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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 computationTue, 04 Dec 2012 17:49:28 -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/2012/Dec/04/t1354661405iav77ij0aujb8it.htm/, Retrieved Fri, 26 Apr 2024 06:13:52 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=196696, Retrieved Fri, 26 Apr 2024 06:13:52 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact116

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [(Partial) Autocorrelation Function] [Unemployment] [2010-11-29 09:05:21] [b98453cac15ba1066b407e146608df68]
- R       [(Partial) Autocorrelation Function] [Autocorrelatie Un...] [2012-12-04 20:09:16] [f8950b13b9b6c1e097d81f3c7491f9a1]
-   P       [(Partial) Autocorrelation Function] [d=1 en Timelags =...] [2012-12-04 20:17:51] [f8950b13b9b6c1e097d81f3c7491f9a1]
- RMP         [Spectral Analysis] [Spectral analysis...] [2012-12-04 20:36:51] [f8950b13b9b6c1e097d81f3c7491f9a1]
- R P           [Spectral Analysis] [Spectral analysis...] [2012-12-04 20:40:07] [f8950b13b9b6c1e097d81f3c7491f9a1]
- RMP               [ARIMA Forecasting] [Arima Forecasting] [2012-12-04 22:49:28] [09cdab5d933081235930b6410ef38881] [Current]
- R P                 [ARIMA Forecasting] [arima forecasting] [2012-12-20 16:25:23] [77d02b0cf2cecd023ffa9a06f056f18d]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
235.1
280.7
264.6
240.7
201.4
240.8
241.1
223.8
206.1
174.7
203.3
220.5
299.5
347.4
338.3
327.7
351.6
396.6
438.8
395.6
363.5
378.8
357
369
464.8
479.1
431.3
366.5
326.3
355.1
331.6
261.3
249
205.5
235.6
240.9
264.9
253.8
232.3
193.8
177
213.2
207.2
180.6
188.6
175.4
199
179.6
225.8
234
200.2
183.6
178.2
203.2
208.5
191.8
172.8
148
159.4
154.5
213.2
196.4
182.8
176.4
153.6
173.2
171
151.2
161.9
157.2
201.7
236.4
356.1
398.3
403.7
384.6
365.8
368.1
367.9
347
343.3
292.9
311.5
300.9
366.9
356.9
329.7
316.2
269
289.3
266.2
253.6
233.8
228.4
253.6
260.1
306.6
309.2
309.5
271
279.9
317.9
298.4
246.7
227.3
209.1
259.9
266
320.6
308.5
282.2
262.7
263.5
313.1
284.3
252.6
250.3
246.5
312.7
333.2
446.4
511.6
515.5
506.4
483.2
522.3
509.8
460.7
405.8
375
378.5
406.8
467.8
469.8
429.8
355.8
332.7
378
360.5
334.7
319.5
323.1
363.6
352.1
411.9
388.6
416.4
360.7
338
417.2
388.4
371.1
331.5
353.7
396.7
447
533.5
565.4
542.3
488.7
467.1
531.3
496.1
444
403.4
386.3
394.1
404.1
462.1
448.1
432.3
386.3
395.2
421.9
382.9
384.2
345.5
323.4
372.6
376
462.7
487
444.2
399.3
394.9
455.4
414
375.5
347
339.4
385.8
378.8
451.8
446.1
422.5
383.1
352.8
445.3
367.5
355.1
326.2
319.8
331.8
340.9
394.1
417.2
369.9
349.2
321.4
405.7
342.9
316.5
284.2
270.9
288.8
278.8
324.4
310.9
299
273
279.3
359.2
305
282.1
250.3
246.5
257.9
266.5
315.9
318.4
295.4
266.4
245.8
362.8
324.9
294.2
289.5
295.2
290.3
272
307.4
328.7
292.9
249.1
230.4
361.5
321.7
277.2
260.7
251
257.6
241.8
287.5
292.3
274.7
254.2
230
339
318.2
287
295.8
284
271
262.7
340.6
379.4
373.3
355.2
338.4
466.9
451
422
429.2
425.9
460.7
463.6
541.4
544.2
517.5
469.4
439.4
549
533
506.1
484
457
481.5
469.5
544.7
541.2
521.5
469.7
434.4
542.6
517.3
485.7
465.8
447
426.6
411.6
467.5
484.5
451.2
417.4
379.9
484.7
455
420.8
416.5
376.3
405.6
405.8
500.8
514
475.5
430.1
414.4
538
526
488.5
520.2
504.4
568.5
610.6
818
830.9
835.9
782
762.3
856.9
820.9
769.6
752.2
724.4
723.1
719.5
817.4
803.3
752.5
689
630.4
765.5
757.7
732.2
702.6
683.3
709.5
702.2
784.8
810.9
755.6
656.8
615.1
745.3
694.1
675.7
643.7
622.1
634.6
588
689.7
673.9
647.9
568.8
545.7
632.6
643.8
593.1
579.7
546
562.9
572.5

