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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 computationMon, 19 Dec 2011 05:34:05 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Dec/19/t1324291109fgpyuhyarjmuc4p.htm/, Retrieved Wed, 15 May 2024 19:19:33 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=157265, Retrieved Wed, 15 May 2024 19:19:33 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact108

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-12 13:32:37] [76963dc1903f0f612b6153510a3818cf]
- R  D  [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-17 12:14:40] [76963dc1903f0f612b6153510a3818cf]
-         [Univariate Explorative Data Analysis] [Run Sequence Plot...] [2008-12-22 18:19:51] [1ce0d16c8f4225c977b42c8fa93bc163]
- RMP       [Univariate Data Series] [Identifying Integ...] [2009-11-22 12:08:06] [b98453cac15ba1066b407e146608df68]
- RMP         [(Partial) Autocorrelation Function] [Births] [2010-11-29 09:36:27] [b98453cac15ba1066b407e146608df68]
- RMPD            [ARIMA Forecasting] [] [2011-12-19 10:34:05] [c8f7c4812ba63eaa5bf379ee3b4bd6a3] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
179.257
179.947
179.094
181.624
184.954
187.928
187.151
189.959
192.492
191.103
191.737
192.31
192.013
192.106
192.141
194.58
196.421
199.021
198.136
199.426
200.997
201.277
201.663
202.874
204.256
205.597
205.471
211.064
212.856
217.036
219.302
219.759
221.388
220.834
221.788
222.358
222.972
224.164
224.915
226.294
224.69
227.021
229.284
229.189
230.032
229.389
231.053
232.56
232.681
231.555
231.428
232.141
234.939
235.424
235.471
236.355
238.693
236.958
237.06
239.282
238.252
241.552
236.23
238.909
240.723
242.12
242.1
243.276
244.677
243.494
244.902
245.247
245.578
243.052
238.121
241.863
241.203
243.634
242.351
245.18
246.126
244.424
245.166
247.258
245.094
246.02
243.082
245.555
243.685
247.277
245.029
246.169
246.778
244.577
246.048
245.775
245.328
245.477
241.903
243.219
248.088
248.521
247.389
249.057
248.916
249.193
250.768
253.106
249.829
249.447
246.755
250.785
250.14
255.755
254.671
253.919
253.741
252.729
253.81
256.653
255.231
258.405
251.061
254.811
254.895
258.325
257.608
258.759
258.621
257.852
260.56
262.358
260.812
261.165
257.164
260.72
259.581
264.743
261.845
262.262
261.631
258.953
259.966
262.85
262.204
263.418
262.752
266.433
267.722
266.003
262.971
265.521
264.676
270.223
269.508
268.457
265.814
266.68
263.018
269.285
269.829
270.911
266.844
271.244
269.907
271.296
270.157
271.322
267.179
264.101
265.518
269.419
268.714
272.482
268.351
268.175
270.674
272.764
272.599
270.333
270.846
270.491
269.16
274.027
273.784
276.663
274.525
271.344
271.115
270.798
273.911
273.985
271.917
273.338
270.601
273.547
275.363
281.229
277.793
279.913
282.5
280.041
282.166
290.304
283.519
287.816
285.226
287.595
289.741
289.148
288.301
290.155
289.648
288.225
289.351
294.735
305.333
309.03
310.215
321.935
325.734
320.846
323.023
319.753
321.753
320.757
324.479
324.641
322.767
324.181
321.389
327.897
334.287
332.653
334.819
335.264
339.622
342.44
346.585
