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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, 20 Dec 2010 15:06:20 +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/20/t1292857445l5atidfjh0feaz3.htm/, Retrieved Sat, 04 May 2024 05:23:56 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=112988, Retrieved Sat, 04 May 2024 05:23:56 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact143

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] [test 7] [2010-12-05 11:13:06] [74be16979710d4c4e7c6647856088456]
-   P         [ARIMA Forecasting] [W9 - Blog 9] [2010-12-06 16:23:47] [1aa8d85d6b335d32b1f6be940e33a166]
-   PD            [ARIMA Forecasting] [ARIMA forecast Li...] [2010-12-20 15:06:20] [47bfda5353cd53c1cf7ea7aa9038654a] [Current]
- RMPD              [Mean Plot] [Mean plot Jenever] [2010-12-20 15:10:29] [1aa8d85d6b335d32b1f6be940e33a166]
- RMPD              [Mean Plot] [Mean plot Whisky] [2010-12-20 15:15:47] [1aa8d85d6b335d32b1f6be940e33a166]
- RMP               [Mean Plot] [Mean plot Likeur] [2010-12-20 15:17:56] [1aa8d85d6b335d32b1f6be940e33a166]
- RMPD              [Bivariate Kernel Density Estimation] [Bivariate Kernell...] [2010-12-20 15:24:35] [1aa8d85d6b335d32b1f6be940e33a166]
- RMPD              [Bivariate Kernel Density Estimation] [Bivariate Kernell...] [2010-12-20 15:27:48] [1aa8d85d6b335d32b1f6be940e33a166]
- RMPD              [Bivariate Kernel Density Estimation] [Bivariate Kernell...] [2010-12-20 15:30:25] [1aa8d85d6b335d32b1f6be940e33a166]
-   PD              [ARIMA Forecasting] [ARIMA forecast Wh...] [2010-12-21 14:41:20] [1aa8d85d6b335d32b1f6be940e33a166]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
25,00
25,09
25,03
25,21
25,33
25,23
25,13
25,03
25,03
25,15
25,18
24,90
25,18
25,25
25,28
25,32
25,27
25,22
25,14
25,41
25,72
25,66
25,65
25,27
23,90
24,06
24,33
24,39
24,39
24,49
24,83
25,08
25,11
25,13
25,17
25,11
25,35
25,36
25,35
25,34
25,39
25,58
25,71
25,66
25,74
25,73
25,72
25,55
25,71
25,92
25,93
26,00
26,02
26,08
26,17
26,18
26,21
26,28
26,34
26,17
26,38
26,36
26,27
26,26
26,49
26,99
27,14
27,10
27,01
26,93
26,97
26,35
26,93

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'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112988&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112988&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112988&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'George Udny Yule' @ 72.249.76.132






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[61])
4925.71-------
5025.92-------
5125.93-------
5226-------
5326.02-------
5426.08-------
5526.17-------
5626.18-------
5726.21-------
5826.28-------
5926.34-------
6026.17-------
6126.38-------
6226.3626.471826.048626.8950.30230.66460.99470.6646
6326.2726.399725.738527.0610.35030.54690.91810.5233
6426.2626.456325.661227.25140.31420.6770.86970.5746
6526.4926.411925.47627.34780.4350.62480.79410.5266
6626.9926.446825.407127.48640.15290.46750.75540.5501
6727.1426.419425.272227.56660.10910.16480.6650.5268
6827.126.440925.20527.67670.14790.13380.66050.5385
6927.0126.42425.098427.74960.19310.15880.62420.5259
7026.9326.437325.032827.84170.24580.21210.58690.5318
7126.9726.426924.943927.90980.23640.2530.54570.5247
7226.3526.43524.880427.98960.45730.250.63090.5277
7326.9326.428624.803328.05390.27270.53780.52340.5234

