## Free Statistics

of Irreproducible Research!

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, 12 Dec 2013 03:55:54 -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/2013/Dec/12/t1386838570mjy6q8n9cynlm3l.htm/, Retrieved Tue, 07 Dec 2021 12:29:09 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=232221, Retrieved Tue, 07 Dec 2021 12:29:09 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact71
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [ARIMA Forecasting] [] [2013-12-12 08:55:54] [9e6a405f514733ea23d87e4507d39d29] [Current]
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Dataseries X:
164
96
73
49
39
59
169
169
210
278
298
245
200
188
90
79
78
91
167
169
289
247
275
203
223
104
107
85
75
99
135
211
335
488
326
346
261
224
141
148
145
223
272
445
560
612
467
404
518
404
300
210
196
186
247
343
464
680
711
610
513
292
273
322
189
257
324
404
677
858
895
664
628
308
324
248
272

 Summary of computational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 5 seconds R Server 'Herman Ole Andreas Wold' @ wold.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 & 5 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232221&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]5 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232221&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232221&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 Input view raw input (R code) Raw Output view raw output of R engine Computing time 5 seconds R Server 'Herman Ole Andreas Wold' @ wold.wessa.net

 Univariate ARIMA Extrapolation Forecast 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[65]) 53 196 - - - - - - - 54 186 - - - - - - - 55 247 - - - - - - - 56 343 - - - - - - - 57 464 - - - - - - - 58 680 - - - - - - - 59 711 - - - - - - - 60 610 - - - - - - - 61 513 - - - - - - - 62 292 - - - - - - - 63 273 - - - - - - - 64 322 - - - - - - - 65 189 - - - - - - - 66 257 252.1072 168.6425 376.8803 0.4694 0.8392 0.8505 0.8392 67 324 409.6421 261.8088 640.9511 0.234 0.9021 0.9159 0.9692 68 404 537.7032 336.6974 858.708 0.2071 0.904 0.8827 0.9834 69 677 761.3215 469.6354 1234.171 0.3633 0.9307 0.8911 0.9912 70 858 931.5542 567.0283 1530.4233 0.4049 0.7976 0.7948 0.9925 71 895 850.2124 510.9704 1414.6829 0.4382 0.4892 0.6856 0.9892 72 664 737.742 437.8905 1242.9208 0.3874 0.2709 0.6899 0.9834 73 628 702.2996 412.088 1196.8918 0.3842 0.5603 0.7734 0.979 74 308 475.4009 275.783 819.5066 0.1702 0.1924 0.8519 0.9486 75 324 355.9765 204.2075 620.5417 0.4064 0.6389 0.7306 0.892 76 248 310.6836 176.2819 547.5565 0.302 0.4561 0.4627 0.843 77 272 259.9173 145.8996 463.0378 0.4536 0.5458 0.7531 0.7531

\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[65]) \tabularnewline
53 & 196 & - & - & - & - & - & - & - \tabularnewline