335.378
337.01
339.13
341.193
343.507
348.915
346.431
348.322
348.288
346.597
351.076
355.215
350.562
355.266

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' @ jenkins.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=157265&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' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=157265&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=157265&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' @ jenkins.wessa.net






Univariate ARIMA Extrapolation Forecast
timeY[t]F[t]95% LB95% UBp-value(H0: Y[t] = F[t])P(F[t]>Y[t-1])P(F[t]>Y[t-s])P(F[t]>Y[229])
217305.333-------
218309.03-------
219310.215-------
220321.935-------
221325.734-------
222320.846-------
223323.023-------
224319.753-------
225321.753-------
226320.757-------
227324.479-------
228324.641-------
229322.767-------
230324.181324.1333319.7412328.52550.49150.72910.729
231321.389322.6381316.7813328.49480.3380.302810.4828
232327.897326.7237319.6677333.77980.37220.93080.90830.8641
233334.287327.8156319.7398335.89140.05810.49210.69330.8898
234332.653328.8943319.9135337.87510.2060.11960.96050.9094
235334.819327.6908317.8882337.49340.0770.16060.82470.8376
236335.264327.9921317.4314338.55270.08860.10260.93690.8339
237339.622328.6049317.3371339.87270.02770.12340.88330.8451
238342.44328.2302316.2971340.16330.00980.03070.89020.8152
239346.585329.5294316.9661342.09260.00390.0220.78460.8543
240335.378331.2544318.0911344.41760.26960.01120.83760.8968
241337.01330.8224317.0853344.55950.18870.25790.87480.8748
242339.13331.9914317.5268346.45610.16670.24820.8550.8943
243341.193330.5512315.4149345.68750.08410.13330.88230.8433
244343.507334.5373318.7555350.31910.13260.20420.79520.9281
245348.915335.6034319.2018352.0050.05580.17250.56250.9375
246346.431336.6564319.6575353.65530.12990.07880.67780.9454
247348.322335.4815317.9057353.05740.07610.1110.52940.9219
248348.288335.7756317.6412353.91010.08810.08750.5220.9201
249346.597336.3738317.6974355.05030.14170.10560.36660.9234
250351.076336.0081316.8051355.21120.0620.13990.25580.9117
251355.215337.2763317.5607356.99190.03730.08510.17740.9254
252350.562338.9602318.745359.17540.13030.05750.63580.9418
253355.266338.5386317.8358359.24130.05660.12750.55750.9323

\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[229]) \tabularnewline
217 & 305.333 & - & - & - & - & - & - & - \tabularnewline
218 & 309.03 & - & - & - & - & - & - & - \tabularnewline
219 & 310.215 & - & - & - & - & - & - & - \tabularnewline
220 & 321.935 & - & - & - & - & - & - & - \tabularnewline
221 & 325.734 & - & - & - & - & - & - & - \tabularnewline
222 & 320.846 & - & - & - & - & - & - & - \tabularnewline
223 & 323.023 & - & - & - & - & - & - & - \tabularnewline
224 & 319.753 & - & - & - & - & - & - & - \tabularnewline
225 & 321.753 & - & - & - & - & - & - & - \tabularnewline
226 & 320.757 & - & - & - & - & - & - & - \tabularnewline
227 & 324.479 & - & - & - & - & - & - & - \tabularnewline
228 & 324.641 & - & - & - & - & - & - & - \tabularnewline
229 & 322.767 & - & - & - & - & - & - & - \tabularnewline
