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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 07:06:40 -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/t1229954842gqdt4quruo74430.htm/, Retrieved Sun, 12 May 2024 14:46:30 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=36074, Retrieved Sun, 12 May 2024 14:46:30 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact221

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 PD            [ARIMA Forecasting] [Forecast BEL20] [2008-12-22 14:06:40] [ee28d11f695cd3bc1f8bbd77ba77987a] [Current]
- RMPD              [ARIMA Forecasting] [] [2009-12-30 23:10:28] [74be16979710d4c4e7c6647856088456]
- RMPD              [ARIMA Forecasting] [] [2009-12-30 23:10:28] [74be16979710d4c4e7c6647856088456]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
2196.72
2350.44
2440.25
2408.64
2472.81
2407.6
2454.62
2448.05
2497.84
2645.64
2756.76
2849.27
2921.44
2981.85
3080.58
3106.22
3119.31
3061.26
3097.31
3161.69
3257.16
3277.01
3295.32
3363.99
3494.17
3667.03
3813.06
3917.96
3895.51
3801.06
3570.12
3701.61
3862.27
3970.1
4138.52
4199.75
4290.89
4443.91
4502.64
4356.98
4591.27
4696.96
4621.4
4562.84
4202.52
4296.49
4435.23
4105.18
4116.68
3844.49
3720.98
3674.4
3857.62
3801.06
3504.37
3032.6
3047.03
2962.34
2197.82
2014.45

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'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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36074&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36074&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36074&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'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])
364199.75-------
374290.89-------
384443.91-------
394502.64-------
404356.98-------
414591.27-------
424696.96-------
434621.4-------
444562.84-------
454202.52-------
464296.49-------
474435.23-------
484105.18-------
494116.683982.35123741.52364223.17880.13710.15870.0060.1587
503844.493982.35123577.99384386.70850.2520.25750.01260.2758
513720.983982.35123463.68774501.01470.16160.69880.02460.3213
523674.43982.35123370.37184594.33050.1620.79870.11510.347
533857.623982.35123289.51234675.190.36210.80820.04250.3641
543801.063982.35123217.15014747.55220.32120.62530.03360.3765
553504.373982.35123151.06334813.63910.12990.66550.06590.3861
563032.63982.35123089.85664874.84570.01850.85310.10120.3937
573047.033982.35123032.58624932.11610.02680.9750.32480.3999
582962.343982.35122978.57814986.12420.02320.96610.26980.4052
592197.823982.35122927.33115037.37125e-040.9710.20010.4097
602014.453982.35122878.46075086.24172e-040.99920.41370.4137

