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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_arimaforecasting.wasp
Title produced by softwareARIMA Forecasting
Date of computationMon, 22 Dec 2008 06:09:43 -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/2008/Dec/22/t1229951417q5yppcla369oqc0.htm/, Retrieved Mon, 13 May 2024 04:31:30 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=36041, Retrieved Mon, 13 May 2024 04:31:30 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact233

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [Central tendency:...] [2008-12-12 12:54:43] [73d6180dc45497329efd1b6934a84aba]
- RMP   [ARIMA Backward Selection] [ARIMA goudprijs] [2008-12-14 20:12:57] [73d6180dc45497329efd1b6934a84aba]
- RMPD    [ARIMA Forecasting] [ARIMA forecast: O...] [2008-12-14 22:42:36] [73d6180dc45497329efd1b6934a84aba]
-   PD      [ARIMA Forecasting] [arima forecast ol...] [2008-12-16 16:27:50] [73d6180dc45497329efd1b6934a84aba]
-   P         [ARIMA Forecasting] [Lambda -0,2 ARIMA...] [2008-12-19 21:26:09] [73d6180dc45497329efd1b6934a84aba]
- R  D            [ARIMA Forecasting] [ARIMA Forecast olie] [2008-12-22 13:09:43] [ee28d11f695cd3bc1f8bbd77ba77987a] [Current]
- RMPD              [ARIMA Forecasting] [] [2009-12-30 22:22:39] [74be16979710d4c4e7c6647856088456]
-   PD                [ARIMA Forecasting] [] [2009-12-31 10:35:36] [74be16979710d4c4e7c6647856088456]
-   PD                [ARIMA Forecasting] [] [2009-12-31 10:39:14] [74be16979710d4c4e7c6647856088456]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
29.59
30.7
30.52
32.67
33.19
37.13
35.54
37.75
41.84
42.94
49.14
44.61
40.22
44.23
45.85
53.38
53.26
51.8
55.3
57.81
63.96
63.77
59.15
56.12
57.42
63.52
61.71
63.01
68.18
72.03
69.75
74.41
74.33
64.24
60.03
59.44
62.5
55.04
58.34
61.92
67.65
67.68
70.3
75.26
71.44
76.36
81.71
92.6
90.6
92.23
94.09
102.79
109.65
124.05
132.69
135.81
116.07
101.42
75.73
55.48

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' @ 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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36041&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' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36041&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36041&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' @ 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[48])
3659.44-------
3762.5-------
3855.04-------
3958.34-------
4061.92-------
4167.65-------
4267.68-------
4370.3-------
4475.26-------
4571.44-------
4676.36-------
4781.71-------
4892.6-------
4990.693.78480.1497110.29840.35280.55590.99990.5559
5092.2393.984674.5639119.80240.4470.60140.99840.5419
5194.0994.008670.5036127.57230.49810.54140.98140.5328
52102.7994.012267.309134.49030.33540.49850.93990.5273
53109.6594.012764.6555140.90690.25670.35690.86470.5235
54124.0594.012762.3748146.99470.13320.28150.8350.5208
55132.6994.012760.369152.85280.09880.15850.78520.5188
56135.8194.012758.5756158.54420.10210.12010.71550.5171
57116.0794.012756.9521164.11190.26870.12130.7360.5158
58101.4294.012755.4683169.58690.42380.28360.67650.5146
5975.7394.012754.1015174.99220.32910.42890.61710.5136
6055.4894.012752.8343180.34570.19080.6610.51280.5128

\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[48]) \tabularnewline
