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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, 09 Dec 2009 10:42:31 -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/09/t1260380605vd73xophde2v8lw.htm/, Retrieved Sun, 06 Apr 2025 05:44:29 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=65084, Retrieved Sun, 06 Apr 2025 05:44:29 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact238

Tree of Dependent Computations

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] [WS10 berekening 7...] [2009-12-09 17:42:31] [37de18e38c1490dd77c2b362ed87f3bb] [Current]
-   P       [ARIMA Forecasting] [WS 10 TG 1] [2009-12-10 14:00:13] [a21bac9c8d3d56fdec8be4e719e2c7ed]
-             [ARIMA Forecasting] [BDM 6] [2009-12-11 10:14:15] [f5d341d4bbba73282fc6e80153a6d315]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
101.3
106.3
94
102.8
102
105.1
92.4
81.4
105.8
120.3
100.7
88.8
94.3
99.9
103.4
103.3
98.8
104.2
91.2
74.7
108.5
114.5
96.9
89.6
97.1
100.3
122.6
115.4
109
129.1
102.8
96.2
127.7
128.9
126.5
119.8
113.2
114.1
134.1
130
121.8
132.1
105.3
103
117.1
126.3
138.1
119.5
138
135.5
178.6
162.2
176.9
204.9
132.2
142.5
164.3
174.9
175.4
143

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=65084&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=65084&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=65084&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[32])
2074.7-------
21108.5-------
22114.5-------
2396.9-------
2489.6-------
2597.1-------
26100.3-------
27122.6-------
28115.4-------
29109-------
30129.1-------
31102.8-------
3296.2-------
33127.7122.5071100.67153.04650.36950.95430.81570.9543
34128.9129.5576104.3393166.16450.4860.53960.78990.963
35126.5111.492391.1338140.24290.15310.11770.84010.8514
36119.899.278981.7185123.76240.05020.01470.78080.5973
37113.299.90879.409130.40730.19650.10060.57160.5942
38114.1108.460481.8573152.19380.40020.41590.64270.7087
39134.1114.197284.0485166.30710.2270.50150.3760.7508
40130111.923382.1655163.62280.24660.20020.44760.7244
41121.8106.799478.57155.63420.27360.17590.46480.6647
42132.1104.879976.5008154.83280.14280.25340.1710.6333
43105.3106.730376.3983162.22690.47990.18510.55520.645
44103109.313976.8615170.9530.42040.55080.66170.6617
45117.1109.818476.4363174.60470.41280.58170.29430.6598
46126.3108.45375.0955173.9140.29650.39790.27020.6431
47138.1107.230473.7891173.73960.18150.28710.28510.6274
48119.5107.277373.0938176.74110.36510.19220.36190.6227
49138108.100872.8158181.63090.21270.38060.44590.6245
50135.5108.6372.4573185.67380.24710.22750.44470.6241
51178.6108.445771.7971187.82030.04160.2520.26320.6188