54 & 186 & - & - & - & - & - & - & - \tabularnewline
55 & 247 & - & - & - & - & - & - & - \tabularnewline
56 & 343 & - & - & - & - & - & - & - \tabularnewline
57 & 464 & - & - & - & - & - & - & - \tabularnewline
58 & 680 & - & - & - & - & - & - & - \tabularnewline
59 & 711 & - & - & - & - & - & - & - \tabularnewline
60 & 610 & - & - & - & - & - & - & - \tabularnewline
61 & 513 & - & - & - & - & - & - & - \tabularnewline
62 & 292 & - & - & - & - & - & - & - \tabularnewline
63 & 273 & - & - & - & - & - & - & - \tabularnewline
64 & 322 & - & - & - & - & - & - & - \tabularnewline
65 & 189 & - & - & - & - & - & - & - \tabularnewline
66 & 257 & 252.1072 & 168.6425 & 376.8803 & 0.4694 & 0.8392 & 0.8505 & 0.8392 \tabularnewline
67 & 324 & 409.6421 & 261.8088 & 640.9511 & 0.234 & 0.9021 & 0.9159 & 0.9692 \tabularnewline
68 & 404 & 537.7032 & 336.6974 & 858.708 & 0.2071 & 0.904 & 0.8827 & 0.9834 \tabularnewline
69 & 677 & 761.3215 & 469.6354 & 1234.171 & 0.3633 & 0.9307 & 0.8911 & 0.9912 \tabularnewline
70 & 858 & 931.5542 & 567.0283 & 1530.4233 & 0.4049 & 0.7976 & 0.7948 & 0.9925 \tabularnewline
71 & 895 & 850.2124 & 510.9704 & 1414.6829 & 0.4382 & 0.4892 & 0.6856 & 0.9892 \tabularnewline
72 & 664 & 737.742 & 437.8905 & 1242.9208 & 0.3874 & 0.2709 & 0.6899 & 0.9834 \tabularnewline
73 & 628 & 702.2996 & 412.088 & 1196.8918 & 0.3842 & 0.5603 & 0.7734 & 0.979 \tabularnewline
74 & 308 & 475.4009 & 275.783 & 819.5066 & 0.1702 & 0.1924 & 0.8519 & 0.9486 \tabularnewline
75 & 324 & 355.9765 & 204.2075 & 620.5417 & 0.4064 & 0.6389 & 0.7306 & 0.892 \tabularnewline
76 & 248 & 310.6836 & 176.2819 & 547.5565 & 0.302 & 0.4561 & 0.4627 & 0.843 \tabularnewline
77 & 272 & 259.9173 & 145.8996 & 463.0378 & 0.4536 & 0.5458 & 0.7531 & 0.7531 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232221&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[65])[/C][/ROW]
[ROW][C]53[/C][C]196[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]54[/C][C]186[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]55[/C][C]247[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]56[/C][C]343[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]57[/C][C]464[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]58[/C][C]680[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]59[/C][C]711[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]60[/C][C]610[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]61[/C][C]513[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]62[/C][C]292[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]63[/C][C]273[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]64[/C][C]322[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]65[/C][C]189[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]66[/C][C]257[/C][C]252.1072[/C][C]168.6425[/C][C]376.8803[/C][C]0.4694[/C][C]0.8392[/C][C]0.8505[/C][C]0.8392[/C][/ROW]