230 & 324.181 & 324.1333 & 319.7412 & 328.5255 & 0.4915 & 0.729 & 1 & 0.729 \tabularnewline
231 & 321.389 & 322.6381 & 316.7813 & 328.4948 & 0.338 & 0.3028 & 1 & 0.4828 \tabularnewline
232 & 327.897 & 326.7237 & 319.6677 & 333.7798 & 0.3722 & 0.9308 & 0.9083 & 0.8641 \tabularnewline
233 & 334.287 & 327.8156 & 319.7398 & 335.8914 & 0.0581 & 0.4921 & 0.6933 & 0.8898 \tabularnewline
234 & 332.653 & 328.8943 & 319.9135 & 337.8751 & 0.206 & 0.1196 & 0.9605 & 0.9094 \tabularnewline
235 & 334.819 & 327.6908 & 317.8882 & 337.4934 & 0.077 & 0.1606 & 0.8247 & 0.8376 \tabularnewline
236 & 335.264 & 327.9921 & 317.4314 & 338.5527 & 0.0886 & 0.1026 & 0.9369 & 0.8339 \tabularnewline
237 & 339.622 & 328.6049 & 317.3371 & 339.8727 & 0.0277 & 0.1234 & 0.8833 & 0.8451 \tabularnewline
238 & 342.44 & 328.2302 & 316.2971 & 340.1633 & 0.0098 & 0.0307 & 0.8902 & 0.8152 \tabularnewline
239 & 346.585 & 329.5294 & 316.9661 & 342.0926 & 0.0039 & 0.022 & 0.7846 & 0.8543 \tabularnewline
240 & 335.378 & 331.2544 & 318.0911 & 344.4176 & 0.2696 & 0.0112 & 0.8376 & 0.8968 \tabularnewline
241 & 337.01 & 330.8224 & 317.0853 & 344.5595 & 0.1887 & 0.2579 & 0.8748 & 0.8748 \tabularnewline
242 & 339.13 & 331.9914 & 317.5268 & 346.4561 & 0.1667 & 0.2482 & 0.855 & 0.8943 \tabularnewline
243 & 341.193 & 330.5512 & 315.4149 & 345.6875 & 0.0841 & 0.1333 & 0.8823 & 0.8433 \tabularnewline
244 & 343.507 & 334.5373 & 318.7555 & 350.3191 & 0.1326 & 0.2042 & 0.7952 & 0.9281 \tabularnewline
245 & 348.915 & 335.6034 & 319.2018 & 352.005 & 0.0558 & 0.1725 & 0.5625 & 0.9375 \tabularnewline
246 & 346.431 & 336.6564 & 319.6575 & 353.6553 & 0.1299 & 0.0788 & 0.6778 & 0.9454 \tabularnewline
247 & 348.322 & 335.4815 & 317.9057 & 353.0574 & 0.0761 & 0.111 & 0.5294 & 0.9219 \tabularnewline
248 & 348.288 & 335.7756 & 317.6412 & 353.9101 & 0.0881 & 0.0875 & 0.522 & 0.9201 \tabularnewline
249 & 346.597 & 336.3738 & 317.6974 & 355.0503 & 0.1417 & 0.1056 & 0.3666 & 0.9234 \tabularnewline
250 & 351.076 & 336.0081 & 316.8051 & 355.2112 & 0.062 & 0.1399 & 0.2558 & 0.9117 \tabularnewline
251 & 355.215 & 337.2763 & 317.5607 & 356.9919 & 0.0373 & 0.0851 & 0.1774 & 0.9254 \tabularnewline
252 & 350.562 & 338.9602 & 318.745 & 359.1754 & 0.1303 & 0.0575 & 0.6358 & 0.9418 \tabularnewline
253 & 355.266 & 338.5386 & 317.8358 & 359.2413 & 0.0566 & 0.1275 & 0.5575 & 0.9323 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=157265&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[229])[/C][/ROW]
[ROW][C]217[/C][C]305.333[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]218[/C][C]309.03[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]219[/C][C]310.215[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]220[/C][C]321.935[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]221[/C][C]325.734[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]222[/C][C]320.846[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]223[/C][C]323.023[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]224[/C][C]319.753[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