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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, 21 Dec 2009 14:37:13 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Dec/21/t12614314679zp20dewcp96t4u.htm/, Retrieved Sun, 05 May 2024 09:07:14 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=70401, Retrieved Sun, 05 May 2024 09:07:14 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact95

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Bivariate Data Series] [Bivariate dataset] [2008-01-05 23:51:08] [74be16979710d4c4e7c6647856088456]
F RMPD  [Univariate Explorative Data Analysis] [Colombia Coffee] [2008-01-07 14:21:11] [74be16979710d4c4e7c6647856088456]
F RMPD    [Univariate Data Series] [] [2009-10-14 08:30:28] [74be16979710d4c4e7c6647856088456]
- RMPD        [ARIMA Forecasting] [Paper] [2009-12-21 21:37:13] [e339dd08bcbfc073ac7494f09a949034] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
17,7
17,1
16,4
16
15,6
14,9
13,7
12,8
11,9
11,6
13,9
16,5
16,8
16,4
15,6
15,1
14,7
14,1
13,2
12,3
11,6
11,2
13,3
15,8
16,3
16,1
15,6
15,2
15
14,4
13,5
12,8
12,3
12,2
14,5
17,2
18
18,1
18
18,3
18,7
18,6
18,3
17,9
17,4
17,4
20,1
23,2
24,2
24,2
23,9
23,8
23,8
23,3
22,4
21,5
20,5
19,9
22
24,9
25,7
25,3
24,4
23,8
23,5
23
22,2
21,4
20,3
19,5
21,7
24,7
25,3
24,9
24,1
23,4
23,1
22,4
21,3
20,3
19,3
18,7
21
24
24,8
24,2
23,3
22,7
22,3
21,8
21,2
20,5
19,7
19,2
21,2
23,9
24,8
24,2
23
22,2
21,8
21,2
20,5
19,7
19
18,4
20,7
24,5
26
25,2
24,1
23,7
23,5
23,1
22,7
22,5
21,7
20,5
21,9
22,9
21,5
19
17
16,1
15,9
15,7
15,1
14,8
14,3
14,5
18,9
21,6
20,4
17,9
15,7
14,5
14
13,9
14,4
15,8
15,6
14,7
16,7
17,9
18,7
20,1
19,5
19,4
18,6
17,8
17,1
16,5
15,5
14,9
18,6
19,1
18,8
18,2
18
19
20,7
21,2
20,7
19,6
18,6
18,7
23,8
24,9
24,8
23,8
22,3
21,7
20,7
19,7
18,4
17,4
17
18
23,8
25,5
25,6
23,7
22
21,3
20,7
20,4
20,3
20,4
19,8
19,5
23,1
23,5
23,5
22,9
21,9
21,5
20,5
20,2
19,4
19,2
18,8
18,8
22,6
23,3
23
21,4
19,9
18,8
18,6
18,4
18,6
19,9
19,2
18,4
21,1
20,5
19,1
18,1
17
17,1
17,4
16,8
15,3
14,3
13,4
15,3
22,1
23,7
22,2
19,5
16,6
17,3
19,8
21,2
21,5
20,6
19,1
19,6
23,5
24

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' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70401&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' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=70401&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70401&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' @ 72.249.127.135






Univariate ARIMA Extrapolation Forecast
timeY[t]F[t]95% LB95% UBp-value(H0: Y[t] = F[t])P(F[t]>Y[t-1])P(F[t]>Y[t-s])P(F[t]>Y[228])
21620.5-------
21719.1-------
21818.1-------
21917-------
22017.1-------
22117.4-------
22216.8-------
22315.3-------
22414.3-------
22513.4-------
22615.3-------
22722.1-------
22823.7-------
22922.222.597821.492223.70350.24030.025410.0254
23019.520.104817.751222.45840.30730.04050.95250.0014
23116.617.469313.978820.95980.31270.12710.60392e-04
23217.316.358812.056720.66090.3340.45630.36784e-04
23319.816.467711.66521.27030.08690.3670.35180.0016
23421.216.493911.385621.60210.03550.10230.45320.0028
23521.516.160210.826721.49380.02490.0320.6240.0028
23620.616.314510.759821.86910.06520.03360.76140.0046
23719.115.52369.712521.33460.11390.04340.76310.0029
23819.616.302710.195422.410.1450.18470.62620.0088
23923.521.442515.02227.86310.2650.71310.42050.2454
2402422.128215.405428.8510.29260.34460.32340.3234