[ROW][C]67[/C][C]324[/C][C]409.6421[/C][C]261.8088[/C][C]640.9511[/C][C]0.234[/C][C]0.9021[/C][C]0.9159[/C][C]0.9692[/C][/ROW]
[ROW][C]68[/C][C]404[/C][C]537.7032[/C][C]336.6974[/C][C]858.708[/C][C]0.2071[/C][C]0.904[/C][C]0.8827[/C][C]0.9834[/C][/ROW]
[ROW][C]69[/C][C]677[/C][C]761.3215[/C][C]469.6354[/C][C]1234.171[/C][C]0.3633[/C][C]0.9307[/C][C]0.8911[/C][C]0.9912[/C][/ROW]
[ROW][C]70[/C][C]858[/C][C]931.5542[/C][C]567.0283[/C][C]1530.4233[/C][C]0.4049[/C][C]0.7976[/C][C]0.7948[/C][C]0.9925[/C][/ROW]
[ROW][C]71[/C][C]895[/C][C]850.2124[/C][C]510.9704[/C][C]1414.6829[/C][C]0.4382[/C][C]0.4892[/C][C]0.6856[/C][C]0.9892[/C][/ROW]
[ROW][C]72[/C][C]664[/C][C]737.742[/C][C]437.8905[/C][C]1242.9208[/C][C]0.3874[/C][C]0.2709[/C][C]0.6899[/C][C]0.9834[/C][/ROW]
[ROW][C]73[/C][C]628[/C][C]702.2996[/C][C]412.088[/C][C]1196.8918[/C][C]0.3842[/C][C]0.5603[/C][C]0.7734[/C][C]0.979[/C][/ROW]
[ROW][C]74[/C][C]308[/C][C]475.4009[/C][C]275.783[/C][C]819.5066[/C][C]0.1702[/C][C]0.1924[/C][C]0.8519[/C][C]0.9486[/C][/ROW]
[ROW][C]75[/C][C]324[/C][C]355.9765[/C][C]204.2075[/C][C]620.5417[/C][C]0.4064[/C][C]0.6389[/C][C]0.7306[/C][C]0.892[/C][/ROW]
[ROW][C]76[/C][C]248[/C][C]310.6836[/C][C]176.2819[/C][C]547.5565[/C][C]0.302[/C][C]0.4561[/C][C]0.4627[/C][C]0.843[/C][/ROW]
[ROW][C]77[/C][C]272[/C][C]259.9173[/C][C]145.8996[/C][C]463.0378[/C][C]0.4536[/C][C]0.5458[/C][C]0.7531[/C][C]0.7531[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232221&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232221&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 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[65]) 53 196 - - - - - - - 54 186 - - - - - - - 55 247 - - - - - - - 56 343 - - - - - - - 57 464 - - - - - - - 58 680 - - - - - - - 59 711 - - - - - - - 60 610 - - - - - - - 61 513 - - - - - - - 62 292 - - - - - - - 63 273 - - - - - - - 64 322 - - - - - - - 65 189 - - - - - - - 66 257 252.1072 168.6425 376.8803 0.4694 0.8392 0.8505 0.8392 67 324 409.6421 261.8088 640.9511 0.234 0.9021 0.9159 0.9692 68 404 537.7032 336.6974 858.708 0.2071 0.904 0.8827 0.9834 69 677 761.3215 469.6354 1234.171 0.3633 0.9307 0.8911 0.9912 70 858 931.5542 567.0283 1530.4233 0.4049 0.7976 0.7948 0.9925 71 895 850.2124 510.9704 1414.6829 0.4382 0.4892 0.6856 0.9892 72 664 737.742 437.8905 1242.9208 0.3874 0.2709 0.6899 0.9834 73 628 702.2996 412.088 1196.8918 0.3842 0.5603 0.7734 0.979 74 308 475.4009 275.783 819.5066 0.1702 0.1924 0.8519 0.9486 75 324 355.9765 204.2075 620.5417 0.4064 0.6389 0.7306 0.892 76 248 310.6836 176.2819 547.5565 0.302 0.4561 0.4627 0.843 77 272 259.9173 145.8996 463.0378 0.4536 0.5458 0.7531 0.7531