52162.2107.979471.0134189.25870.09550.04430.29770.6118
53176.9107.785570.3595191.48740.05280.10130.37140.6069
54204.9107.956269.8878194.73970.01430.05970.29280.6047
55132.2108.197869.4728198.17540.30050.01760.52520.6031
56142.5108.249368.9954201.04860.23470.30650.54410.6004
57164.3108.126968.4552203.41970.1240.23980.42680.5969
58174.9108.011267.9278205.83740.09010.12970.3570.5935
59175.4108.012767.4619208.63620.09470.09630.27890.591
60143108.088867.0417211.67880.25450.10140.41450.589

\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[32]) \tabularnewline
20 & 74.7 & - & - & - & - & - & - & - \tabularnewline
21 & 108.5 & - & - & - & - & - & - & - \tabularnewline
22 & 114.5 & - & - & - & - & - & - & - \tabularnewline
23 & 96.9 & - & - & - & - & - & - & - \tabularnewline
24 & 89.6 & - & - & - & - & - & - & - \tabularnewline
25 & 97.1 & - & - & - & - & - & - & - \tabularnewline
26 & 100.3 & - & - & - & - & - & - & - \tabularnewline
27 & 122.6 & - & - & - & - & - & - & - \tabularnewline
28 & 115.4 & - & - & - & - & - & - & - \tabularnewline
29 & 109 & - & - & - & - & - & - & - \tabularnewline
30 & 129.1 & - & - & - & - & - & - & - \tabularnewline
31 & 102.8 & - & - & - & - & - & - & - \tabularnewline
32 & 96.2 & - & - & - & - & - & - & - \tabularnewline
33 & 127.7 & 122.5071 & 100.67 & 153.0465 & 0.3695 & 0.9543 & 0.8157 & 0.9543 \tabularnewline
34 & 128.9 & 129.5576 & 104.3393 & 166.1645 & 0.486 & 0.5396 & 0.7899 & 0.963 \tabularnewline
35 & 126.5 & 111.4923 & 91.1338 & 140.2429 & 0.1531 & 0.1177 & 0.8401 & 0.8514 \tabularnewline
36 & 119.8 & 99.2789 & 81.7185 & 123.7624 & 0.0502 & 0.0147 & 0.7808 & 0.5973 \tabularnewline
37 & 113.2 & 99.908 & 79.409 & 130.4073 & 0.1965 & 0.1006 & 0.5716 & 0.5942 \tabularnewline
38 & 114.1 & 108.4604 & 81.8573 & 152.1938 & 0.4002 & 0.4159 & 0.6427 & 0.7087 \tabularnewline
39 & 134.1 & 114.1972 & 84.0485 & 166.3071 & 0.227 & 0.5015 & 0.376 & 0.7508 \tabularnewline
40 & 130 & 111.9233 & 82.1655 & 163.6228 & 0.2466 & 0.2002 & 0.4476 & 0.7244 \tabularnewline
41 & 121.8 & 106.7994 & 78.57 & 155.6342 & 0.2736 & 0.1759 & 0.4648 & 0.6647 \tabularnewline
42 & 132.1 & 104.8799 & 76.5008 & 154.8328 & 0.1428 & 0.2534 & 0.171 & 0.6333 \tabularnewline
43 & 105.3 & 106.7303 & 76.3983 & 162.2269 & 0.4799 & 0.1851 & 0.5552 & 0.645 \tabularnewline
44 & 103 & 109.3139 & 76.8615 & 170.953 & 0.4204 & 0.5508 & 0.6617 & 0.6617 \tabularnewline
45 & 117.1 & 109.8184 & 76.4363 & 174.6047 & 0.4128 & 0.5817 & 0.2943 & 0.6598 \tabularnewline
46 & 126.3 & 108.453 & 75.0955 & 173.914 & 0.2965 & 0.3979 & 0.2702 & 0.6431 \tabularnewline
47 & 138.1 & 107.2304 & 73.7891 & 173.7396 & 0.1815 & 0.2871 & 0.2851 & 0.6274 \tabularnewline