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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 & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=196696&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]3 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=196696&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=196696&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 time3 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[360])
348702.2-------
349784.8-------
350810.9-------
351755.6-------
352656.8-------
353615.1-------
354745.3-------
355694.1-------
356675.7-------
357643.7-------
358622.1-------
359634.6-------
360588-------
361689.7680.2776638.6305721.92470.3287101
362673.9678.8203615.296742.34450.43970.368600.9975
363647.9635.5818549.5679721.59580.38950.19130.00310.8609
364568.8565.1592458.7077671.61070.47330.06380.04580.337
365545.7525.5172400.1266650.90770.37620.24930.08070.1644
366632.6644.3949501.5612787.22870.43570.91220.08310.7805
367643.8612.8733453.8881771.85850.35150.40390.15830.6204
368593.1582.5934408.5883756.59850.45290.24530.14710.4757
369579.7563.7839375.7355751.83240.43410.380.20240.4004
370546541.7675340.5207743.01440.48360.35590.2170.3263
371562.9560.2588346.5462773.97150.49030.5520.24770.3996
372572.5546.0112320.4712771.55120.4090.44170.35760.3576

\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[360]) \tabularnewline
348 & 702.2 & - & - & - & - & - & - & - \tabularnewline
349 & 784.8 & - & - & - & - & - & - & - \tabularnewline
350 & 810.9 & - & - & - & - & - & - & - \tabularnewline
351 & 755.6 & - & - & - & - & - & - & - \tabularnewline
352 & 656.8 & - & - & - & - & - & - & - \tabularnewline
353 & 615.1 & - & - & - & - & - & - & - \tabularnewline
354 & 745.3 & - & - & - & - & - & - & - \tabularnewline
355 & 694.1 & - & - & - & - & - & - & - \tabularnewline
356 & 675.7 & - & - & - & - & - & - & - \tabularnewline
357 & 643.7 & - & - & - & - & - & - & - \tabularnewline
358 & 622.1 & - & - & - & - & - & - & - \tabularnewline
359 & 634.6 & - & - & - & - & - & - & - \tabularnewline
360 & 588 & - & - & - & - & - & - & - \tabularnewline
361 & 689.7 & 680.2776 & 638.6305 & 721.9247 & 0.3287 & 1 & 0 & 1 \tabularnewline
362 & 673.9 & 678.8203 & 615.296 & 742.3445 & 0.4397 & 0.3686 & 0 & 0.9975 \tabularnewline
363 & 647.9 & 635.5818 & 549.5679 & 721.5958 & 0.3895 & 0.1913 & 0.0031 & 0.8609 \tabularnewline
364 & 568.8 & 565.1592 & 458.7077 & 671.6107 & 0.4733 & 0.0638 & 0.0458 & 0.337 \tabularnewline
365 & 545.7 & 525.5172 & 400.1266 & 650.9077 & 0.3762 & 0.2493 & 0.0807 & 0.1644 \tabularnewline
366 & 632.6 & 644.3949 & 501.5612 & 787.2287 & 0.4357 & 0.9122 & 0.0831 & 0.7805 \tabularnewline
367 & 643.8 & 612.8733 & 453.8881 & 771.8585 & 0.3515 & 0.4039 & 0.1583 & 0.6204 \tabularnewline
368 & 593.1 & 582.5934 & 408.5883 & 756.5985 & 0.4529 & 0.2453 & 0.1471 & 0.4757 \tabularnewline
369 & 579.7 & 563.7839 & 375.7355 & 751.8324 & 0.4341 & 0.38 & 0.2024 & 0.4004 \tabularnewline
370 & 546 & 541.7675 & 340.5207 & 743.0144 & 0.4836 & 0.3559 & 0.217 & 0.3263 \tabularnewline
371 & 562.9 & 560.2588 & 346.5462 & 773.9715 & 0.4903 & 0.552 & 0.2477 & 0.3996 \tabularnewline
372 & 572.5 & 546.0112 & 320.4712 & 771.5512 & 0.409 & 0.4417 & 0.3576 & 0.3576 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=196696&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[360])[/C][/ROW]
