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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 computationSat, 04 Dec 2010 16:25:58 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/04/t129147984889xpleybxpowl1e.htm/, Retrieved Sat, 04 May 2024 23:20:09 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=105203, Retrieved Sat, 04 May 2024 23:20:09 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact180

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   [Standard Deviation-Mean Plot] [Unemployment] [2010-11-29 10:34:47] [b98453cac15ba1066b407e146608df68]
- RMP     [ARIMA Forecasting] [Unemployment] [2010-11-29 20:46:45] [b98453cac15ba1066b407e146608df68]
-   PD        [ARIMA Forecasting] [WS9 - ARIMA Forec...] [2010-12-04 16:25:58] [934c3727858e074bf543f25f5906ed72] [Current]
-   P           [ARIMA Forecasting] [WS9 - ARIMA Forec...] [2010-12-04 16:58:46] [8ef49741e164ec6343c90c7935194465]
- R  D            [ARIMA Forecasting] [WS 9 - Forecasting] [2010-12-06 21:55:40] [18fa53e8b37a5effc0c5f8a5122cdd2d]
-   PD              [ARIMA Forecasting] [Paper - C&S ARIMA ] [2010-12-21 16:44:16] [18fa53e8b37a5effc0c5f8a5122cdd2d]
-                 [ARIMA Forecasting] [WS 9 arima] [2010-12-07 10:08:07] [8214fe6d084e5ad7598b249a26cc9f06]
-   PD              [ARIMA Forecasting] [paper arima forec...] [2010-12-10 12:43:26] [8214fe6d084e5ad7598b249a26cc9f06]
-   PD                [ARIMA Forecasting] [arima forecasting...] [2010-12-22 20:45:09] [8214fe6d084e5ad7598b249a26cc9f06]
-    D                  [ARIMA Forecasting] [arima forecast la...] [2010-12-22 21:48:20] [8214fe6d084e5ad7598b249a26cc9f06]
-   PD                [ARIMA Forecasting] [arima forecasting...] [2010-12-22 22:14:04] [8214fe6d084e5ad7598b249a26cc9f06]
- R PD            [ARIMA Forecasting] [WS9 - ARIMA Forec...] [2010-12-07 11:26:44] [1f5baf2b24e732d76900bb8178fc04e7]
-                   [ARIMA Forecasting] [WS9 - ARIMA Forec...] [2010-12-07 11:48:16] [1f5baf2b24e732d76900bb8178fc04e7]
- R P                 [ARIMA Forecasting] [Arima Forecasting] [2011-12-06 23:26:48] [19d77e37efa419fdc040c74a96874aff]
- R P                 [ARIMA Forecasting] [Arima Forecasting 13] [2011-12-06 23:30:39] [19d77e37efa419fdc040c74a96874aff]
- R P                 [ARIMA Forecasting] [Arima Forecasting 11] [2011-12-06 23:38:06] [19d77e37efa419fdc040c74a96874aff]
- R P                 [ARIMA Forecasting] [Arima Forecasting 24] [2011-12-06 23:42:39] [19d77e37efa419fdc040c74a96874aff]
-                   [ARIMA Forecasting] [WS9 - ARIMA Forec...] [2010-12-07 11:50:46] [1f5baf2b24e732d76900bb8178fc04e7]
- R PD            [ARIMA Forecasting] [WS9 - ARIMA Forec...] [2010-12-07 11:34:20] [1f5baf2b24e732d76900bb8178fc04e7]
-   P               [ARIMA Forecasting] [] [2010-12-12 15:31:30] [7d64bf19f34ddcdf2626356c9d5bd60d]
-   PD              [ARIMA Forecasting] [Paper - ARIMA For...] [2010-12-14 16:47:42] [1f5baf2b24e732d76900bb8178fc04e7]
-   P             [ARIMA Forecasting] [] [2010-12-13 13:23:59] [1908ef7bb1a3d37a854f5aaad1a1c348]
-   PD            [ARIMA Forecasting] [ARIMA Forecasting...] [2010-12-14 11:24:37] [8ef49741e164ec6343c90c7935194465]
-   P               [ARIMA Forecasting] [ARIMA Forecasting...] [2010-12-19 13:22:59] [8ef49741e164ec6343c90c7935194465]
- R PD            [ARIMA Forecasting] [Paper; ARIMA Fore...] [2010-12-21 16:44:15] [8ffb4cfa64b4677df0d2c448735a40bb]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
167.16
179.84
174.44
180.35
193.17
195.16
202.43
189.91
195.98
212.09
205.81
204.31
196.07
199.98
199.1
198.31
195.72
223.04
238.41
259.73
326.54
335.15
321.81
368.62
369.59
425
439.72
362.23
328.76
348.55
328.18
329.34
295.55
237.38
226.85
220.14
239.36
224.69
230.98
233.47
256.7
253.41
224.95
210.37
191.09
198.85
211.04
206.25
201.19
194.37
191.08
192.87
181.61
157.67
196.14
246.35
271.9