48 & 119.5 & 107.2773 & 73.0938 & 176.7411 & 0.3651 & 0.1922 & 0.3619 & 0.6227 \tabularnewline
49 & 138 & 108.1008 & 72.8158 & 181.6309 & 0.2127 & 0.3806 & 0.4459 & 0.6245 \tabularnewline
50 & 135.5 & 108.63 & 72.4573 & 185.6738 & 0.2471 & 0.2275 & 0.4447 & 0.6241 \tabularnewline
51 & 178.6 & 108.4457 & 71.7971 & 187.8203 & 0.0416 & 0.252 & 0.2632 & 0.6188 \tabularnewline
52 & 162.2 & 107.9794 & 71.0134 & 189.2587 & 0.0955 & 0.0443 & 0.2977 & 0.6118 \tabularnewline
53 & 176.9 & 107.7855 & 70.3595 & 191.4874 & 0.0528 & 0.1013 & 0.3714 & 0.6069 \tabularnewline
54 & 204.9 & 107.9562 & 69.8878 & 194.7397 & 0.0143 & 0.0597 & 0.2928 & 0.6047 \tabularnewline
55 & 132.2 & 108.1978 & 69.4728 & 198.1754 & 0.3005 & 0.0176 & 0.5252 & 0.6031 \tabularnewline
56 & 142.5 & 108.2493 & 68.9954 & 201.0486 & 0.2347 & 0.3065 & 0.5441 & 0.6004 \tabularnewline
57 & 164.3 & 108.1269 & 68.4552 & 203.4197 & 0.124 & 0.2398 & 0.4268 & 0.5969 \tabularnewline
58 & 174.9 & 108.0112 & 67.9278 & 205.8374 & 0.0901 & 0.1297 & 0.357 & 0.5935 \tabularnewline
59 & 175.4 & 108.0127 & 67.4619 & 208.6362 & 0.0947 & 0.0963 & 0.2789 & 0.591 \tabularnewline
60 & 143 & 108.0888 & 67.0417 & 211.6788 & 0.2545 & 0.1014 & 0.4145 & 0.589 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=65084&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[32])[/C][/ROW]
[ROW][C]20[/C][C]74.7[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]21[/C][C]108.5[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]22[/C][C]114.5[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]23[/C][C]96.9[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]24[/C][C]89.6[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]25[/C][C]97.1[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]26[/C][C]100.3[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]27[/C][C]122.6[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]28[/C][C]115.4[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]29[/C][C]109[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]30[/C][C]129.1[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]31[/C][C]102.8[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]32[/C][C]96.2[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]33[/C][C]127.7[/C][C]122.5071[/C][C]100.67[/C][C]153.0465[/C][C]0.3695[/C][C]0.9543[/C][C]0.8157[/C][C]0.9543[/C][/ROW]
[ROW][C]34[/C][C]128.9[/C][C]129.5576[/C][C]104.3393[/C][C]166.1645[/C][C]0.486[/C][C]0.5396[/C][C]0.7899[/C][C]0.963[/C][/ROW]
[ROW][C]35[/C][C]126.5[/C][C]111.4923[/C][C]91.1338[/C][C]140.2429[/C][C]0.1531[/C][C]0.1177[/C][C]0.8401[/C][C]0.8514[/C][/ROW]