]225[/C][C]321.753[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]226[/C][C]320.757[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]227[/C][C]324.479[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]228[/C][C]324.641[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]229[/C][C]322.767[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]230[/C][C]324.181[/C][C]324.1333[/C][C]319.7412[/C][C]328.5255[/C][C]0.4915[/C][C]0.729[/C][C]1[/C][C]0.729[/C][/ROW]
[ROW][C]231[/C][C]321.389[/C][C]322.6381[/C][C]316.7813[/C][C]328.4948[/C][C]0.338[/C][C]0.3028[/C][C]1[/C][C]0.4828[/C][/ROW]
[ROW][C]232[/C][C]327.897[/C][C]326.7237[/C][C]319.6677[/C][C]333.7798[/C][C]0.3722[/C][C]0.9308[/C][C]0.9083[/C][C]0.8641[/C][/ROW]
[ROW][C]233[/C][C]334.287[/C][C]327.8156[/C][C]319.7398[/C][C]335.8914[/C][C]0.0581[/C][C]0.4921[/C][C]0.6933[/C][C]0.8898[/C][/ROW]
[ROW][C]234[/C][C]332.653[/C][C]328.8943[/C][C]319.9135[/C][C]337.8751[/C][C]0.206[/C][C]0.1196[/C][C]0.9605[/C][C]0.9094[/C][/ROW]
[ROW][C]235[/C][C]334.819[/C][C]327.6908[/C][C]317.8882[/C][C]337.4934[/C][C]0.077[/C][C]0.1606[/C][C]0.8247[/C][C]0.8376[/C][/ROW]
[ROW][C]236[/C][C]335.264[/C][C]327.9921[/C][C]317.4314[/C][C]338.5527[/C][C]0.0886[/C][C]0.1026[/C][C]0.9369[/C][C]0.8339[/C][/ROW]
[ROW][C]237[/C][C]339.622[/C][C]328.6049[/C][C]317.3371[/C][C]339.8727[/C][C]0.0277[/C][C]0.1234[/C][C]0.8833[/C][C]0.8451[/C][/ROW]
[ROW][C]238[/C][C]342.44[/C][C]328.2302[/C][C]316.2971[/C][C]340.1633[/C][C]0.0098[/C][C]0.0307[/C][C]0.8902[/C][C]0.8152[/C][/ROW]
[ROW][C]239[/C][C]346.585[/C][C]329.5294[/C][C]316.9661[/C][C]342.0926[/C][C]0.0039[/C][C]0.022[/C][C]0.7846[/C][C]0.8543[/C][/ROW]
[ROW][C]240[/C][C]335.378[/C][C]331.2544[/C][C]318.0911[/C][C]344.4176[/C][C]0.2696[/C][C]0.0112[/C][C]0.8376[/C][C]0.8968[/C][/ROW]
[ROW][C]241[/C][C]337.01[/C][C]330.8224[/C][C]317.0853[/C][C]344.5595[/C][C]0.1887[/C][C]0.2579[/C][C]0.8748[/C][C]0.8748[/C][/ROW]
[ROW][C]242[/C][C]339.13[/C][C]331.9914[/C][C]317.5268[/C][C]346.4561[/C][C]0.1667[/C][C]0.2482[/C][C]0.855[/C][C]0.8943[/C][/ROW]
[ROW][C]243[/C][C]341.193[/C][C]330.5512[/C][C]315.4149[/C][C]345.6875[/C][C]0.0841[/C][C]0.1333[/C][C]0.8823[/C][C]0.8433[/C][/ROW]
[ROW][C]244[/C][C]343.507[/C][C]334.5373[/C][C]318.7555[/C][C]350.3191[/C][C]0.1326[/C][C]0.2042[/C][C]0.7952[/C][C]0.9281[/C][/ROW]
[ROW][C]245[/C][C]348.915[/C][C]335.6034[/C][C]319.2018[/C][C]352.005[/C][C]0.0558[/C][C]0.1725[/C][C]0.5625[/C][C]0.9375[/C][/ROW]
[ROW][C]246[/C][C]346.431[/C][C]336.6564[/C][C]319.6575[/C][C]353.6553[/C][C]0.1299[/C][C]0.0788[/C][C]0.6778[/C][C]0.9454[/C][/ROW]
[ROW][C]247[/C][C]348.322[/C][C]335.4815[/C][C]317.9057[/C][C]353.0574[/C][C]0.0761[/C][C]0.111[/C][C]0.5294[/C][C]0.9219[/C][/ROW]
[ROW][C]248[/C][C]348.288[/C][C]335.7756[/C][C]317.6412[/C][C]353.9101[/C][C]0.0881[/C][C]0.0875[/C][C]0.522[/C][C]0.9201[/C][/ROW]
[ROW][C]249[/C][C]346.597[/C][C]336.3738[/C][C]317.6974[/C][C]355.0503[/C][C]0.1417[/C][C]0.1056[/C][C]0.3666[/C][C]0.9234[/C][/ROW]