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=105203&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=105203&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=105203&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 time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24






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[45])
33295.55-------
34237.38-------
35226.85-------
36220.14-------
37239.36-------
38224.69-------
39230.98-------
40233.47-------
41256.7-------
42253.41-------
43224.95-------
44210.37-------
45191.09-------
46198.85192.7578147.7596237.75610.39540.5290.0260.529
47211.04198.1646123.8087272.52040.36720.49280.22480.574
48206.25182.404487.3637277.44510.31140.27740.21820.4289
49201.19180.653668.6863292.62090.35960.32710.15210.4275
50194.37162.492835.8412289.14440.31090.27460.16790.329
51191.08156.918817.1169296.72080.3160.29980.14960.3159
52192.87183.642531.8251335.45990.45260.46180.260.4617
53181.61193.555330.606356.50460.44290.50330.22380.5118
54157.67186.925713.5578360.29350.37040.5240.22610.4812
55196.14196.092512.8976379.28740.49980.65950.37880.5213
56246.35196.76234.2414389.28330.30680.50250.44490.523
57271.9209.91368.498411.32920.27320.36150.57270.5727

\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[45]) \tabularnewline
33 & 295.55 & - & - & - & - & - & - & - \tabularnewline
34 & 237.38 & - & - & - & - & - & - & - \tabularnewline
35 & 226.85 & - & - & - & - & - & - & - \tabularnewline
36 & 220.14 & - & - & - & - & - & - & - \tabularnewline
37 & 239.36 & - & - & - & - & - & - & - \tabularnewline
38 & 224.69 & - & - & - & - & - & - & - \tabularnewline
39 & 230.98 & - & - & - & - & - & - & - \tabularnewline
40 & 233.47 & - & - & - & - & - & - & - \tabularnewline
41 & 256.7 & - & - & - & - & - & - & - \tabularnewline
42 & 253.41 & - & - & - & - & - & - & - \tabularnewline
43 & 224.95 & - & - & - & - & - & - & - \tabularnewline
44 & 210.37 & - & - & - & - & - & - & - \tabularnewline
45 & 191.09 & - & - & - & - & - & - & - \tabularnewline
46 & 198.85 & 192.7578 & 147.7596 & 237.7561 & 0.3954 & 0.529 & 0.026 & 0.529 \tabularnewline
47 & 211.04 & 198.1646 & 123.8087 & 272.5204 & 0.3672 & 0.4928 & 0.2248 & 0.574 \tabularnewline
48 & 206.25 & 182.4044 & 87.3637 & 277.4451 & 0.3114 & 0.2774 & 0.2182 & 0.4289 \tabularnewline
49 & 201.19 & 180.6536 & 68.6863 & 292.6209 & 0.3596 & 0.3271 & 0.1521 & 0.4275 \tabularnewline
50 & 194.37 & 162.4928 & 35.8412 & 289.1444 & 0.3109 & 0.2746 & 0.1679 & 0.329 \tabularnewline
51 & 191.08 & 156.9188 & 17.1169 & 296.7208 & 0.316 & 0.2998 & 0.1496 & 0.3159 \tabularnewline
52 & 192.87 & 183.6425 & 31.8251 & 335.4599 & 0.4526 & 0.4618 & 0.26 & 0.4617 \tabularnewline
53 & 181.61 & 193.5553 & 30.606 & 356.5046 & 0.4429 & 0.5033 & 0.2238 & 0.5118 \tabularnewline
54 & 157.67 & 186.9257 & 13.5578 & 360.2935 & 0.3704 & 0.524 & 0.2261 & 0.4812 \tabularnewline
55 & 196.14 & 196.0925 & 12.8976 & 379.2874 & 0.4998 & 0.6595 & 0.3788 & 0.5213 \tabularnewline
56 & 246.35 & 196.7623 & 4.2414 & 389.2833 & 0.3068 & 0.5025 & 0.4449 & 0.523 \tabularnewline
57 & 271.9 & 209.9136 & 8.498 & 411.3292 & 0.2732 & 0.3615 & 0.5727 & 0.5727 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=105203&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[45])[/C][/ROW]