[ROW][C]348[/C][C]702.2[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]349[/C][C]784.8[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]350[/C][C]810.9[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]351[/C][C]755.6[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]352[/C][C]656.8[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]353[/C][C]615.1[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]354[/C][C]745.3[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]355[/C][C]694.1[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]356[/C][C]675.7[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]357[/C][C]643.7[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]358[/C][C]622.1[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]359[/C][C]634.6[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]360[/C][C]588[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]361[/C][C]689.7[/C][C]680.2776[/C][C]638.6305[/C][C]721.9247[/C][C]0.3287[/C][C]1[/C][C]0[/C][C]1[/C][/ROW]
[ROW][C]362[/C][C]673.9[/C][C]678.8203[/C][C]615.296[/C][C]742.3445[/C][C]0.4397[/C][C]0.3686[/C][C]0[/C][C]0.9975[/C][/ROW]
[ROW][C]363[/C][C]647.9[/C][C]635.5818[/C][C]549.5679[/C][C]721.5958[/C][C]0.3895[/C][C]0.1913[/C][C]0.0031[/C][C]0.8609[/C][/ROW]
[ROW][C]364[/C][C]568.8[/C][C]565.1592[/C][C]458.7077[/C][C]671.6107[/C][C]0.4733[/C][C]0.0638[/C][C]0.0458[/C][C]0.337[/C][/ROW]
[ROW][C]365[/C][C]545.7[/C][C]525.5172[/C][C]400.1266[/C][C]650.9077[/C][C]0.3762[/C][C]0.2493[/C][C]0.0807[/C][C]0.1644[/C][/ROW]
[ROW][C]366[/C][C]632.6[/C][C]644.3949[/C][C]501.5612[/C][C]787.2287[/C][C]0.4357[/C][C]0.9122[/C][C]0.0831[/C][C]0.7805[/C][/ROW]
[ROW][C]367[/C][C]643.8[/C][C]612.8733[/C][C]453.8881[/C][C]771.8585[/C][C]0.3515[/C][C]0.4039[/C][C]0.1583[/C][C]0.6204[/C][/ROW]
[ROW][C]368[/C][C]593.1[/C][C]582.5934[/C][C]408.5883[/C][C]756.5985[/C][C]0.4529[/C][C]0.2453[/C][C]0.1471[/C][C]0.4757[/C][/ROW]
[ROW][C]369[/C][C]579.7[/C][C]563.7839[/C][C]375.7355[/C][C]751.8324[/C][C]0.4341[/C][C]0.38[/C][C]0.2024[/C][C]0.4004[/C][/ROW]
[ROW][C]370[/C][C]546[/C][C]541.7675[/C][C]340.5207[/C][C]743.0144[/C][C]0.4836[/C][C]0.3559[/C][C]0.217[/C][C]0.3263[/C][/ROW]
[ROW][C]371[/C][C]562.9[/C][C]560.2588[/C][C]346.5462[/C][C]773.9715[/C][C]0.4903[/C][C]0.552[/C][C]0.2477[/C][C]0.3996[/C][/ROW]
[ROW][C]372[/C][C]572.5[/C][C]546.0112[/C][C]320.4712[/C][C]771.5512[/C][C]0.409[/C][C]0.4417[/C][C]0.3576[/C][C]0.3576[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=196696&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=196696&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[360])
348702.2-------
349784.8-------
350810.9-------
351755.6-------
352656.8-------
353615.1-------
354745.3-------
355694.1-------
356675.7-------
357643.7-------
358622.1-------
359634.6-------
360588-------
361689.7680.2776638.6305721.92470.3287101
362673.9678.8203615.296742.34450.43970.368600.9975
363647.9635.5818549.5679721.59580.38950.19130.00310.8609
364568.8565.1592458.7077671.61070.47330.06380.04580.337
365545.7525.5172400.1266650.90770.37620.24930.08070.1644
366632.6644.3949501.5612787.22870.43570.91220.08310.7805
367643.8612.8733453.8881771.85850.35150.40390.15830.6204
368593.1582.5934408.5883756.59850.45290.24530.14710.4757
369579.7563.7839375.7355751.83240.43410.380.20240.4004
370546541.7675340.5207743.01440.48360.35590.2170.3263
371562.9560.2588346.5462773.97150.49030.5520.24770.3996
372572.5546.0112320.4712771.55120.4090.44170.35760.3576






Univariate ARIMA Extrapolation Forecast Performance
time% S.E.PEMAPESq.EMSERMSE
3610.03120.0139088.78200
3620.0477-0.00720.010524.20956.49557.5164
3630.0690.01940.0135151.737288.24289.3938
3640.09610.00640.011713.255269.49598.3364
3650.12170.03840.0171407.347137.066111.7075
3660.1131-0.01830.0173139.1205137.408511.7221
3670.13240.05050.022956.4598254.415815.9504
3680.15240.0180.0215110.3886236.412415.3757
