191.63420.28680.30780.29130.48
661688.171491.28451176.59152232.03970.30120.29730.29860.4811
671658.041491.2831169.52172273.18750.3380.31080.3320.4821
681613.461491.28231162.76682315.16110.38570.34580.31190.483
691595.111491.2821156.29852358.04880.40720.39120.33060.4838
701558.831491.28181150.0922401.94230.44220.41160.3720.4846
711526.651491.28181144.12572446.93670.47110.44490.44430.4853
721475.191491.28171138.38082493.13110.48740.47240.44640.486






Univariate ARIMA Extrapolation Forecast Performance
time% S.E.PEMAPESq.EMSERMSE
490.02160.041903961.721200
500.03940.06480.05349445.21796703.469581.8747
510.0560.10430.070324410.605512605.8482112.2758
520.07140.11110.080527694.255216377.95127.9764
530.08570.12790.0936633.901820429.1403142.9305
540.09940.13060.096838172.112223386.3023152.9258
550.11240.11350.099228789.63124158.2064155.4291
560.12520.13580.103741200.953826288.5498162.1374
570.13730.12880.106536981.893127476.6991165.761
580.14970.10040.105922485.967726977.626164.2487
590.16170.04520.10044550.511324938.7974157.9202
600.17380.04590.09594697.518223252.0241152.4861
610.18640.06620.09369743.789222212.9291149.04
620.19940.07620.092312899.117221547.6568146.7912
630.21260.11430.093829065.345322048.836148.4885
640.2260.12030.095532196.511122683.0657150.609
650.23960.13490.097840446.003423727.9444154.0388
660.25340.1320.099738763.889724563.2747156.7268
670.26750.11180.100327807.911524734.0451157.2706
680.28190.08190.099414927.399224243.7128155.7039
690.29650.06960.09810780.262323602.5961153.6314
700.31160.04530.09564562.756222737.1488150.7884
710.3270.02370.09251250.912221802.9646147.6583
720.3428-0.01080.0891258.94420905.2971144.5866