\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[61]) \tabularnewline
49 & 25.71 & - & - & - & - & - & - & - \tabularnewline
50 & 25.92 & - & - & - & - & - & - & - \tabularnewline
51 & 25.93 & - & - & - & - & - & - & - \tabularnewline
52 & 26 & - & - & - & - & - & - & - \tabularnewline
53 & 26.02 & - & - & - & - & - & - & - \tabularnewline
54 & 26.08 & - & - & - & - & - & - & - \tabularnewline
55 & 26.17 & - & - & - & - & - & - & - \tabularnewline
56 & 26.18 & - & - & - & - & - & - & - \tabularnewline
57 & 26.21 & - & - & - & - & - & - & - \tabularnewline
58 & 26.28 & - & - & - & - & - & - & - \tabularnewline
59 & 26.34 & - & - & - & - & - & - & - \tabularnewline
60 & 26.17 & - & - & - & - & - & - & - \tabularnewline
61 & 26.38 & - & - & - & - & - & - & - \tabularnewline
62 & 26.36 & 26.4718 & 26.0486 & 26.895 & 0.3023 & 0.6646 & 0.9947 & 0.6646 \tabularnewline
63 & 26.27 & 26.3997 & 25.7385 & 27.061 & 0.3503 & 0.5469 & 0.9181 & 0.5233 \tabularnewline
64 & 26.26 & 26.4563 & 25.6612 & 27.2514 & 0.3142 & 0.677 & 0.8697 & 0.5746 \tabularnewline
65 & 26.49 & 26.4119 & 25.476 & 27.3478 & 0.435 & 0.6248 & 0.7941 & 0.5266 \tabularnewline
66 & 26.99 & 26.4468 & 25.4071 & 27.4864 & 0.1529 & 0.4675 & 0.7554 & 0.5501 \tabularnewline
67 & 27.14 & 26.4194 & 25.2722 & 27.5666 & 0.1091 & 0.1648 & 0.665 & 0.5268 \tabularnewline
68 & 27.1 & 26.4409 & 25.205 & 27.6767 & 0.1479 & 0.1338 & 0.6605 & 0.5385 \tabularnewline
69 & 27.01 & 26.424 & 25.0984 & 27.7496 & 0.1931 & 0.1588 & 0.6242 & 0.5259 \tabularnewline
70 & 26.93 & 26.4373 & 25.0328 & 27.8417 & 0.2458 & 0.2121 & 0.5869 & 0.5318 \tabularnewline
71 & 26.97 & 26.4269 & 24.9439 & 27.9098 & 0.2364 & 0.253 & 0.5457 & 0.5247 \tabularnewline
72 & 26.35 & 26.435 & 24.8804 & 27.9896 & 0.4573 & 0.25 & 0.6309 & 0.5277 \tabularnewline
73 & 26.93 & 26.4286 & 24.8033 & 28.0539 & 0.2727 & 0.5378 & 0.5234 & 0.5234 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112988&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[61])[/C][/ROW]
[ROW][C]49[/C][C]25.71[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]50[/C][C]25.92[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]51[/C][C]25.93[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]52[/C][C]26[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]53[/C][C]26.02[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]54[/C][C]26.08[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]55[/C][C]26.17[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]56[/C][C]26.18[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]57[/C][C]26.21[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]58[/C][C]26.28[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]59[/C][C]26.34[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]60[/C][C]26.17[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]61[/C][C]26.38[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]62[/C][C]26.36[/C][C]26.4718[/C][C]26.0486[/C][C]26.895[/C][C]0.3023[/C][C]0.6646[/C][C]0.9947[/C][C]0.6646[/C][/ROW]