[ROW][C]36[/C][C]119.8[/C][C]99.2789[/C][C]81.7185[/C][C]123.7624[/C][C]0.0502[/C][C]0.0147[/C][C]0.7808[/C][C]0.5973[/C][/ROW]
[ROW][C]37[/C][C]113.2[/C][C]99.908[/C][C]79.409[/C][C]130.4073[/C][C]0.1965[/C][C]0.1006[/C][C]0.5716[/C][C]0.5942[/C][/ROW]
[ROW][C]38[/C][C]114.1[/C][C]108.4604[/C][C]81.8573[/C][C]152.1938[/C][C]0.4002[/C][C]0.4159[/C][C]0.6427[/C][C]0.7087[/C][/ROW]
[ROW][C]39[/C][C]134.1[/C][C]114.1972[/C][C]84.0485[/C][C]166.3071[/C][C]0.227[/C][C]0.5015[/C][C]0.376[/C][C]0.7508[/C][/ROW]
[ROW][C]40[/C][C]130[/C][C]111.9233[/C][C]82.1655[/C][C]163.6228[/C][C]0.2466[/C][C]0.2002[/C][C]0.4476[/C][C]0.7244[/C][/ROW]
[ROW][C]41[/C][C]121.8[/C][C]106.7994[/C][C]78.57[/C][C]155.6342[/C][C]0.2736[/C][C]0.1759[/C][C]0.4648[/C][C]0.6647[/C][/ROW]
[ROW][C]42[/C][C]132.1[/C][C]104.8799[/C][C]76.5008[/C][C]154.8328[/C][C]0.1428[/C][C]0.2534[/C][C]0.171[/C][C]0.6333[/C][/ROW]
[ROW][C]43[/C][C]105.3[/C][C]106.7303[/C][C]76.3983[/C][C]162.2269[/C][C]0.4799[/C][C]0.1851[/C][C]0.5552[/C][C]0.645[/C][/ROW]
[ROW][C]44[/C][C]103[/C][C]109.3139[/C][C]76.8615[/C][C]170.953[/C][C]0.4204[/C][C]0.5508[/C][C]0.6617[/C][C]0.6617[/C][/ROW]
[ROW][C]45[/C][C]117.1[/C][C]109.8184[/C][C]76.4363[/C][C]174.6047[/C][C]0.4128[/C][C]0.5817[/C][C]0.2943[/C][C]0.6598[/C][/ROW]
[ROW][C]46[/C][C]126.3[/C][C]108.453[/C][C]75.0955[/C][C]173.914[/C][C]0.2965[/C][C]0.3979[/C][C]0.2702[/C][C]0.6431[/C][/ROW]
[ROW][C]47[/C][C]138.1[/C][C]107.2304[/C][C]73.7891[/C][C]173.7396[/C][C]0.1815[/C][C]0.2871[/C][C]0.2851[/C][C]0.6274[/C][/ROW]
[ROW][C]48[/C][C]119.5[/C][C]107.2773[/C][C]73.0938[/C][C]176.7411[/C][C]0.3651[/C][C]0.1922[/C][C]0.3619[/C][C]0.6227[/C][/ROW]
[ROW][C]49[/C][C]138[/C][C]108.1008[/C][C]72.8158[/C][C]181.6309[/C][C]0.2127[/C][C]0.3806[/C][C]0.4459[/C][C]0.6245[/C][/ROW]
[ROW][C]50[/C][C]135.5[/C][C]108.63[/C][C]72.4573[/C][C]185.6738[/C][C]0.2471[/C][C]0.2275[/C][C]0.4447[/C][C]0.6241[/C][/ROW]
[ROW][C]51[/C][C]178.6[/C][C]108.4457[/C][C]71.7971[/C][C]187.8203[/C][C]0.0416[/C][C]0.252[/C][C]0.2632[/C][C]0.6188[/C][/ROW]
[ROW][C]52[/C][C]162.2[/C][C]107.9794[/C][C]71.0134[/C][C]189.2587[/C][C]0.0955[/C][C]0.0443[/C][C]0.2977[/C][C]0.6118[/C][/ROW]
[ROW][C]53[/C][C]176.9[/C][C]107.7855[/C][C]70.3595[/C][C]191.4874[/C][C]0.0528[/C][C]0.1013[/C][C]0.3714[/C][C]0.6069[/C][/ROW]
[ROW][C]54[/C][C]204.9[/C][C]107.9562[/C][C]69.8878[/C][C]194.7397[/C][C]0.0143[/C][C]0.0597[/C][C]0.2928[/C][C]0.6047[/C][/ROW]
[ROW][C]55[/C][C]132.2[/C][C]108.1978[/C][C]69.4728[/C][C]198.1754[/C][C]0.3005[/C][C]0.0176[/C][C]0.5252[/C][C]0.6031[/C][/ROW]
[ROW][C]56[/C][C]142.5[/C][C]108.2493[/C][C]68.9954[/C][C]201.0486[/C][C]0.2347[/C][C]0.3065[/C][C]0.5441[/C][C]0.6004[/C][/ROW]