\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[228]) \tabularnewline
216 & 20.5 & - & - & - & - & - & - & - \tabularnewline
217 & 19.1 & - & - & - & - & - & - & - \tabularnewline
218 & 18.1 & - & - & - & - & - & - & - \tabularnewline
219 & 17 & - & - & - & - & - & - & - \tabularnewline
220 & 17.1 & - & - & - & - & - & - & - \tabularnewline
221 & 17.4 & - & - & - & - & - & - & - \tabularnewline
222 & 16.8 & - & - & - & - & - & - & - \tabularnewline
223 & 15.3 & - & - & - & - & - & - & - \tabularnewline
224 & 14.3 & - & - & - & - & - & - & - \tabularnewline
225 & 13.4 & - & - & - & - & - & - & - \tabularnewline
226 & 15.3 & - & - & - & - & - & - & - \tabularnewline
227 & 22.1 & - & - & - & - & - & - & - \tabularnewline
228 & 23.7 & - & - & - & - & - & - & - \tabularnewline
229 & 22.2 & 22.5978 & 21.4922 & 23.7035 & 0.2403 & 0.0254 & 1 & 0.0254 \tabularnewline
230 & 19.5 & 20.1048 & 17.7512 & 22.4584 & 0.3073 & 0.0405 & 0.9525 & 0.0014 \tabularnewline
231 & 16.6 & 17.4693 & 13.9788 & 20.9598 & 0.3127 & 0.1271 & 0.6039 & 2e-04 \tabularnewline
232 & 17.3 & 16.3588 & 12.0567 & 20.6609 & 0.334 & 0.4563 & 0.3678 & 4e-04 \tabularnewline
233 & 19.8 & 16.4677 & 11.665 & 21.2703 & 0.0869 & 0.367 & 0.3518 & 0.0016 \tabularnewline
234 & 21.2 & 16.4939 & 11.3856 & 21.6021 & 0.0355 & 0.1023 & 0.4532 & 0.0028 \tabularnewline
235 & 21.5 & 16.1602 & 10.8267 & 21.4938 & 0.0249 & 0.032 & 0.624 & 0.0028 \tabularnewline
236 & 20.6 & 16.3145 & 10.7598 & 21.8691 & 0.0652 & 0.0336 & 0.7614 & 0.0046 \tabularnewline
237 & 19.1 & 15.5236 & 9.7125 & 21.3346 & 0.1139 & 0.0434 & 0.7631 & 0.0029 \tabularnewline
238 & 19.6 & 16.3027 & 10.1954 & 22.41 & 0.145 & 0.1847 & 0.6262 & 0.0088 \tabularnewline
239 & 23.5 & 21.4425 & 15.022 & 27.8631 & 0.265 & 0.7131 & 0.4205 & 0.2454 \tabularnewline
240 & 24 & 22.1282 & 15.4054 & 28.851 & 0.2926 & 0.3446 & 0.3234 & 0.3234 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70401&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[228])[/C][/ROW]
[ROW][C]216[/C][C]20.5[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]217[/C][C]19.1[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]218[/C][C]18.1[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]219[/C][C]17[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]220[/C][C]17.1[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]221[/C][C]17.4[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]222[/C][C]16.8[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]223[/C][C]15.3[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]224[/C][C]14.3[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]225[/C][C]13.4[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]226[/C][C]15.3[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]227[/C][C]22.1[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]228[/C][C]23.7[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]229[/C][C]22.2[/C][C]22.5978[/C][C]21.4922[/C][C]23.7035[/C][C]0.2403[/C][C]0.0254[/C][C]1[/C][C]0.0254[/C][/ROW]