\begin{tabular}{lllllllll}
\hline
Univariate ARIMA Extrapolation Forecast Performance \tabularnewline
time & % S.E. & PE & MAPE & Sq.E & MSE & RMSE \tabularnewline
49 & 0.0216 & 0.0419 & 0 & 3961.7212 & 0 & 0 \tabularnewline
50 & 0.0394 & 0.0648 & 0.0534 & 9445.2179 & 6703.4695 & 81.8747 \tabularnewline
51 & 0.056 & 0.1043 & 0.0703 & 24410.6055 & 12605.8482 & 112.2758 \tabularnewline
52 & 0.0714 & 0.1111 & 0.0805 & 27694.2552 & 16377.95 & 127.9764 \tabularnewline
53 & 0.0857 & 0.1279 & 0.09 & 36633.9018 & 20429.1403 & 142.9305 \tabularnewline
54 & 0.0994 & 0.1306 & 0.0968 & 38172.1122 & 23386.3023 & 152.9258 \tabularnewline
55 & 0.1124 & 0.1135 & 0.0992 & 28789.631 & 24158.2064 & 155.4291 \tabularnewline
56 & 0.1252 & 0.1358 & 0.1037 & 41200.9538 & 26288.5498 & 162.1374 \tabularnewline
57 & 0.1373 & 0.1288 & 0.1065 & 36981.8931 & 27476.6991 & 165.761 \tabularnewline
58 & 0.1497 & 0.1004 & 0.1059 & 22485.9677 & 26977.626 & 164.2487 \tabularnewline
59 & 0.1617 & 0.0452 & 0.1004 & 4550.5113 & 24938.7974 & 157.9202 \tabularnewline
60 & 0.1738 & 0.0459 & 0.0959 & 4697.5182 & 23252.0241 & 152.4861 \tabularnewline
61 & 0.1864 & 0.0662 & 0.0936 & 9743.7892 & 22212.9291 & 149.04 \tabularnewline
62 & 0.1994 & 0.0762 & 0.0923 & 12899.1172 & 21547.6568 & 146.7912 \tabularnewline
63 & 0.2126 & 0.1143 & 0.0938 & 29065.3453 & 22048.836 & 148.4885 \tabularnewline
64 & 0.226 & 0.1203 & 0.0955 & 32196.5111 & 22683.0657 & 150.609 \tabularnewline
65 & 0.2396 & 0.1349 & 0.0978 & 40446.0034 & 23727.9444 & 154.0388 \tabularnewline
66 & 0.2534 & 0.132 & 0.0997 & 38763.8897 & 24563.2747 & 156.7268 \tabularnewline
67 & 0.2675 & 0.1118 & 0.1003 & 27807.9115 & 24734.0451 & 157.2706 \tabularnewline
68 & 0.2819 & 0.0819 & 0.0994 & 14927.3992 & 24243.7128 & 155.7039 \tabularnewline
69 & 0.2965 & 0.0696 & 0.098 & 10780.2623 & 23602.5961 & 153.6314 \tabularnewline
70 & 0.3116 & 0.0453 & 0.0956 & 4562.7562 & 22737.1488 & 150.7884 \tabularnewline
71 & 0.327 & 0.0237 & 0.0925 & 1250.9122 & 21802.9646 & 147.6583 \tabularnewline
72 & 0.3428 & -0.0108 & 0.0891 & 258.944 & 20905.2971 & 144.5866 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=71359&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]0.0216[/C][C]0.0419[/C][C]0[/C][C]3961.7212[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]50[/C][C]0.0394[/C][C]0.0648[/C][C]0.0534[/C][C]9445.2179[/C][C]6703.4695[/C][C]81.8747[/C][/ROW]
[ROW][C]51[/C][C]0.056[/C][C]0.1043[/C][C]0.0703[/C][C]24410.6055[/C][C]12605.8482[/C][C]112.2758[/C][/ROW]
[ROW][C]52[/C][C]0.0714[/C][C]0.1111[/C][C]0.0805[/C][C]27694.2552[/C][C]16377.95[/C][C]127.9764[/C][/ROW]
[ROW][C]53[/C][C]0.0857[/C][C]0.1279[/C][C]0.09[/C][C]36633.9018[/C][C]20429.1403[/C][C]142.9305[/C][/ROW]
[ROW][C]54[/C][C]0.0994[/C][C]0.1306[/C][C]0.0968[/C][C]38172.1122[/C][C]23386.3023[/C][C]152.9258[/C][/ROW]
[ROW][C]55[/C][C]0.1124[/C][C]0.1135[/C][C]0.0992[/C][C]28789.631[/C][C]24158.2064[/C][C]155.4291[/C][/ROW]
[ROW][C]56[/C][C]0.1252[/C][C]0.1358[/C][C]0.1037[/C][C]41200.9538[/C][C]26288.5498[/C][C]162.1374[/C][/ROW]
[ROW][C]57[/C][C]0.1373[/C][C]0.1288[/C][C]0.1065[/C][C]36981.8931[/C][C]27476.6991[/C][C]165.761[/C][/ROW]
[ROW][C]58[/C][C]0.1497[/C][C]0.1004[/C][C]0.1059[/C][C]22485.9677[/C][C]26977.626[/C][C]164.2487[/C][/ROW]
[ROW][C]59[/C][C]0.1617[/C][C]0.0452[/C][C]0.1004[/C][C]4550.5113[/C][C]24938.7974[/C][C]157.9202[/C][/ROW]
[ROW][C]60[/C][C]0.1738[/C][C]0.0459[/C][C]0.0959[/C][C]4697.5182[/C][C]23252.0241[/C][C]152.4861[/C][/ROW]
[ROW][C]61[/C][C]0.1864[/C][C]0.0662[/C][C]0.0936[/C][C]9743.7892[/C][C]22212.9291[/C][C]149.04[/C][/ROW]
[ROW][C]62[/C][C]0.1994[/C][C]0.0762[/C][C]0.0923[/C][C]12899.1172[/C][C]21547.6568[/C][C]146.7912[/C][/ROW]
[ROW][C]63[/C][C]0.2126[/C][C]0.1143[/C][C]0.0938[/C][C]29065.3453[/C][C]22048.836[/C][C]148.4885[/C][/ROW]
[ROW][C]64[/C][C]0.226[/C][C]0.1203[/C][C]0.0955[/C][C]32196.5111[/C][C]22683.0657[/C][C]150.609[/C][/ROW]
[ROW][C]65[/C][C]0.2396[/C][C]0.1349[/C][C]0.0978[/C][C]40446.0034[/C][C]23727.9444[/C][C]154.0388[/C][/ROW]
[ROW][C]66[/C][C]0.2534[/C][C]0.132[/C][C]0.0997[/C][C]38763.8897[/C][C]24563.2747[/C][C]156.7268[/C][/ROW]
[ROW][C]67[/C][C]0.2675[/C][C]0.1118[/C][C]0.1003[/C][C]27807.9115[/C][C]24734.0451[/C][C]157.2706[/C][/ROW]
[ROW][C]68[/C][C]0.2819[/C][C]0.0819[/C][C]0.0994[/C][C]14927.3992[/C][C]24243.7128[/C][C]155.7039[/C][/ROW]
[ROW][C]69[/C][C]0.2965[/C][C]0.0696[/C][C]0.098[/C][C]10780.2623[/C][C]23602.5961[/C][C]153.6314[/C][/ROW]
[ROW][C]70[/C][C]0.3116[/C][C]0.0453[/C][C]0.0956[/C][C]4562.7562[/C][C]22737.1488[/C][C]150.7884[/C][/ROW]
[ROW][C]71[/C][C]0.327[/C][C]0.0237[/C][C]0.0925[/C][C]1250.9122[/C][C]21802.9646[/C][C]147.6583[/C][/ROW]
[ROW][C]72[/C][C]0.3428[/C][C]-0.0108[/C][C]0.0891[/C][C]258.944[/C][C]20905.2971[/C][C]144.5866[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=71359&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=71359&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
490.02160.041903961.721200
500.03940.06480.05349445.21796703.469581.8747
510.0560.10430.070324410.605512605.8482112.2758
520.07140.11110.080527694.255216377.95127.9764
530.08570.12790.0936633.901820429.1403142.9305
540.09940.13060.096838172.112223386.3023152.9258
550.11240.11350.099228789.63124158.2064155.4291
560.12520.13580.103741200.953826288.5498162.1374
570.13730.12880.106536981.893127476.6991165.761
580.14970.10040.105922485.967726977.626164.2487
590.16170.04520.10044550.511324938.7974157.9202
600.17380.04590.09594697.518223252.0241152.4861
610.18640.06620.09369743.789222212.9291149.04
620.19940.07620.092312899.117221547.6568146.7912
630.21260.11430.093829065.345322048.836148.4885
640.2260.12030.095532196.511122683.0657150.609
650.23960.13490.097840446.003423727.9444154.0388
660.25340.1320.099738763.889724563.2747156.7268
670.26750.11180.100327807.911524734.0451157.2706
680.28190.08190.099414927.399224243.7128155.7039
690.29650.06960.09810780.262323602.5961153.6314
700.31160.04530.09564562.756222737.1488150.7884
710.3270.02370.09251250.912221802.9646147.6583
720.3428-0.01080.0891258.94420905.2971144.5866


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 60 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;
Parameters (R input):
par1 = 24 ; par2 = -1.7 ; par3 = 1 ; par4 = 0 ; 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')