[ROW][C]57[/C][C]164.3[/C][C]108.1269[/C][C]68.4552[/C][C]203.4197[/C][C]0.124[/C][C]0.2398[/C][C]0.4268[/C][C]0.5969[/C][/ROW]
[ROW][C]58[/C][C]174.9[/C][C]108.0112[/C][C]67.9278[/C][C]205.8374[/C][C]0.0901[/C][C]0.1297[/C][C]0.357[/C][C]0.5935[/C][/ROW]
[ROW][C]59[/C][C]175.4[/C][C]108.0127[/C][C]67.4619[/C][C]208.6362[/C][C]0.0947[/C][C]0.0963[/C][C]0.2789[/C][C]0.591[/C][/ROW]
[ROW][C]60[/C][C]143[/C][C]108.0888[/C][C]67.0417[/C][C]211.6788[/C][C]0.2545[/C][C]0.1014[/C][C]0.4145[/C][C]0.589[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=65084&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=65084&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[32])
2074.7-------
21108.5-------
22114.5-------
2396.9-------
2489.6-------
2597.1-------
26100.3-------
27122.6-------
28115.4-------
29109-------
30129.1-------
31102.8-------
3296.2-------
33127.7122.5071100.67153.04650.36950.95430.81570.9543
34128.9129.5576104.3393166.16450.4860.53960.78990.963
35126.5111.492391.1338140.24290.15310.11770.84010.8514
36119.899.278981.7185123.76240.05020.01470.78080.5973
37113.299.90879.409130.40730.19650.10060.57160.5942
38114.1108.460481.8573152.19380.40020.41590.64270.7087
39134.1114.197284.0485166.30710.2270.50150.3760.7508
40130111.923382.1655163.62280.24660.20020.44760.7244
41121.8106.799478.57155.63420.27360.17590.46480.6647
42132.1104.879976.5008154.83280.14280.25340.1710.6333
43105.3106.730376.3983162.22690.47990.18510.55520.645
44103109.313976.8615170.9530.42040.55080.66170.6617
45117.1109.818476.4363174.60470.41280.58170.29430.6598
46126.3108.45375.0955173.9140.29650.39790.27020.6431
47138.1107.230473.7891173.73960.18150.28710.28510.6274
48119.5107.277373.0938176.74110.36510.19220.36190.6227
49138108.100872.8158181.63090.21270.38060.44590.6245
50135.5108.6372.4573185.67380.24710.22750.44470.6241
51178.6108.445771.7971187.82030.04160.2520.26320.6188
52162.2107.979471.0134189.25870.09550.04430.29770.6118
53176.9107.785570.3595191.48740.05280.10130.37140.6069
54204.9107.956269.8878194.73970.01430.05970.29280.6047
55132.2108.197869.4728198.17540.30050.01760.52520.6031
56142.5108.249368.9954201.04860.23470.30650.54410.6004
57164.3108.126968.4552203.41970.1240.23980.42680.5969
58174.9108.011267.9278205.83740.09010.12970.3570.5935
59175.4108.012767.4619208.63620.09470.09630.27890.591
60143108.088867.0417211.67880.25450.10140.41450.589






Univariate ARIMA Extrapolation Forecast Performance
time% S.E.PEMAPESq.EMSERMSE
330.12720.0424026.966500
340.1442-0.00510.02370.432513.69953.7013
350.13160.13460.0607225.2384.20979.1766
360.12580.20670.0972421.1153168.436112.9783
370.15580.1330.1044176.6772170.084313.0416