[ROW][C]230[/C][C]19.5[/C][C]20.1048[/C][C]17.7512[/C][C]22.4584[/C][C]0.3073[/C][C]0.0405[/C][C]0.9525[/C][C]0.0014[/C][/ROW]
[ROW][C]231[/C][C]16.6[/C][C]17.4693[/C][C]13.9788[/C][C]20.9598[/C][C]0.3127[/C][C]0.1271[/C][C]0.6039[/C][C]2e-04[/C][/ROW]
[ROW][C]232[/C][C]17.3[/C][C]16.3588[/C][C]12.0567[/C][C]20.6609[/C][C]0.334[/C][C]0.4563[/C][C]0.3678[/C][C]4e-04[/C][/ROW]
[ROW][C]233[/C][C]19.8[/C][C]16.4677[/C][C]11.665[/C][C]21.2703[/C][C]0.0869[/C][C]0.367[/C][C]0.3518[/C][C]0.0016[/C][/ROW]
[ROW][C]234[/C][C]21.2[/C][C]16.4939[/C][C]11.3856[/C][C]21.6021[/C][C]0.0355[/C][C]0.1023[/C][C]0.4532[/C][C]0.0028[/C][/ROW]
[ROW][C]235[/C][C]21.5[/C][C]16.1602[/C][C]10.8267[/C][C]21.4938[/C][C]0.0249[/C][C]0.032[/C][C]0.624[/C][C]0.0028[/C][/ROW]
[ROW][C]236[/C][C]20.6[/C][C]16.3145[/C][C]10.7598[/C][C]21.8691[/C][C]0.0652[/C][C]0.0336[/C][C]0.7614[/C][C]0.0046[/C][/ROW]
[ROW][C]237[/C][C]19.1[/C][C]15.5236[/C][C]9.7125[/C][C]21.3346[/C][C]0.1139[/C][C]0.0434[/C][C]0.7631[/C][C]0.0029[/C][/ROW]
[ROW][C]238[/C][C]19.6[/C][C]16.3027[/C][C]10.1954[/C][C]22.41[/C][C]0.145[/C][C]0.1847[/C][C]0.6262[/C][C]0.0088[/C][/ROW]
[ROW][C]239[/C][C]23.5[/C][C]21.4425[/C][C]15.022[/C][C]27.8631[/C][C]0.265[/C][C]0.7131[/C][C]0.4205[/C][C]0.2454[/C][/ROW]
[ROW][C]240[/C][C]24[/C][C]22.1282[/C][C]15.4054[/C][C]28.851[/C][C]0.2926[/C][C]0.3446[/C][C]0.3234[/C][C]0.3234[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=70401&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70401&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[228])
21620.5-------
21719.1-------
21818.1-------
21917-------
22017.1-------
22117.4-------
22216.8-------
22315.3-------
22414.3-------
22513.4-------
22615.3-------
22722.1-------
22823.7-------
22922.222.597821.492223.70350.24030.025410.0254
23019.520.104817.751222.45840.30730.04050.95250.0014
23116.617.469313.978820.95980.31270.12710.60392e-04
23217.316.358812.056720.66090.3340.45630.36784e-04
23319.816.467711.66521.27030.08690.3670.35180.0016
23421.216.493911.385621.60210.03550.10230.45320.0028
23521.516.160210.826721.49380.02490.0320.6240.0028
23620.616.314510.759821.86910.06520.03360.76140.0046
23719.115.52369.712521.33460.11390.04340.76310.0029
23819.616.302710.195422.410.1450.18470.62620.0088
23923.521.442515.02227.86310.2650.71310.42050.2454
2402422.128215.405428.8510.29260.34460.32340.3234