 Univariate ARIMA Extrapolation Forecast Performance time % S.E. PE MAPE sMAPE Sq.E MSE RMSE ScaledE MASE 66 0.2525 0.019 0.019 0.0192 23.9395 0 0 0.0401 0.0401 67 0.2881 -0.2643 0.1417 0.1263 7334.5676 3679.2535 60.6569 -0.7025 0.3713 68 0.3046 -0.3309 0.2048 0.1789 17876.5523 8411.6865 91.7152 -1.0967 0.6131 69 0.3169 -0.1246 0.1847 0.1635 7110.1137 8086.2933 89.9238 -0.6917 0.6328 70 0.328 -0.0857 0.1649 0.1472 5410.2257 7551.0798 86.8969 -0.6034 0.6269 71 0.3387 0.05 0.1458 0.1312 2005.9292 6626.888 81.4057 0.3674 0.5836 72 0.3494 -0.1111 0.1408 0.1275 5437.8829 6457.0301 80.3556 -0.6049 0.5867 73 0.3593 -0.1183 0.138 0.1255 5520.4358 6339.9558 79.6238 -0.6095 0.5895 74 0.3693 -0.5435 0.1831 0.1591 28023.0617 8749.1898 93.5371 -1.3732 0.6766 75 0.3792 -0.0987 0.1746 0.1526 1022.4982 7976.5207 89.3114 -0.2623 0.6352 76 0.389 -0.2528 0.1817 0.1591 3929.2298 7608.5851 87.2272 -0.5142 0.6242 77 0.3987 0.0444 0.1703 0.1496 145.9912 6986.7023 83.5865 0.0991 0.5804

\begin{tabular}{lllllllll}
\hline
Univariate ARIMA Extrapolation Forecast Performance \tabularnewline
time & % S.E. & PE & MAPE & sMAPE & Sq.E & MSE & RMSE & ScaledE & MASE \tabularnewline
66 & 0.2525 & 0.019 & 0.019 & 0.0192 & 23.9395 & 0 & 0 & 0.0401 & 0.0401 \tabularnewline
67 & 0.2881 & -0.2643 & 0.1417 & 0.1263 & 7334.5676 & 3679.2535 & 60.6569 & -0.7025 & 0.3713 \tabularnewline
68 & 0.3046 & -0.3309 & 0.2048 & 0.1789 & 17876.5523 & 8411.6865 & 91.7152 & -1.0967 & 0.6131 \tabularnewline
69 & 0.3169 & -0.1246 & 0.1847 & 0.1635 & 7110.1137 & 8086.2933 & 89.9238 & -0.6917 & 0.6328 \tabularnewline
70 & 0.328 & -0.0857 & 0.1649 & 0.1472 & 5410.2257 & 7551.0798 & 86.8969 & -0.6034 & 0.6269 \tabularnewline
71 & 0.3387 & 0.05 & 0.1458 & 0.1312 & 2005.9292 & 6626.888 & 81.4057 & 0.3674 & 0.5836 \tabularnewline
72 & 0.3494 & -0.1111 & 0.1408 & 0.1275 & 5437.8829 & 6457.0301 & 80.3556 & -0.6049 & 0.5867 \tabularnewline
73 & 0.3593 & -0.1183 & 0.138 & 0.1255 & 5520.4358 & 6339.9558 & 79.6238 & -0.6095 & 0.5895 \tabularnewline
74 & 0.3693 & -0.5435 & 0.1831 & 0.1591 & 28023.0617 & 8749.1898 & 93.5371 & -1.3732 & 0.6766 \tabularnewline
75 & 0.3792 & -0.0987 & 0.1746 & 0.1526 & 1022.4982 & 7976.5207 & 89.3114 & -0.2623 & 0.6352 \tabularnewline
76 & 0.389 & -0.2528 & 0.1817 & 0.1591 & 3929.2298 & 7608.5851 & 87.2272 & -0.5142 & 0.6242 \tabularnewline
77 & 0.3987 & 0.0444 & 0.1703 & 0.1496 & 145.9912 & 6986.7023 & 83.5865 & 0.0991 & 0.5804 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232221&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]sMAPE[/C][C]Sq.E[/C][C]MSE[/C][C]RMSE[/C][C]ScaledE[/C][C]MASE[/C][/ROW]
[ROW][C]66[/C][C]0.2525[/C][C]0.019[/C][C]0.019[/C][C]0.0192[/C][C]23.9395[/C][C]0[/C][C]0[/C][C]0.0401[/C][C]0.0401[/C][/ROW]
[ROW][C]67[/C][C]0.2881[/C][C]-0.2643[/C][C]0.1417[/C][C]0.1263[/C][C]7334.5676[/C][C]3679.2535[/C][C]60.6569[/C][C]-0.7025[/C][C]0.3713[/C][/ROW]