380.20570.0520.095631.8054147.037812.1259
390.23280.17430.1069396.1197182.620913.5137
400.23570.16150.1137326.7675200.639314.1647
410.23330.14050.1167225.0183203.34814.26
420.2430.25950.131740.9319257.106416.0345
430.2653-0.01340.12032.0458233.919115.2944
440.2877-0.05780.115139.8651217.747914.7563
450.3010.06630.111353.0219205.076714.3205
460.3080.16460.1151318.5169213.179614.6007
470.31650.28790.1266952.9352262.496616.2017
480.33040.11390.1258149.3943255.427715.9821
490.3470.27660.1347893.9623292.988617.1169
500.36190.24740.141721.9946316.822217.7995
510.37340.64690.16764921.6247559.180323.647
520.3840.50210.18432939.8746678.21526.0426
530.39620.64120.20614776.82873.386629.5531
540.41010.8980.23759398.10421260.873835.5088
550.42430.22180.2368576.10791231.101435.0871
560.43740.31640.24021173.10881228.68535.0526
570.44960.51950.25133155.41541305.754236.1352
580.46210.61930.26554474.10681427.61437.7838
590.47530.62390.27884541.04961542.926439.2801
600.4890.3230.28031218.79471531.350339.1325

\begin{tabular}{lllllllll}
\hline
Univariate ARIMA Extrapolation Forecast Performance \tabularnewline
time & % S.E. & PE & MAPE & Sq.E & MSE & RMSE \tabularnewline
33 & 0.1272 & 0.0424 & 0 & 26.9665 & 0 & 0 \tabularnewline
34 & 0.1442 & -0.0051 & 0.0237 & 0.4325 & 13.6995 & 3.7013 \tabularnewline
35 & 0.1316 & 0.1346 & 0.0607 & 225.23 & 84.2097 & 9.1766 \tabularnewline
36 & 0.1258 & 0.2067 & 0.0972 & 421.1153 & 168.4361 & 12.9783 \tabularnewline
37 & 0.1558 & 0.133 & 0.1044 & 176.6772 & 170.0843 & 13.0416 \tabularnewline
38 & 0.2057 & 0.052 & 0.0956 & 31.8054 & 147.0378 & 12.1259 \tabularnewline
39 & 0.2328 & 0.1743 & 0.1069 & 396.1197 & 182.6209 & 13.5137 \tabularnewline
40 & 0.2357 & 0.1615 & 0.1137 & 326.7675 & 200.6393 & 14.1647 \tabularnewline
41 & 0.2333 & 0.1405 & 0.1167 & 225.0183 & 203.348 & 14.26 \tabularnewline
42 & 0.243 & 0.2595 & 0.131 & 740.9319 & 257.1064 & 16.0345 \tabularnewline
43 & 0.2653 & -0.0134 & 0.1203 & 2.0458 & 233.9191 & 15.2944 \tabularnewline
44 & 0.2877 & -0.0578 & 0.1151 & 39.8651 & 217.7479 & 14.7563 \tabularnewline
45 & 0.301 & 0.0663 & 0.1113 & 53.0219 & 205.0767 & 14.3205 \tabularnewline
46 & 0.308 & 0.1646 & 0.1151 & 318.5169 & 213.1796 & 14.6007 \tabularnewline
47 & 0.3165 & 0.2879 & 0.1266 & 952.9352 & 262.4966 & 16.2017 \tabularnewline
48 & 0.3304 & 0.1139 & 0.1258 & 149.3943 & 255.4277 & 15.9821 \tabularnewline
49 & 0.347 & 0.2766 & 0.1347 & 893.9623 & 292.9886 & 17.1169 \tabularnewline
50 & 0.3619 & 0.2474 & 0.141 & 721.9946 & 316.8222 & 17.7995 \tabularnewline
51 & 0.3734 & 0.6469 & 0.1676 & 4921.6247 & 559.1803 & 23.647 \tabularnewline
52 & 0.384 & 0.5021 & 0.1843 & 2939.8746 & 678.215 & 26.0426 \tabularnewline