3690.17020.02820.0223253.3215238.291215.4367
3700.18950.00780.020817.9138216.253514.7056
3710.19460.00470.01946.9757197.228214.0438
3720.21070.04850.0218701.6544239.263715.4682

\begin{tabular}{lllllllll}
\hline
Univariate ARIMA Extrapolation Forecast Performance \tabularnewline
time & % S.E. & PE & MAPE & Sq.E & MSE & RMSE \tabularnewline
361 & 0.0312 & 0.0139 & 0 & 88.782 & 0 & 0 \tabularnewline
362 & 0.0477 & -0.0072 & 0.0105 & 24.209 & 56.4955 & 7.5164 \tabularnewline
363 & 0.069 & 0.0194 & 0.0135 & 151.7372 & 88.2428 & 9.3938 \tabularnewline
364 & 0.0961 & 0.0064 & 0.0117 & 13.2552 & 69.4959 & 8.3364 \tabularnewline
365 & 0.1217 & 0.0384 & 0.0171 & 407.347 & 137.0661 & 11.7075 \tabularnewline
366 & 0.1131 & -0.0183 & 0.0173 & 139.1205 & 137.4085 & 11.7221 \tabularnewline
367 & 0.1324 & 0.0505 & 0.022 & 956.4598 & 254.4158 & 15.9504 \tabularnewline
368 & 0.1524 & 0.018 & 0.0215 & 110.3886 & 236.4124 & 15.3757 \tabularnewline
369 & 0.1702 & 0.0282 & 0.0223 & 253.3215 & 238.2912 & 15.4367 \tabularnewline
370 & 0.1895 & 0.0078 & 0.0208 & 17.9138 & 216.2535 & 14.7056 \tabularnewline
371 & 0.1946 & 0.0047 & 0.0194 & 6.9757 & 197.2282 & 14.0438 \tabularnewline
372 & 0.2107 & 0.0485 & 0.0218 & 701.6544 & 239.2637 & 15.4682 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=196696&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]361[/C][C]0.0312[/C][C]0.0139[/C][C]0[/C][C]88.782[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]362[/C][C]0.0477[/C][C]-0.0072[/C][C]0.0105[/C][C]24.209[/C][C]56.4955[/C][C]7.5164[/C][/ROW]
[ROW][C]363[/C][C]0.069[/C][C]0.0194[/C][C]0.0135[/C][C]151.7372[/C][C]88.2428[/C][C]9.3938[/C][/ROW]
[ROW][C]364[/C][C]0.0961[/C][C]0.0064[/C][C]0.0117[/C][C]13.2552[/C][C]69.4959[/C][C]8.3364[/C][/ROW]
[ROW][C]365[/C][C]0.1217[/C][C]0.0384[/C][C]0.0171[/C][C]407.347[/C][C]137.0661[/C][C]11.7075[/C][/ROW]
[ROW][C]366[/C][C]0.1131[/C][C]-0.0183[/C][C]0.0173[/C][C]139.1205[/C][C]137.4085[/C][C]11.7221[/C][/ROW]
[ROW][C]367[/C][C]0.1324[/C][C]0.0505[/C][C]0.022[/C][C]956.4598[/C][C]254.4158[/C][C]15.9504[/C][/ROW]
[ROW][C]368[/C][C]0.1524[/C][C]0.018[/C][C]0.0215[/C][C]110.3886[/C][C]236.4124[/C][C]15.3757[/C][/ROW]
[ROW][C]369[/C][C]0.1702[/C][C]0.0282[/C][C]0.0223[/C][C]253.3215[/C][C]238.2912[/C][C]15.4367[/C][/ROW]
[ROW][C]370[/C][C]0.1895[/C][C]0.0078[/C][C]0.0208[/C][C]17.9138[/C][C]216.2535[/C][C]14.7056[/C][/ROW]
[ROW][C]371[/C][C]0.1946[/C][C]0.0047[/C][C]0.0194[/C][C]6.9757[/C][C]197.2282[/C][C]14.0438[/C][/ROW]
[ROW][C]372[/C][C]0.2107[/C][C]0.0485[/C][C]0.0218[/C][C]701.6544[/C][C]239.2637[/C][C]15.4682[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=196696&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=196696&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
3610.03120.0139088.78200
3620.0477-0.00720.010524.20956.49557.5164
3630.0690.01940.0135151.737288.24289.3938
3640.09610.00640.011713.255269.49598.3364
3650.12170.03840.0171407.347137.066111.7075
3660.1131-0.01830.0173139.1205137.408511.7221
3670.13240.05050.022956.4598254.415815.9504
3680.15240.0180.0215110.3886236.412415.3757
3690.17020.02820.0223253.3215238.291215.4367
3700.18950.00780.020817.9138216.253514.7056
3710.19460.00470.01946.9757197.228214.0438
3720.21070.04850.0218701.6544239.263715.4682


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 12 ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = 2 ; par7 = 1 ; par8 = 0 ; par9 = 1 ; par10 = FALSE ;
Parameters (R input):
par1 = 12 ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = 2 ; par7 = 1 ; 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')