[ROW][C]68[/C][C]0.3046[/C][C]-0.3309[/C][C]0.2048[/C][C]0.1789[/C][C]17876.5523[/C][C]8411.6865[/C][C]91.7152[/C][C]-1.0967[/C][C]0.6131[/C][/ROW]
[ROW][C]69[/C][C]0.3169[/C][C]-0.1246[/C][C]0.1847[/C][C]0.1635[/C][C]7110.1137[/C][C]8086.2933[/C][C]89.9238[/C][C]-0.6917[/C][C]0.6328[/C][/ROW]
[ROW][C]70[/C][C]0.328[/C][C]-0.0857[/C][C]0.1649[/C][C]0.1472[/C][C]5410.2257[/C][C]7551.0798[/C][C]86.8969[/C][C]-0.6034[/C][C]0.6269[/C][/ROW]
[ROW][C]71[/C][C]0.3387[/C][C]0.05[/C][C]0.1458[/C][C]0.1312[/C][C]2005.9292[/C][C]6626.888[/C][C]81.4057[/C][C]0.3674[/C][C]0.5836[/C][/ROW]
[ROW][C]72[/C][C]0.3494[/C][C]-0.1111[/C][C]0.1408[/C][C]0.1275[/C][C]5437.8829[/C][C]6457.0301[/C][C]80.3556[/C][C]-0.6049[/C][C]0.5867[/C][/ROW]
[ROW][C]73[/C][C]0.3593[/C][C]-0.1183[/C][C]0.138[/C][C]0.1255[/C][C]5520.4358[/C][C]6339.9558[/C][C]79.6238[/C][C]-0.6095[/C][C]0.5895[/C][/ROW]
[ROW][C]74[/C][C]0.3693[/C][C]-0.5435[/C][C]0.1831[/C][C]0.1591[/C][C]28023.0617[/C][C]8749.1898[/C][C]93.5371[/C][C]-1.3732[/C][C]0.6766[/C][/ROW]
[ROW][C]75[/C][C]0.3792[/C][C]-0.0987[/C][C]0.1746[/C][C]0.1526[/C][C]1022.4982[/C][C]7976.5207[/C][C]89.3114[/C][C]-0.2623[/C][C]0.6352[/C][/ROW]
[ROW][C]76[/C][C]0.389[/C][C]-0.2528[/C][C]0.1817[/C][C]0.1591[/C][C]3929.2298[/C][C]7608.5851[/C][C]87.2272[/C][C]-0.5142[/C][C]0.6242[/C][/ROW]
[ROW][C]77[/C][C]0.3987[/C][C]0.0444[/C][C]0.1703[/C][C]0.1496[/C][C]145.9912[/C][C]6986.7023[/C][C]83.5865[/C][C]0.0991[/C][C]0.5804[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232221&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232221&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. PE MAPE sMAPE Sq.E MSE RMSE ScaledE MASE 66 0.2525 0.019 0.019 0.0192 23.9395 0 0 0.0401 0.0401 67 0.2881 -0.2643 0.1417 0.1263 7334.5676 3679.2535 60.6569 -0.7025 0.3713 68 0.3046 -0.3309 0.2048 0.1789 17876.5523 8411.6865 91.7152 -1.0967 0.6131 69 0.3169 -0.1246 0.1847 0.1635 7110.1137 8086.2933 89.9238 -0.6917 0.6328 70 0.328 -0.0857 0.1649 0.1472 5410.2257 7551.0798 86.8969 -0.6034 0.6269 71 0.3387 0.05 0.1458 0.1312 2005.9292 6626.888 81.4057 0.3674 0.5836 72 0.3494 -0.1111 0.1408 0.1275 5437.8829 6457.0301 80.3556 -0.6049 0.5867 73 0.3593 -0.1183 0.138 0.1255 5520.4358 6339.9558 79.6238 -0.6095 0.5895 74 0.3693 -0.5435 0.1831 0.1591 28023.0617 8749.1898 93.5371 -1.3732 0.6766 75 0.3792 -0.0987 0.1746 0.1526 1022.4982 7976.5207 89.3114 -0.2623 0.6352 76 0.389 -0.2528 0.1817 0.1591 3929.2298 7608.5851 87.2272 -0.5142 0.6242 77 0.3987 0.0444 0.1703 0.1496 145.9912 6986.7023 83.5865 0.0991 0.5804

Parameters (Session):
par1 = 12 ; par2 = 0.0 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = 1 ; par7 = 1 ; par8 = 1 ; par9 = 1 ; par10 = FALSE ;
Parameters (R input):
par1 = 12 ; par2 = 0.0 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = 1 ; par7 = 1 ; par8 = 1 ; par9 = 1 ; par10 = FALSE ;