36 & 59.44 & - & - & - & - & - & - & - \tabularnewline
37 & 62.5 & - & - & - & - & - & - & - \tabularnewline
38 & 55.04 & - & - & - & - & - & - & - \tabularnewline
39 & 58.34 & - & - & - & - & - & - & - \tabularnewline
40 & 61.92 & - & - & - & - & - & - & - \tabularnewline
41 & 67.65 & - & - & - & - & - & - & - \tabularnewline
42 & 67.68 & - & - & - & - & - & - & - \tabularnewline
43 & 70.3 & - & - & - & - & - & - & - \tabularnewline
44 & 75.26 & - & - & - & - & - & - & - \tabularnewline
45 & 71.44 & - & - & - & - & - & - & - \tabularnewline
46 & 76.36 & - & - & - & - & - & - & - \tabularnewline
47 & 81.71 & - & - & - & - & - & - & - \tabularnewline
48 & 92.6 & - & - & - & - & - & - & - \tabularnewline
49 & 90.6 & 93.784 & 80.1497 & 110.2984 & 0.3528 & 0.5559 & 0.9999 & 0.5559 \tabularnewline
50 & 92.23 & 93.9846 & 74.5639 & 119.8024 & 0.447 & 0.6014 & 0.9984 & 0.5419 \tabularnewline
51 & 94.09 & 94.0086 & 70.5036 & 127.5723 & 0.4981 & 0.5414 & 0.9814 & 0.5328 \tabularnewline
52 & 102.79 & 94.0122 & 67.309 & 134.4903 & 0.3354 & 0.4985 & 0.9399 & 0.5273 \tabularnewline
53 & 109.65 & 94.0127 & 64.6555 & 140.9069 & 0.2567 & 0.3569 & 0.8647 & 0.5235 \tabularnewline
54 & 124.05 & 94.0127 & 62.3748 & 146.9947 & 0.1332 & 0.2815 & 0.835 & 0.5208 \tabularnewline
55 & 132.69 & 94.0127 & 60.369 & 152.8528 & 0.0988 & 0.1585 & 0.7852 & 0.5188 \tabularnewline
56 & 135.81 & 94.0127 & 58.5756 & 158.5442 & 0.1021 & 0.1201 & 0.7155 & 0.5171 \tabularnewline
57 & 116.07 & 94.0127 & 56.9521 & 164.1119 & 0.2687 & 0.1213 & 0.736 & 0.5158 \tabularnewline
58 & 101.42 & 94.0127 & 55.4683 & 169.5869 & 0.4238 & 0.2836 & 0.6765 & 0.5146 \tabularnewline
59 & 75.73 & 94.0127 & 54.1015 & 174.9922 & 0.3291 & 0.4289 & 0.6171 & 0.5136 \tabularnewline
60 & 55.48 & 94.0127 & 52.8343 & 180.3457 & 0.1908 & 0.661 & 0.5128 & 0.5128 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36041&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[48])[/C][/ROW]
[ROW][C]36[/C][C]59.44[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]37[/C][C]62.5[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]38[/C][C]55.04[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]39[/C][C]58.34[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]40[/C][C]61.92[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]41[/C][C]67.65[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]42[/C][C]67.68[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]43[/C][C]70.3[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]44[/C][C]75.26[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]45[/C][C]71.44[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]46[/C][C]76.36[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]47[/C][C]81.71[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]48[/C][C]92.6[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]49[/C][C]90.6[/C][C]93.784[/C][C]80.1497[/C][C]110.2984[/C][C]0.3528[/C][C]0.5559[/C][C]0.9999[/C][C]0.5559[/C][/ROW]
[ROW][C]50[/C][C]92.23[/C][C]93.9846[/C][C]74.5639[/C][C]119.8024[/C][C]0.447[/C][C]0.6014[/C][C]0.9984[/C][C]0.5419[/C][/ROW]
[ROW][C]51[/C][C]94.09[/C][C]94.0086[/C][C]70.5036[/C][C]127.5723[/C][C]0.4981[/C][C]0.5414[/C][C]0.9814[/C][C]0.5328[/C][/ROW]
[ROW][C]52[/C][C]102.79[/C][C]94.0122[/C][C]67.309[/C][C]134.4903[/C][C]0.3354[/C][C]0.4985[/C][C]0.9399[/C][C]0.5273[/C][/ROW]