[ROW][C]250[/C][C]351.076[/C][C]336.0081[/C][C]316.8051[/C][C]355.2112[/C][C]0.062[/C][C]0.1399[/C][C]0.2558[/C][C]0.9117[/C][/ROW]
[ROW][C]251[/C][C]355.215[/C][C]337.2763[/C][C]317.5607[/C][C]356.9919[/C][C]0.0373[/C][C]0.0851[/C][C]0.1774[/C][C]0.9254[/C][/ROW]
[ROW][C]252[/C][C]350.562[/C][C]338.9602[/C][C]318.745[/C][C]359.1754[/C][C]0.1303[/C][C]0.0575[/C][C]0.6358[/C][C]0.9418[/C][/ROW]
[ROW][C]253[/C][C]355.266[/C][C]338.5386[/C][C]317.8358[/C][C]359.2413[/C][C]0.0566[/C][C]0.1275[/C][C]0.5575[/C][C]0.9323[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=157265&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=157265&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[229])
217305.333-------
218309.03-------
219310.215-------
220321.935-------
221325.734-------
222320.846-------
223323.023-------
224319.753-------
225321.753-------
226320.757-------
227324.479-------
228324.641-------
229322.767-------
230324.181324.1333319.7412328.52550.49150.72910.729
231321.389322.6381316.7813328.49480.3380.302810.4828
232327.897326.7237319.6677333.77980.37220.93080.90830.8641
233334.287327.8156319.7398335.89140.05810.49210.69330.8898
234332.653328.8943319.9135337.87510.2060.11960.96050.9094
235334.819327.6908317.8882337.49340.0770.16060.82470.8376
236335.264327.9921317.4314338.55270.08860.10260.93690.8339
237339.622328.6049317.3371339.87270.02770.12340.88330.8451
238342.44328.2302316.2971340.16330.00980.03070.89020.8152
239346.585329.5294316.9661342.09260.00390.0220.78460.8543
240335.378331.2544318.0911344.41760.26960.01120.83760.8968
241337.01330.8224317.0853344.55950.18870.25790.87480.8748
242339.13331.9914317.5268346.45610.16670.24820.8550.8943
243341.193330.5512315.4149345.68750.08410.13330.88230.8433
244343.507334.5373318.7555350.31910.13260.20420.79520.9281
245348.915335.6034319.2018352.0050.05580.17250.56250.9375
246346.431336.6564319.6575353.65530.12990.07880.67780.9454
247348.322335.4815317.9057353.05740.07610.1110.52940.9219
248348.288335.7756317.6412353.91010.08810.08750.5220.9201
249346.597336.3738317.6974355.05030.14170.10560.36660.9234
250351.076336.0081316.8051355.21120.0620.13990.25580.9117
251355.215337.2763317.5607356.99190.03730.08510.17740.9254
252350.562338.9602318.745359.17540.13030.05750.63580.9418
253355.266338.5386317.8358359.24130.05660.12750.55750.9323






Univariate ARIMA Extrapolation Forecast Performance
time% S.E.PEMAPESq.EMSERMSE
2300.00691e-0400.002300
2310.0093-0.00390.0021.56020.78120.8839
2320.0110.00360.00251.37650.97970.9898
2330.01260.01970.006841.879111.20453.3473
2340.01390.01140.007814.127811.78923.4335
2350.01530.02180.010150.811918.2934.277
2360.01640.02220.011852.88123.23414.8202
2370.01750.03350.0145121.377335.5025.9584
2380.01850.04330.0177201.918153.99277.348
2390.01950.05180.0211290.894977.68298.8138
2400.02030.01240.020317.004372.16678.4951
2410.02120.01870.020238.286169.34338.3273
2420.02220.02150.020350.959167.92918.2419
2430.02340.03220.0212113.247971.16628.436
2440.02410.02680.021580.455971.78558.4726
2450.02490.03970.0227177.198878.37388.8529
2460.02580.0290.02395.542979.38388.9098