[ROW][C]63[/C][C]26.27[/C][C]26.3997[/C][C]25.7385[/C][C]27.061[/C][C]0.3503[/C][C]0.5469[/C][C]0.9181[/C][C]0.5233[/C][/ROW]
[ROW][C]64[/C][C]26.26[/C][C]26.4563[/C][C]25.6612[/C][C]27.2514[/C][C]0.3142[/C][C]0.677[/C][C]0.8697[/C][C]0.5746[/C][/ROW]
[ROW][C]65[/C][C]26.49[/C][C]26.4119[/C][C]25.476[/C][C]27.3478[/C][C]0.435[/C][C]0.6248[/C][C]0.7941[/C][C]0.5266[/C][/ROW]
[ROW][C]66[/C][C]26.99[/C][C]26.4468[/C][C]25.4071[/C][C]27.4864[/C][C]0.1529[/C][C]0.4675[/C][C]0.7554[/C][C]0.5501[/C][/ROW]
[ROW][C]67[/C][C]27.14[/C][C]26.4194[/C][C]25.2722[/C][C]27.5666[/C][C]0.1091[/C][C]0.1648[/C][C]0.665[/C][C]0.5268[/C][/ROW]
[ROW][C]68[/C][C]27.1[/C][C]26.4409[/C][C]25.205[/C][C]27.6767[/C][C]0.1479[/C][C]0.1338[/C][C]0.6605[/C][C]0.5385[/C][/ROW]
[ROW][C]69[/C][C]27.01[/C][C]26.424[/C][C]25.0984[/C][C]27.7496[/C][C]0.1931[/C][C]0.1588[/C][C]0.6242[/C][C]0.5259[/C][/ROW]
[ROW][C]70[/C][C]26.93[/C][C]26.4373[/C][C]25.0328[/C][C]27.8417[/C][C]0.2458[/C][C]0.2121[/C][C]0.5869[/C][C]0.5318[/C][/ROW]
[ROW][C]71[/C][C]26.97[/C][C]26.4269[/C][C]24.9439[/C][C]27.9098[/C][C]0.2364[/C][C]0.253[/C][C]0.5457[/C][C]0.5247[/C][/ROW]
[ROW][C]72[/C][C]26.35[/C][C]26.435[/C][C]24.8804[/C][C]27.9896[/C][C]0.4573[/C][C]0.25[/C][C]0.6309[/C][C]0.5277[/C][/ROW]
[ROW][C]73[/C][C]26.93[/C][C]26.4286[/C][C]24.8033[/C][C]28.0539[/C][C]0.2727[/C][C]0.5378[/C][C]0.5234[/C][C]0.5234[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112988&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112988&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[61])
4925.71-------
5025.92-------
5125.93-------
5226-------
5326.02-------
5426.08-------
5526.17-------
5626.18-------
5726.21-------
5826.28-------
5926.34-------
6026.17-------
6126.38-------
6226.3626.471826.048626.8950.30230.66460.99470.6646
6326.2726.399725.738527.0610.35030.54690.91810.5233
6426.2626.456325.661227.25140.31420.6770.86970.5746
6526.4926.411925.47627.34780.4350.62480.79410.5266
6626.9926.446825.407127.48640.15290.46750.75540.5501
6727.1426.419425.272227.56660.10910.16480.6650.5268
6827.126.440925.20527.67670.14790.13380.66050.5385
6927.0126.42425.098427.74960.19310.15880.62420.5259
7026.9326.437325.032827.84170.24580.21210.58690.5318
7126.9726.426924.943927.90980.23640.2530.54570.5247
7226.3526.43524.880427.98960.45730.250.63090.5277
7326.9326.428624.803328.05390.27270.53780.52340.5234