53 & 0.3962 & 0.6412 & 0.2061 & 4776.82 & 873.3866 & 29.5531 \tabularnewline
54 & 0.4101 & 0.898 & 0.2375 & 9398.1042 & 1260.8738 & 35.5088 \tabularnewline
55 & 0.4243 & 0.2218 & 0.2368 & 576.1079 & 1231.1014 & 35.0871 \tabularnewline
56 & 0.4374 & 0.3164 & 0.2402 & 1173.1088 & 1228.685 & 35.0526 \tabularnewline
57 & 0.4496 & 0.5195 & 0.2513 & 3155.4154 & 1305.7542 & 36.1352 \tabularnewline
58 & 0.4621 & 0.6193 & 0.2655 & 4474.1068 & 1427.614 & 37.7838 \tabularnewline
59 & 0.4753 & 0.6239 & 0.2788 & 4541.0496 & 1542.9264 & 39.2801 \tabularnewline
60 & 0.489 & 0.323 & 0.2803 & 1218.7947 & 1531.3503 & 39.1325 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=65084&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]33[/C][C]0.1272[/C][C]0.0424[/C][C]0[/C][C]26.9665[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]34[/C][C]0.1442[/C][C]-0.0051[/C][C]0.0237[/C][C]0.4325[/C][C]13.6995[/C][C]3.7013[/C][/ROW]
[ROW][C]35[/C][C]0.1316[/C][C]0.1346[/C][C]0.0607[/C][C]225.23[/C][C]84.2097[/C][C]9.1766[/C][/ROW]
[ROW][C]36[/C][C]0.1258[/C][C]0.2067[/C][C]0.0972[/C][C]421.1153[/C][C]168.4361[/C][C]12.9783[/C][/ROW]
[ROW][C]37[/C][C]0.1558[/C][C]0.133[/C][C]0.1044[/C][C]176.6772[/C][C]170.0843[/C][C]13.0416[/C][/ROW]
[ROW][C]38[/C][C]0.2057[/C][C]0.052[/C][C]0.0956[/C][C]31.8054[/C][C]147.0378[/C][C]12.1259[/C][/ROW]
[ROW][C]39[/C][C]0.2328[/C][C]0.1743[/C][C]0.1069[/C][C]396.1197[/C][C]182.6209[/C][C]13.5137[/C][/ROW]
[ROW][C]40[/C][C]0.2357[/C][C]0.1615[/C][C]0.1137[/C][C]326.7675[/C][C]200.6393[/C][C]14.1647[/C][/ROW]
[ROW][C]41[/C][C]0.2333[/C][C]0.1405[/C][C]0.1167[/C][C]225.0183[/C][C]203.348[/C][C]14.26[/C][/ROW]
[ROW][C]42[/C][C]0.243[/C][C]0.2595[/C][C]0.131[/C][C]740.9319[/C][C]257.1064[/C][C]16.0345[/C][/ROW]
[ROW][C]43[/C][C]0.2653[/C][C]-0.0134[/C][C]0.1203[/C][C]2.0458[/C][C]233.9191[/C][C]15.2944[/C][/ROW]
[ROW][C]44[/C][C]0.2877[/C][C]-0.0578[/C][C]0.1151[/C][C]39.8651[/C][C]217.7479[/C][C]14.7563[/C][/ROW]
[ROW][C]45[/C][C]0.301[/C][C]0.0663[/C][C]0.1113[/C][C]53.0219[/C][C]205.0767[/C][C]14.3205[/C][/ROW]
[ROW][C]46[/C][C]0.308[/C][C]0.1646[/C][C]0.1151[/C][C]318.5169[/C][C]213.1796[/C][C]14.6007[/C][/ROW]
[ROW][C]47[/C][C]0.3165[/C][C]0.2879[/C][C]0.1266[/C][C]952.9352[/C][C]262.4966[/C][C]16.2017[/C][/ROW]
[ROW][C]48[/C][C]0.3304[/C][C]0.1139[/C][C]0.1258[/C][C]149.3943[/C][C]255.4277[/C][C]15.9821[/C][/ROW]
[ROW][C]49[/C][C]0.347[/C][C]0.2766[/C][C]0.1347[/C][C]893.9623[/C][C]292.9886[/C][C]17.1169[/C][/ROW]
[ROW][C]50[/C][C]0.3619[/C][C]0.2474[/C][C]0.141[/C][C]721.9946[/C][C]316.8222[/C][C]17.7995[/C][/ROW]
[ROW][C]51[/C][C]0.3734[/C][C]0.6469[/C][C]0.1676[/C][C]4921.6247[/C][C]559.1803[/C][C]23.647[/C][/ROW]