Univariate ARIMA Extrapolation Forecast Performance
time% S.E.PEMAPESq.EMSERMSE
2290.025-0.017600.158300
2300.0597-0.03010.02380.36580.2620.5119
2310.1019-0.04980.03250.75570.42660.6531
2320.13420.05750.03870.88580.54140.7358
2330.14880.20240.071511.10452.6541.6291
2340.1580.28530.107122.14765.90292.4296
2350.16840.33040.13928.5139.13293.0221
2360.17370.26270.154518.365710.2873.2073
2370.1910.23040.162912.790910.56523.2504
2380.19110.20230.166810.872210.59593.2551
2390.15280.0960.16044.233210.01753.165
2400.1550.08460.15413.50369.47473.0781

\begin{tabular}{lllllllll}
\hline
Univariate ARIMA Extrapolation Forecast Performance \tabularnewline
time & % S.E. & PE & MAPE & Sq.E & MSE & RMSE \tabularnewline
229 & 0.025 & -0.0176 & 0 & 0.1583 & 0 & 0 \tabularnewline
230 & 0.0597 & -0.0301 & 0.0238 & 0.3658 & 0.262 & 0.5119 \tabularnewline
231 & 0.1019 & -0.0498 & 0.0325 & 0.7557 & 0.4266 & 0.6531 \tabularnewline
232 & 0.1342 & 0.0575 & 0.0387 & 0.8858 & 0.5414 & 0.7358 \tabularnewline
233 & 0.1488 & 0.2024 & 0.0715 & 11.1045 & 2.654 & 1.6291 \tabularnewline
234 & 0.158 & 0.2853 & 0.1071 & 22.1476 & 5.9029 & 2.4296 \tabularnewline
235 & 0.1684 & 0.3304 & 0.139 & 28.513 & 9.1329 & 3.0221 \tabularnewline
236 & 0.1737 & 0.2627 & 0.1545 & 18.3657 & 10.287 & 3.2073 \tabularnewline
237 & 0.191 & 0.2304 & 0.1629 & 12.7909 & 10.5652 & 3.2504 \tabularnewline
238 & 0.1911 & 0.2023 & 0.1668 & 10.8722 & 10.5959 & 3.2551 \tabularnewline
239 & 0.1528 & 0.096 & 0.1604 & 4.2332 & 10.0175 & 3.165 \tabularnewline
240 & 0.155 & 0.0846 & 0.1541 & 3.5036 & 9.4747 & 3.0781 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70401&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]229[/C][C]0.025[/C][C]-0.0176[/C][C]0[/C][C]0.1583[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]230[/C][C]0.0597[/C][C]-0.0301[/C][C]0.0238[/C][C]0.3658[/C][C]0.262[/C][C]0.5119[/C][/ROW]
[ROW][C]231[/C][C]0.1019[/C][C]-0.0498[/C][C]0.0325[/C][C]0.7557[/C][C]0.4266[/C][C]0.6531[/C][/ROW]
[ROW][C]232[/C][C]0.1342[/C][C]0.0575[/C][C]0.0387[/C][C]0.8858[/C][C]0.5414[/C][C]0.7358[/C][/ROW]
[ROW][C]233[/C][C]0.1488[/C][C]0.2024[/C][C]0.0715[/C][C]11.1045[/C][C]2.654[/C][C]1.6291[/C][/ROW]
[ROW][C]234[/C][C]0.158[/C][C]0.2853[/C][C]0.1071[/C][C]22.1476[/C][C]5.9029[/C][C]2.4296[/C][/ROW]
[ROW][C]235[/C][C]0.1684[/C][C]0.3304[/C][C]0.139[/C][C]28.513[/C][C]9.1329[/C][C]3.0221[/C][/ROW]
[ROW][C]236[/C][C]0.1737[/C][C]0.2627[/C][C]0.1545[/C][C]18.3657[/C][C]10.287[/C][C]3.2073[/C][/ROW]
[ROW][C]237[/C][C]0.191[/C][C]0.2304[/C][C]0.1629[/C][C]12.7909[/C][C]10.5652[/C][C]3.2504[/C][/ROW]
[ROW][C]238[/C][C]0.1911[/C][C]0.2023[/C][C]0.1668[/C][C]10.8722[/C][C]10.5959[/C][C]3.2551[/C][/ROW]
[ROW][C]239[/C][C]0.1528[/C][C]0.096[/C][C]0.1604[/C][C]4.2332[/C][C]10.0175[/C][C]3.165[/C][/ROW]
[ROW][C]240[/C][C]0.155[/C][C]0.0846[/C][C]0.1541[/C][C]3.5036[/C][C]9.4747[/C][C]3.0781[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=70401&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70401&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
2290.025-0.017600.158300
2300.0597-0.03010.02380.36580.2620.5119
2310.1019-0.04980.03250.75570.42660.6531
2320.13420.05750.03870.88580.54140.7358
2330.14880.20240.071511.10452.6541.6291
2340.1580.28530.107122.14765.90292.4296
2350.16840.33040.13928.5139.13293.0221
2360.17370.26270.154518.365710.2873.2073
2370.1910.23040.162912.790910.56523.2504
2380.19110.20230.166810.872210.59593.2551
2390.15280.0960.16044.233210.01753.165
2400.1550.08460.15413.50369.47473.0781


Figures (Output of Computation)

Input Parameters & R Code

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