[ROW][C]33[/C][C]295.55[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]34[/C][C]237.38[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]35[/C][C]226.85[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]36[/C][C]220.14[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]37[/C][C]239.36[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]38[/C][C]224.69[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]39[/C][C]230.98[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]40[/C][C]233.47[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]41[/C][C]256.7[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]42[/C][C]253.41[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]43[/C][C]224.95[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]44[/C][C]210.37[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]45[/C][C]191.09[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]46[/C][C]198.85[/C][C]192.7578[/C][C]147.7596[/C][C]237.7561[/C][C]0.3954[/C][C]0.529[/C][C]0.026[/C][C]0.529[/C][/ROW]
[ROW][C]47[/C][C]211.04[/C][C]198.1646[/C][C]123.8087[/C][C]272.5204[/C][C]0.3672[/C][C]0.4928[/C][C]0.2248[/C][C]0.574[/C][/ROW]
[ROW][C]48[/C][C]206.25[/C][C]182.4044[/C][C]87.3637[/C][C]277.4451[/C][C]0.3114[/C][C]0.2774[/C][C]0.2182[/C][C]0.4289[/C][/ROW]
[ROW][C]49[/C][C]201.19[/C][C]180.6536[/C][C]68.6863[/C][C]292.6209[/C][C]0.3596[/C][C]0.3271[/C][C]0.1521[/C][C]0.4275[/C][/ROW]
[ROW][C]50[/C][C]194.37[/C][C]162.4928[/C][C]35.8412[/C][C]289.1444[/C][C]0.3109[/C][C]0.2746[/C][C]0.1679[/C][C]0.329[/C][/ROW]
[ROW][C]51[/C][C]191.08[/C][C]156.9188[/C][C]17.1169[/C][C]296.7208[/C][C]0.316[/C][C]0.2998[/C][C]0.1496[/C][C]0.3159[/C][/ROW]
[ROW][C]52[/C][C]192.87[/C][C]183.6425[/C][C]31.8251[/C][C]335.4599[/C][C]0.4526[/C][C]0.4618[/C][C]0.26[/C][C]0.4617[/C][/ROW]
[ROW][C]53[/C][C]181.61[/C][C]193.5553[/C][C]30.606[/C][C]356.5046[/C][C]0.4429[/C][C]0.5033[/C][C]0.2238[/C][C]0.5118[/C][/ROW]
[ROW][C]54[/C][C]157.67[/C][C]186.9257[/C][C]13.5578[/C][C]360.2935[/C][C]0.3704[/C][C]0.524[/C][C]0.2261[/C][C]0.4812[/C][/ROW]
[ROW][C]55[/C][C]196.14[/C][C]196.0925[/C][C]12.8976[/C][C]379.2874[/C][C]0.4998[/C][C]0.6595[/C][C]0.3788[/C][C]0.5213[/C][/ROW]
[ROW][C]56[/C][C]246.35[/C][C]196.7623[/C][C]4.2414[/C][C]389.2833[/C][C]0.3068[/C][C]0.5025[/C][C]0.4449[/C][C]0.523[/C][/ROW]
[ROW][C]57[/C][C]271.9[/C][C]209.9136[/C][C]8.498[/C][C]411.3292[/C][C]0.2732[/C][C]0.3615[/C][C]0.5727[/C][C]0.5727[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=105203&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=105203&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[45])
33295.55-------
34237.38-------
35226.85-------
36220.14-------
37239.36-------
38224.69-------
39230.98-------
40233.47-------
41256.7-------
42253.41-------
43224.95-------
44210.37-------
45191.09-------
46198.85192.7578147.7596237.75610.39540.5290.0260.529
47211.04198.1646123.8087272.52040.36720.49280.22480.574
48206.25182.404487.3637277.44510.31140.27740.21820.4289
49201.19180.653668.6863292.62090.35960.32710.15210.4275
50194.37162.492835.8412289.14440.31090.27460.16790.329
51191.08156.918817.1169296.72080.3160.29980.14960.3159
52192.87183.642531.8251335.45990.45260.46180.260.4617
53181.61193.555330.606356.50460.44290.50330.22380.5118
54157.67186.925713.5578360.29350.37040.5240.22610.4812
55196.14196.092512.8976379.28740.49980.65950.37880.5213
56246.35196.76234.2414389.28330.30680.50250.44490.523
57271.9209.91368.498411.32920.27320.36150.57270.5727






Univariate ARIMA Extrapolation Forecast Performance
time% S.E.PEMAPESq.EMSERMSE
460.11910.0316037.114400
470.19140.0650.0483165.777101.445710.072
480.26580.13070.0758568.6142257.168516.0365
490.31620.11370.0852421.7445298.312517.2717
500.39770.19620.10741016.1551441.88121.021
510.45460.21770.12581166.9843562.731623.722
520.42180.05020.11585.1466494.505222.2375
530.4295-0.06170.1084142.6905450.528321.2257
540.4732-0.15650.1137855.8943495.56922.2614
550.47662e-040.10240.0023446.012321.119
560.49920.2520.1162458.9386629.005625.08
570.48950.29530.13093842.3139896.781329.9463