[ROW][C]53[/C][C]109.65[/C][C]94.0127[/C][C]64.6555[/C][C]140.9069[/C][C]0.2567[/C][C]0.3569[/C][C]0.8647[/C][C]0.5235[/C][/ROW]
[ROW][C]54[/C][C]124.05[/C][C]94.0127[/C][C]62.3748[/C][C]146.9947[/C][C]0.1332[/C][C]0.2815[/C][C]0.835[/C][C]0.5208[/C][/ROW]
[ROW][C]55[/C][C]132.69[/C][C]94.0127[/C][C]60.369[/C][C]152.8528[/C][C]0.0988[/C][C]0.1585[/C][C]0.7852[/C][C]0.5188[/C][/ROW]
[ROW][C]56[/C][C]135.81[/C][C]94.0127[/C][C]58.5756[/C][C]158.5442[/C][C]0.1021[/C][C]0.1201[/C][C]0.7155[/C][C]0.5171[/C][/ROW]
[ROW][C]57[/C][C]116.07[/C][C]94.0127[/C][C]56.9521[/C][C]164.1119[/C][C]0.2687[/C][C]0.1213[/C][C]0.736[/C][C]0.5158[/C][/ROW]
[ROW][C]58[/C][C]101.42[/C][C]94.0127[/C][C]55.4683[/C][C]169.5869[/C][C]0.4238[/C][C]0.2836[/C][C]0.6765[/C][C]0.5146[/C][/ROW]
[ROW][C]59[/C][C]75.73[/C][C]94.0127[/C][C]54.1015[/C][C]174.9922[/C][C]0.3291[/C][C]0.4289[/C][C]0.6171[/C][C]0.5136[/C][/ROW]
[ROW][C]60[/C][C]55.48[/C][C]94.0127[/C][C]52.8343[/C][C]180.3457[/C][C]0.1908[/C][C]0.661[/C][C]0.5128[/C][C]0.5128[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36041&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36041&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[48])
3659.44-------
3762.5-------
3855.04-------
3958.34-------
4061.92-------
4167.65-------
4267.68-------
4370.3-------
4475.26-------
4571.44-------
4676.36-------
4781.71-------
4892.6-------
4990.693.78480.1497110.29840.35280.55590.99990.5559
5092.2393.984674.5639119.80240.4470.60140.99840.5419
5194.0994.008670.5036127.57230.49810.54140.98140.5328
52102.7994.012267.309134.49030.33540.49850.93990.5273
53109.6594.012764.6555140.90690.25670.35690.86470.5235
54124.0594.012762.3748146.99470.13320.28150.8350.5208
55132.6994.012760.369152.85280.09880.15850.78520.5188
56135.8194.012758.5756158.54420.10210.12010.71550.5171
57116.0794.012756.9521164.11190.26870.12130.7360.5158
58101.4294.012755.4683169.58690.42380.28360.67650.5146
5975.7394.012754.1015174.99220.32910.42890.61710.5136
6055.4894.012752.8343180.34570.19080.6610.51280.5128






Univariate ARIMA Extrapolation Forecast Performance
time% S.E.PEMAPESq.EMSERMSE
490.0898-0.0340.002810.13810.84480.9192
500.1402-0.01870.00163.07860.25660.5065
510.18229e-041e-040.00666e-040.0235
520.21970.09340.007877.04996.42082.5339
530.25450.16630.0139244.526520.37724.5141
540.28750.31950.0266902.238275.18658.671
550.31930.41140.03431495.9313124.660911.1652
560.35020.44460.0371747.0118145.584312.0658
570.38040.23460.0196486.523140.54366.3674
580.41010.07880.006654.86764.57232.1383
590.4395-0.19450.0162334.258227.85495.2778
600.4685-0.40990.03421484.7713123.730911.1234

\begin{tabular}{lllllllll}
\hline
Univariate ARIMA Extrapolation Forecast Performance \tabularnewline
time & % S.E. & PE & MAPE & Sq.E & MSE & RMSE \tabularnewline
49 & 0.0898 & -0.034 & 0.0028 & 10.1381 & 0.8448 & 0.9192 \tabularnewline
50 & 0.1402 & -0.0187 & 0.0016 & 3.0786 & 0.2566 & 0.5065 \tabularnewline
51 & 0.1822 & 9e-04 & 1e-04 & 0.0066 & 6e-04 & 0.0235 \tabularnewline
52 & 0.2197 & 0.0934 & 0.0078 & 77.0499 & 6.4208 & 2.5339 \tabularnewline
53 & 0.2545 & 0.1663 & 0.0139 & 244.5265 & 20.3772 & 4.5141 \tabularnewline
54 & 0.2875 & 0.3195 & 0.0266 & 902.2382 & 75.1865 & 8.671 \tabularnewline
55 & 0.3193 & 0.4114 & 0.0343 & 1495.9313 & 124.6609 & 11.1652 \tabularnewline