R code (references can be found in the software module):
par1 <- as.numeric(par1) #cut off periodspar2 <- as.numeric(par2) #lambdapar3 <- as.numeric(par3) #degree of non-seasonal differencingpar4 <- as.numeric(par4) #degree of seasonal differencingpar5 <- as.numeric(par5) #seasonal periodpar6 <- as.numeric(par6) #ppar7 <- as.numeric(par7) #qpar8 <- as.numeric(par8) #Ppar9 <- as.numeric(par9) #Qif (par10 == 'TRUE') par10 <- TRUEif (par10 == 'FALSE') par10 <- FALSEif (par2 == 0) x <- log(x)if (par2 != 0) x <- x^par2lx <- length(x)first <- lx - 2*par1nx <- lx - par1nx1 <- nx + 1fx <- lx - nxif (fx < 1) {fx <- par5nx1 <- lx + fx - 1first <- lx - 2*fx}first <- 1if (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 <- lblb <- ubub <- 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.spe <- array(0, dim=fx)perf.scalederr <- array(0, dim=fx)perf.mase <- array(0, dim=fx)perf.mase1 <- array(0, dim=fx)perf.mape <- array(0, dim=fx)perf.smape <- array(0, dim=fx)perf.mape1 <- array(0, dim=fx)perf.smape1 <- 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)perf.scaleddenom <- 0for (i in 2:fx) {perf.scaleddenom = perf.scaleddenom + abs(x[nx+i] - x[nx+i-1])}perf.scaleddenom = perf.scaleddenom / (fx-1)for (i in 1:fx) {locSD <- (ub[i] - forecast$pred[i]) / 1.96perf.scalederr[i] = (x[nx+i] - forecast$pred[i]) / perf.scaleddenomperf.pe[i] = (x[nx+i] - forecast$pred[i]) / x[nx+i]perf.spe[i] = 2*(x[nx+i] - forecast$pred[i]) / (x[nx+i] + forecast$pred[i])perf.se[i] = (x[nx+i] - forecast$pred[i])^2prob.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.smape[1] = abs(perf.spe[1])perf.mape1[1] = perf.mape[1]perf.smape1[1] = perf.smape[1]perf.mse[1] = perf.se[1]perf.mase[1] = abs(perf.scalederr[1])perf.mase1[1] = perf.mase[1]for (i in 2:fx) {perf.mape[i] = perf.mape[i-1] + abs(perf.pe[i])perf.mape1[i] = perf.mape[i] / iperf.smape[i] = perf.smape[i-1] + abs(perf.spe[i])perf.smape1[i] = perf.smape[i] / iperf.mse[i] = perf.mse[i-1] + perf.se[i]perf.mse1[i] = perf.mse[i] / iperf.mase[i] = perf.mase[i-1] + abs(perf.scalederr[i])perf.mase1[i] = perf.mase[i] / i}perf.rmse = sqrt(perf.mse1)bitmap(file='test2.png')plot(forecast$pred, pch=19, type='b',main='ARIMA Extrapolation Forecast', ylab='Forecast and 95% CI', xlab='time',ylim=c(min(lb),max(ub)))dum <- forecast$preddum[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',10,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,'sMAPE',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.element(a,'ScaledE',1,header=TRUE)a<-table.element(a,'MASE',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.smape1[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.element(a,round(perf.scalederr[i],4))a<-table.element(a,round(perf.mase1[i],4))a<-table.row.end(a)}a<-table.end(a)table.save(a,file='mytable1.tab')