\begin{tabular}{lllllllll}
\hline
Univariate ARIMA Extrapolation Forecast Performance \tabularnewline
time & % S.E. & PE & MAPE & Sq.E & MSE & RMSE \tabularnewline
46 & 0.1191 & 0.0316 & 0 & 37.1144 & 0 & 0 \tabularnewline
47 & 0.1914 & 0.065 & 0.0483 & 165.777 & 101.4457 & 10.072 \tabularnewline
48 & 0.2658 & 0.1307 & 0.0758 & 568.6142 & 257.1685 & 16.0365 \tabularnewline
49 & 0.3162 & 0.1137 & 0.0852 & 421.7445 & 298.3125 & 17.2717 \tabularnewline
50 & 0.3977 & 0.1962 & 0.1074 & 1016.1551 & 441.881 & 21.021 \tabularnewline
51 & 0.4546 & 0.2177 & 0.1258 & 1166.9843 & 562.7316 & 23.722 \tabularnewline
52 & 0.4218 & 0.0502 & 0.115 & 85.1466 & 494.5052 & 22.2375 \tabularnewline
53 & 0.4295 & -0.0617 & 0.1084 & 142.6905 & 450.5283 & 21.2257 \tabularnewline
54 & 0.4732 & -0.1565 & 0.1137 & 855.8943 & 495.569 & 22.2614 \tabularnewline
55 & 0.4766 & 2e-04 & 0.1024 & 0.0023 & 446.0123 & 21.119 \tabularnewline
56 & 0.4992 & 0.252 & 0.116 & 2458.9386 & 629.0056 & 25.08 \tabularnewline
57 & 0.4895 & 0.2953 & 0.1309 & 3842.3139 & 896.7813 & 29.9463 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=105203&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]46[/C][C]0.1191[/C][C]0.0316[/C][C]0[/C][C]37.1144[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]47[/C][C]0.1914[/C][C]0.065[/C][C]0.0483[/C][C]165.777[/C][C]101.4457[/C][C]10.072[/C][/ROW]
[ROW][C]48[/C][C]0.2658[/C][C]0.1307[/C][C]0.0758[/C][C]568.6142[/C][C]257.1685[/C][C]16.0365[/C][/ROW]
[ROW][C]49[/C][C]0.3162[/C][C]0.1137[/C][C]0.0852[/C][C]421.7445[/C][C]298.3125[/C][C]17.2717[/C][/ROW]
[ROW][C]50[/C][C]0.3977[/C][C]0.1962[/C][C]0.1074[/C][C]1016.1551[/C][C]441.881[/C][C]21.021[/C][/ROW]
[ROW][C]51[/C][C]0.4546[/C][C]0.2177[/C][C]0.1258[/C][C]1166.9843[/C][C]562.7316[/C][C]23.722[/C][/ROW]
[ROW][C]52[/C][C]0.4218[/C][C]0.0502[/C][C]0.115[/C][C]85.1466[/C][C]494.5052[/C][C]22.2375[/C][/ROW]
[ROW][C]53[/C][C]0.4295[/C][C]-0.0617[/C][C]0.1084[/C][C]142.6905[/C][C]450.5283[/C][C]21.2257[/C][/ROW]
[ROW][C]54[/C][C]0.4732[/C][C]-0.1565[/C][C]0.1137[/C][C]855.8943[/C][C]495.569[/C][C]22.2614[/C][/ROW]
[ROW][C]55[/C][C]0.4766[/C][C]2e-04[/C][C]0.1024[/C][C]0.0023[/C][C]446.0123[/C][C]21.119[/C][/ROW]
[ROW][C]56[/C][C]0.4992[/C][C]0.252[/C][C]0.116[/C][C]2458.9386[/C][C]629.0056[/C][C]25.08[/C][/ROW]
[ROW][C]57[/C][C]0.4895[/C][C]0.2953[/C][C]0.1309[/C][C]3842.3139[/C][C]896.7813[/C][C]29.9463[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=105203&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=105203&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
460.11910.0316037.114400
470.19140.0650.0483165.777101.445710.072
480.26580.13070.0758568.6142257.168516.0365
490.31620.11370.0852421.7445298.312517.2717
500.39770.19620.10741016.1551441.88121.021
510.45460.21770.12581166.9843562.731623.722
520.42180.05020.11585.1466494.505222.2375
530.4295-0.06170.1084142.6905450.528321.2257
540.4732-0.15650.1137855.8943495.56922.2614
550.47662e-040.10240.0023446.012321.119
560.49920.2520.1162458.9386629.005625.08
570.48950.29530.13093842.3139896.781329.9463


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = FALSE ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = 3 ; par7 = 1 ; par8 = 2 ; par9 = 1 ;
Parameters (R input):
par1 = 12 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = 0 ; par7 = 1 ; par8 = 2 ; par9 = 0 ; 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')