56 & 0.3502 & 0.4446 & 0.037 & 1747.0118 & 145.5843 & 12.0658 \tabularnewline
57 & 0.3804 & 0.2346 & 0.0196 & 486.5231 & 40.5436 & 6.3674 \tabularnewline
58 & 0.4101 & 0.0788 & 0.0066 & 54.8676 & 4.5723 & 2.1383 \tabularnewline
59 & 0.4395 & -0.1945 & 0.0162 & 334.2582 & 27.8549 & 5.2778 \tabularnewline
60 & 0.4685 & -0.4099 & 0.0342 & 1484.7713 & 123.7309 & 11.1234 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36041&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]49[/C][C]0.0898[/C][C]-0.034[/C][C]0.0028[/C][C]10.1381[/C][C]0.8448[/C][C]0.9192[/C][/ROW]
[ROW][C]50[/C][C]0.1402[/C][C]-0.0187[/C][C]0.0016[/C][C]3.0786[/C][C]0.2566[/C][C]0.5065[/C][/ROW]
[ROW][C]51[/C][C]0.1822[/C][C]9e-04[/C][C]1e-04[/C][C]0.0066[/C][C]6e-04[/C][C]0.0235[/C][/ROW]
[ROW][C]52[/C][C]0.2197[/C][C]0.0934[/C][C]0.0078[/C][C]77.0499[/C][C]6.4208[/C][C]2.5339[/C][/ROW]
[ROW][C]53[/C][C]0.2545[/C][C]0.1663[/C][C]0.0139[/C][C]244.5265[/C][C]20.3772[/C][C]4.5141[/C][/ROW]
[ROW][C]54[/C][C]0.2875[/C][C]0.3195[/C][C]0.0266[/C][C]902.2382[/C][C]75.1865[/C][C]8.671[/C][/ROW]
[ROW][C]55[/C][C]0.3193[/C][C]0.4114[/C][C]0.0343[/C][C]1495.9313[/C][C]124.6609[/C][C]11.1652[/C][/ROW]
[ROW][C]56[/C][C]0.3502[/C][C]0.4446[/C][C]0.037[/C][C]1747.0118[/C][C]145.5843[/C][C]12.0658[/C][/ROW]
[ROW][C]57[/C][C]0.3804[/C][C]0.2346[/C][C]0.0196[/C][C]486.5231[/C][C]40.5436[/C][C]6.3674[/C][/ROW]
[ROW][C]58[/C][C]0.4101[/C][C]0.0788[/C][C]0.0066[/C][C]54.8676[/C][C]4.5723[/C][C]2.1383[/C][/ROW]
[ROW][C]59[/C][C]0.4395[/C][C]-0.1945[/C][C]0.0162[/C][C]334.2582[/C][C]27.8549[/C][C]5.2778[/C][/ROW]
[ROW][C]60[/C][C]0.4685[/C][C]-0.4099[/C][C]0.0342[/C][C]1484.7713[/C][C]123.7309[/C][C]11.1234[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36041&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36041&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
490.0898-0.0340.002810.13810.84480.9192
500.1402-0.01870.00163.07860.25660.5065
510.18229e-041e-040.00666e-040.0235
520.21970.09340.007877.04996.42082.5339
530.25450.16630.0139244.526520.37724.5141
540.28750.31950.0266902.238275.18658.671
550.31930.41140.03431495.9313124.660911.1652
560.35020.44460.0371747.0118145.584312.0658
570.38040.23460.0196486.523140.54366.3674
580.41010.07880.006654.86764.57232.1383
590.4395-0.19450.0162334.258227.85495.2778
600.4685-0.40990.03421484.7713123.730911.1234


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 12 ; par2 = -0.2 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = 2 ; par7 = 1 ; par8 = 0 ; par9 = 0 ; par10 = FALSE ;
Parameters (R input):
par1 = 12 ; par2 = -0.2 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = 2 ; 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,fx))
(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.se <- array(0, dim=fx)
perf.mse <- 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$pred[i]
perf.mape[i] = perf.mape[i] + abs(perf.pe[i])
perf.se[i] = (x[nx+i] - forecast$pred[i])^2
perf.mse[i] = perf.mse[i] + perf.se[i]
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 = perf.mape / fx
perf.mse = perf.mse / fx
perf.rmse = sqrt(perf.mse)
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[1:12] <- 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.mape[i],4))
a<-table.element(a,round(perf.se[i],4))
a<-table.element(a,round(perf.mse[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')