2470.02670.03830.0239164.878384.13359.1724
2480.02760.03730.0246156.559187.94539.3779
2490.02830.03040.0249104.512988.77379.422
2500.02920.04480.0258227.041295.35799.7651
2510.02980.05320.0271321.7962105.650510.2786
2520.03040.03420.0274134.6006106.909210.3397
2530.03120.04940.0283279.8062114.113310.6824

\begin{tabular}{lllllllll}
\hline
Univariate ARIMA Extrapolation Forecast Performance \tabularnewline
time & % S.E. & PE & MAPE & Sq.E & MSE & RMSE \tabularnewline
230 & 0.0069 & 1e-04 & 0 & 0.0023 & 0 & 0 \tabularnewline
231 & 0.0093 & -0.0039 & 0.002 & 1.5602 & 0.7812 & 0.8839 \tabularnewline
232 & 0.011 & 0.0036 & 0.0025 & 1.3765 & 0.9797 & 0.9898 \tabularnewline
233 & 0.0126 & 0.0197 & 0.0068 & 41.8791 & 11.2045 & 3.3473 \tabularnewline
234 & 0.0139 & 0.0114 & 0.0078 & 14.1278 & 11.7892 & 3.4335 \tabularnewline
235 & 0.0153 & 0.0218 & 0.0101 & 50.8119 & 18.293 & 4.277 \tabularnewline
236 & 0.0164 & 0.0222 & 0.0118 & 52.881 & 23.2341 & 4.8202 \tabularnewline
237 & 0.0175 & 0.0335 & 0.0145 & 121.3773 & 35.502 & 5.9584 \tabularnewline
238 & 0.0185 & 0.0433 & 0.0177 & 201.9181 & 53.9927 & 7.348 \tabularnewline
239 & 0.0195 & 0.0518 & 0.0211 & 290.8949 & 77.6829 & 8.8138 \tabularnewline
240 & 0.0203 & 0.0124 & 0.0203 & 17.0043 & 72.1667 & 8.4951 \tabularnewline
241 & 0.0212 & 0.0187 & 0.0202 & 38.2861 & 69.3433 & 8.3273 \tabularnewline
242 & 0.0222 & 0.0215 & 0.0203 & 50.9591 & 67.9291 & 8.2419 \tabularnewline
243 & 0.0234 & 0.0322 & 0.0212 & 113.2479 & 71.1662 & 8.436 \tabularnewline
244 & 0.0241 & 0.0268 & 0.0215 & 80.4559 & 71.7855 & 8.4726 \tabularnewline
245 & 0.0249 & 0.0397 & 0.0227 & 177.1988 & 78.3738 & 8.8529 \tabularnewline
246 & 0.0258 & 0.029 & 0.023 & 95.5429 & 79.3838 & 8.9098 \tabularnewline
247 & 0.0267 & 0.0383 & 0.0239 & 164.8783 & 84.1335 & 9.1724 \tabularnewline
248 & 0.0276 & 0.0373 & 0.0246 & 156.5591 & 87.9453 & 9.3779 \tabularnewline
249 & 0.0283 & 0.0304 & 0.0249 & 104.5129 & 88.7737 & 9.422 \tabularnewline
250 & 0.0292 & 0.0448 & 0.0258 & 227.0412 & 95.3579 & 9.7651 \tabularnewline
251 & 0.0298 & 0.0532 & 0.0271 & 321.7962 & 105.6505 & 10.2786 \tabularnewline
252 & 0.0304 & 0.0342 & 0.0274 & 134.6006 & 106.9092 & 10.3397 \tabularnewline
253 & 0.0312 & 0.0494 & 0.0283 & 279.8062 & 114.1133 & 10.6824 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=157265&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]230[/C][C]0.0069[/C][C]1e-04[/C][C]0[/C][C]0.0023[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]231[/C][C]0.0093[/C][C]-0.0039[/C][C]0.002[/C][C]1.5602[/C][C]0.7812[/C][C]0.8839[/C][/ROW]
[ROW][C]232[/C][C]0.011[/C][C]0.0036[/C][C]0.0025[/C][C]1.3765[/C][C]0.9797[/C][C]0.9898[/C][/ROW]
[ROW][C]233[/C][C]0.0126[/C][C]0.0197[/C][C]0.0068[/C][C]41.8791[/C][C]11.2045[/C][C]3.3473[/C][/ROW]
[ROW][C]234[/C][C]0.0139[/C][C]0.0114[/C][C]0.0078[/C][C]14.1278[/C][C]11.7892[/C][C]3.4335[/C][/ROW]
[ROW][C]235[/C][C]0.0153[/C][C]0.0218[/C][C]0.0101[/C][C]50.8119[/C][C]18.293[/C][C]4.277[/C][/ROW]
[ROW][C]236[/C][C]0.0164[/C][C]0.0222[/C][C]0.0118[/C][C]52.881[/C][C]23.2341[/C][C]4.8202[/C][/ROW]