Univariate ARIMA Extrapolation Forecast Performance
time% S.E.PEMAPESq.EMSERMSE
620.0082-0.004200.012500
630.0128-0.00490.00460.01680.01470.1211
640.0153-0.00740.00550.03850.02260.1504
650.01810.0030.00490.00610.01850.136
660.02010.02050.0080.29510.07380.2717
670.02220.02730.01120.51930.14810.3848
680.02380.02490.01320.43440.1890.4347
690.02560.02220.01430.34340.20830.4564
700.02710.01860.01480.24280.21210.4606
710.02860.02060.01540.2950.22040.4695
720.03-0.00320.01430.00720.2010.4484
730.03140.0190.01470.25140.20520.453

\begin{tabular}{lllllllll}
\hline
Univariate ARIMA Extrapolation Forecast Performance \tabularnewline
time & % S.E. & PE & MAPE & Sq.E & MSE & RMSE \tabularnewline
62 & 0.0082 & -0.0042 & 0 & 0.0125 & 0 & 0 \tabularnewline
63 & 0.0128 & -0.0049 & 0.0046 & 0.0168 & 0.0147 & 0.1211 \tabularnewline
64 & 0.0153 & -0.0074 & 0.0055 & 0.0385 & 0.0226 & 0.1504 \tabularnewline
65 & 0.0181 & 0.003 & 0.0049 & 0.0061 & 0.0185 & 0.136 \tabularnewline
66 & 0.0201 & 0.0205 & 0.008 & 0.2951 & 0.0738 & 0.2717 \tabularnewline
67 & 0.0222 & 0.0273 & 0.0112 & 0.5193 & 0.1481 & 0.3848 \tabularnewline
68 & 0.0238 & 0.0249 & 0.0132 & 0.4344 & 0.189 & 0.4347 \tabularnewline
69 & 0.0256 & 0.0222 & 0.0143 & 0.3434 & 0.2083 & 0.4564 \tabularnewline
70 & 0.0271 & 0.0186 & 0.0148 & 0.2428 & 0.2121 & 0.4606 \tabularnewline
71 & 0.0286 & 0.0206 & 0.0154 & 0.295 & 0.2204 & 0.4695 \tabularnewline
72 & 0.03 & -0.0032 & 0.0143 & 0.0072 & 0.201 & 0.4484 \tabularnewline
73 & 0.0314 & 0.019 & 0.0147 & 0.2514 & 0.2052 & 0.453 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112988&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]62[/C][C]0.0082[/C][C]-0.0042[/C][C]0[/C][C]0.0125[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]63[/C][C]0.0128[/C][C]-0.0049[/C][C]0.0046[/C][C]0.0168[/C][C]0.0147[/C][C]0.1211[/C][/ROW]
[ROW][C]64[/C][C]0.0153[/C][C]-0.0074[/C][C]0.0055[/C][C]0.0385[/C][C]0.0226[/C][C]0.1504[/C][/ROW]
[ROW][C]65[/C][C]0.0181[/C][C]0.003[/C][C]0.0049[/C][C]0.0061[/C][C]0.0185[/C][C]0.136[/C][/ROW]
[ROW][C]66[/C][C]0.0201[/C][C]0.0205[/C][C]0.008[/C][C]0.2951[/C][C]0.0738[/C][C]0.2717[/C][/ROW]
[ROW][C]67[/C][C]0.0222[/C][C]0.0273[/C][C]0.0112[/C][C]0.5193[/C][C]0.1481[/C][C]0.3848[/C][/ROW]
[ROW][C]68[/C][C]0.0238[/C][C]0.0249[/C][C]0.0132[/C][C]0.4344[/C][C]0.189[/C][C]0.4347[/C][/ROW]
[ROW][C]69[/C][C]0.0256[/C][C]0.0222[/C][C]0.0143[/C][C]0.3434[/C][C]0.2083[/C][C]0.4564[/C][/ROW]
[ROW][C]70[/C][C]0.0271[/C][C]0.0186[/C][C]0.0148[/C][C]0.2428[/C][C]0.2121[/C][C]0.4606[/C][/ROW]
[ROW][C]71[/C][C]0.0286[/C][C]0.0206[/C][C]0.0154[/C][C]0.295[/C][C]0.2204[/C][C]0.4695[/C][/ROW]
[ROW][C]72[/C][C]0.03[/C][C]-0.0032[/C][C]0.0143[/C][C]0.0072[/C][C]0.201[/C][C]0.4484[/C][/ROW]
[ROW][C]73[/C][C]0.0314[/C][C]0.019[/C][C]0.0147[/C][C]0.2514[/C][C]0.2052[/C][C]0.453[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112988&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112988&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
620.0082-0.004200.012500
630.0128-0.00490.00460.01680.01470.1211
640.0153-0.00740.00550.03850.02260.1504
650.01810.0030.00490.00610.01850.136
660.02010.02050.0080.29510.07380.2717
670.02220.02730.01120.51930.14810.3848
680.02380.02490.01320.43440.1890.4347
690.02560.02220.01430.34340.20830.4564
700.02710.01860.01480.24280.21210.4606
710.02860.02060.01540.2950.22040.4695
720.03-0.00320.01430.00720.2010.4484
730.03140.0190.01470.25140.20520.453


Figures (Output of Computation)

Input Parameters & R Code

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