[ROW][C]52[/C][C]0.384[/C][C]0.5021[/C][C]0.1843[/C][C]2939.8746[/C][C]678.215[/C][C]26.0426[/C][/ROW]
[ROW][C]53[/C][C]0.3962[/C][C]0.6412[/C][C]0.2061[/C][C]4776.82[/C][C]873.3866[/C][C]29.5531[/C][/ROW]
[ROW][C]54[/C][C]0.4101[/C][C]0.898[/C][C]0.2375[/C][C]9398.1042[/C][C]1260.8738[/C][C]35.5088[/C][/ROW]
[ROW][C]55[/C][C]0.4243[/C][C]0.2218[/C][C]0.2368[/C][C]576.1079[/C][C]1231.1014[/C][C]35.0871[/C][/ROW]
[ROW][C]56[/C][C]0.4374[/C][C]0.3164[/C][C]0.2402[/C][C]1173.1088[/C][C]1228.685[/C][C]35.0526[/C][/ROW]
[ROW][C]57[/C][C]0.4496[/C][C]0.5195[/C][C]0.2513[/C][C]3155.4154[/C][C]1305.7542[/C][C]36.1352[/C][/ROW]
[ROW][C]58[/C][C]0.4621[/C][C]0.6193[/C][C]0.2655[/C][C]4474.1068[/C][C]1427.614[/C][C]37.7838[/C][/ROW]
[ROW][C]59[/C][C]0.4753[/C][C]0.6239[/C][C]0.2788[/C][C]4541.0496[/C][C]1542.9264[/C][C]39.2801[/C][/ROW]
[ROW][C]60[/C][C]0.489[/C][C]0.323[/C][C]0.2803[/C][C]1218.7947[/C][C]1531.3503[/C][C]39.1325[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=65084&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=65084&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
330.12720.0424026.966500
340.1442-0.00510.02370.432513.69953.7013
350.13160.13460.0607225.2384.20979.1766
360.12580.20670.0972421.1153168.436112.9783
370.15580.1330.1044176.6772170.084313.0416
380.20570.0520.095631.8054147.037812.1259
390.23280.17430.1069396.1197182.620913.5137
400.23570.16150.1137326.7675200.639314.1647
410.23330.14050.1167225.0183203.34814.26
420.2430.25950.131740.9319257.106416.0345
430.2653-0.01340.12032.0458233.919115.2944
440.2877-0.05780.115139.8651217.747914.7563
450.3010.06630.111353.0219205.076714.3205
460.3080.16460.1151318.5169213.179614.6007
470.31650.28790.1266952.9352262.496616.2017
480.33040.11390.1258149.3943255.427715.9821
490.3470.27660.1347893.9623292.988617.1169
500.36190.24740.141721.9946316.822217.7995
510.37340.64690.16764921.6247559.180323.647
520.3840.50210.18432939.8746678.21526.0426
530.39620.64120.20614776.82873.386629.5531
540.41010.8980.23759398.10421260.873835.5088
550.42430.22180.2368576.10791231.101435.0871
560.43740.31640.24021173.10881228.68535.0526
570.44960.51950.25133155.41541305.754236.1352
580.46210.61930.26554474.10681427.61437.7838
590.47530.62390.27884541.04961542.926439.2801
600.4890.3230.28031218.79471531.350339.1325


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 1 ; par2 = 1 ; par3 = 0 ; par4 = 12 ; par5 = 1 ; par6 = 1 ; par7 = 0 ; par8 = 11 ;
Parameters (R input):
par1 = 12 ; par2 = -0.6 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = 3 ; 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')