[ROW][C]237[/C][C]0.0175[/C][C]0.0335[/C][C]0.0145[/C][C]121.3773[/C][C]35.502[/C][C]5.9584[/C][/ROW]
[ROW][C]238[/C][C]0.0185[/C][C]0.0433[/C][C]0.0177[/C][C]201.9181[/C][C]53.9927[/C][C]7.348[/C][/ROW]
[ROW][C]239[/C][C]0.0195[/C][C]0.0518[/C][C]0.0211[/C][C]290.8949[/C][C]77.6829[/C][C]8.8138[/C][/ROW]
[ROW][C]240[/C][C]0.0203[/C][C]0.0124[/C][C]0.0203[/C][C]17.0043[/C][C]72.1667[/C][C]8.4951[/C][/ROW]
[ROW][C]241[/C][C]0.0212[/C][C]0.0187[/C][C]0.0202[/C][C]38.2861[/C][C]69.3433[/C][C]8.3273[/C][/ROW]
[ROW][C]242[/C][C]0.0222[/C][C]0.0215[/C][C]0.0203[/C][C]50.9591[/C][C]67.9291[/C][C]8.2419[/C][/ROW]
[ROW][C]243[/C][C]0.0234[/C][C]0.0322[/C][C]0.0212[/C][C]113.2479[/C][C]71.1662[/C][C]8.436[/C][/ROW]
[ROW][C]244[/C][C]0.0241[/C][C]0.0268[/C][C]0.0215[/C][C]80.4559[/C][C]71.7855[/C][C]8.4726[/C][/ROW]
[ROW][C]245[/C][C]0.0249[/C][C]0.0397[/C][C]0.0227[/C][C]177.1988[/C][C]78.3738[/C][C]8.8529[/C][/ROW]
[ROW][C]246[/C][C]0.0258[/C][C]0.029[/C][C]0.023[/C][C]95.5429[/C][C]79.3838[/C][C]8.9098[/C][/ROW]
[ROW][C]247[/C][C]0.0267[/C][C]0.0383[/C][C]0.0239[/C][C]164.8783[/C][C]84.1335[/C][C]9.1724[/C][/ROW]
[ROW][C]248[/C][C]0.0276[/C][C]0.0373[/C][C]0.0246[/C][C]156.5591[/C][C]87.9453[/C][C]9.3779[/C][/ROW]
[ROW][C]249[/C][C]0.0283[/C][C]0.0304[/C][C]0.0249[/C][C]104.5129[/C][C]88.7737[/C][C]9.422[/C][/ROW]
[ROW][C]250[/C][C]0.0292[/C][C]0.0448[/C][C]0.0258[/C][C]227.0412[/C][C]95.3579[/C][C]9.7651[/C][/ROW]
[ROW][C]251[/C][C]0.0298[/C][C]0.0532[/C][C]0.0271[/C][C]321.7962[/C][C]105.6505[/C][C]10.2786[/C][/ROW]
[ROW][C]252[/C][C]0.0304[/C][C]0.0342[/C][C]0.0274[/C][C]134.6006[/C][C]106.9092[/C][C]10.3397[/C][/ROW]
[ROW][C]253[/C][C]0.0312[/C][C]0.0494[/C][C]0.0283[/C][C]279.8062[/C][C]114.1133[/C][C]10.6824[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=157265&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=157265&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
2300.00691e-0400.002300
2310.0093-0.00390.0021.56020.78120.8839
2320.0110.00360.00251.37650.97970.9898
2330.01260.01970.006841.879111.20453.3473
2340.01390.01140.007814.127811.78923.4335
2350.01530.02180.010150.811918.2934.277
2360.01640.02220.011852.88123.23414.8202
2370.01750.03350.0145121.377335.5025.9584
2380.01850.04330.0177201.918153.99277.348
2390.01950.05180.0211290.894977.68298.8138
2400.02030.01240.020317.004372.16678.4951
2410.02120.01870.020238.286169.34338.3273
2420.02220.02150.020350.959167.92918.2419
2430.02340.03220.0212113.247971.16628.436
2440.02410.02680.021580.455971.78558.4726
2450.02490.03970.0227177.198878.37388.8529
2460.02580.0290.02395.542979.38388.9098
2470.02670.03830.0239164.878384.13359.1724
2480.02760.03730.0246156.559187.94539.3779
2490.02830.03040.0249104.512988.77379.422
2500.02920.04480.0258227.041295.35799.7651
2510.02980.05320.0271321.7962105.650510.2786
2520.03040.03420.0274134.6006106.909210.3397
2530.03120.04940.0283279.8062114.113310.6824


Figures (Output of Computation)

Input Parameters & R Code

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