\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 & 4199.75 & - & - & - & - & - & - & - \tabularnewline
37 & 4290.89 & - & - & - & - & - & - & - \tabularnewline
38 & 4443.91 & - & - & - & - & - & - & - \tabularnewline
39 & 4502.64 & - & - & - & - & - & - & - \tabularnewline
40 & 4356.98 & - & - & - & - & - & - & - \tabularnewline
41 & 4591.27 & - & - & - & - & - & - & - \tabularnewline
42 & 4696.96 & - & - & - & - & - & - & - \tabularnewline
43 & 4621.4 & - & - & - & - & - & - & - \tabularnewline
44 & 4562.84 & - & - & - & - & - & - & - \tabularnewline
45 & 4202.52 & - & - & - & - & - & - & - \tabularnewline
46 & 4296.49 & - & - & - & - & - & - & - \tabularnewline
47 & 4435.23 & - & - & - & - & - & - & - \tabularnewline
48 & 4105.18 & - & - & - & - & - & - & - \tabularnewline
49 & 4116.68 & 3982.3512 & 3741.5236 & 4223.1788 & 0.1371 & 0.1587 & 0.006 & 0.1587 \tabularnewline
50 & 3844.49 & 3982.3512 & 3577.9938 & 4386.7085 & 0.252 & 0.2575 & 0.0126 & 0.2758 \tabularnewline
51 & 3720.98 & 3982.3512 & 3463.6877 & 4501.0147 & 0.1616 & 0.6988 & 0.0246 & 0.3213 \tabularnewline
52 & 3674.4 & 3982.3512 & 3370.3718 & 4594.3305 & 0.162 & 0.7987 & 0.1151 & 0.347 \tabularnewline
53 & 3857.62 & 3982.3512 & 3289.5123 & 4675.19 & 0.3621 & 0.8082 & 0.0425 & 0.3641 \tabularnewline
54 & 3801.06 & 3982.3512 & 3217.1501 & 4747.5522 & 0.3212 & 0.6253 & 0.0336 & 0.3765 \tabularnewline
55 & 3504.37 & 3982.3512 & 3151.0633 & 4813.6391 & 0.1299 & 0.6655 & 0.0659 & 0.3861 \tabularnewline
56 & 3032.6 & 3982.3512 & 3089.8566 & 4874.8457 & 0.0185 & 0.8531 & 0.1012 & 0.3937 \tabularnewline
57 & 3047.03 & 3982.3512 & 3032.5862 & 4932.1161 & 0.0268 & 0.975 & 0.3248 & 0.3999 \tabularnewline
58 & 2962.34 & 3982.3512 & 2978.5781 & 4986.1242 & 0.0232 & 0.9661 & 0.2698 & 0.4052 \tabularnewline
59 & 2197.82 & 3982.3512 & 2927.3311 & 5037.3712 & 5e-04 & 0.971 & 0.2001 & 0.4097 \tabularnewline
60 & 2014.45 & 3982.3512 & 2878.4607 & 5086.2417 & 2e-04 & 0.9992 & 0.4137 & 0.4137 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36074&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]4199.75[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]37[/C][C]4290.89[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]38[/C][C]4443.91[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]39[/C][C]4502.64[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]40[/C][C]4356.98[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]41[/C][C]4591.27[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]42[/C][C]4696.96[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]43[/C][C]4621.4[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]44[/C][C]4562.84[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]45[/C][C]4202.52[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]46[/C][C]4296.49[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]47[/C][C]4435.23[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]48[/C][C]4105.18[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]49[/C][C]4116.68[/C][C]3982.3512[/C][C]3741.5236[/C][C]4223.1788[/C][C]0.1371[/C][C]0.1587[/C][C]0.006[/C][C]0.1587[/C][/ROW]
[ROW][C]50[/C][C]3844.49[/C][C]3982.3512[/C][C]3577.9938[/C][C]4386.7085[/C][C]0.252[/C][C]0.2575[/C][C]0.0126[/C][C]0.2758[/C][/ROW]
[ROW][C]51[/C][C]3720.98[/C][C]3982.3512[/C][C]3463.6877[/C][C]4501.0147[/C][C]0.1616[/C][C]0.6988[/C][C]0.0246[/C][C]0.3213[/C][/ROW]
[ROW][C]52[/C][C]3674.4[/C][C]3982.3512[/C][C]3370.3718[/C][C]4594.3305[/C][C]0.162[/C][C]0.7987[/C][C]0.1151[/C][C]0.347[/C][/ROW]
[ROW][C]53[/C][C]3857.62[/C][C]3982.3512[/C][C]3289.5123[/C][C]4675.19[/C][C]0.3621[/C][C]0.8082[/C][C]0.0425[/C][C]0.3641[/C][/ROW]
[ROW][C]54[/C][C]3801.06[/C][C]3982.3512[/C][C]3217.1501[/C][C]4747.5522[/C][C]0.3212[/C][C]0.6253[/C][C]0.0336[/C][C]0.3765[/C][/ROW]
[ROW][C]55[/C][C]3504.37[/C][C]3982.3512[/C][C]3151.0633[/C][C]4813.6391[/C][C]0.1299[/C][C]0.6655[/C][C]0.0659[/C][C]0.3861[/C][/ROW]
[ROW][C]56[/C][C]3032.6[/C][C]3982.3512[/C][C]3089.8566[/C][C]4874.8457[/C][C]0.0185[/C][C]0.8531[/C][C]0.1012[/C][C]0.3937[/C][/ROW]
[ROW][C]57[/C][C]3047.03[/C][C]3982.3512[/C][C]3032.5862[/C][C]4932.1161[/C][C]0.0268[/C][C]0.975[/C][C]0.3248[/C][C]0.3999[/C][/ROW]
[ROW][C]58[/C][C]2962.34[/C][C]3982.3512[/C][C]2978.5781[/C][C]4986.1242[/C][C]0.0232[/C][C]0.9661[/C][C]0.2698[/C][C]0.4052[/C][/ROW]
[ROW][C]59[/C][C]2197.82[/C][C]3982.3512[/C][C]2927.3311[/C][C]5037.3712[/C][C]5e-04[/C][C]0.971[/C][C]0.2001[/C][C]0.4097[/C][/ROW]
[ROW][C]60[/C][C]2014.45[/C][C]3982.3512[/C][C]2878.4607[/C][C]5086.2417[/C][C]2e-04[/C][C]0.9992[/C][C]0.4137[/C][C]0.4137[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36074&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36074&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])
364199.75-------
374290.89-------
384443.91-------
394502.64-------
404356.98-------
414591.27-------
424696.96-------
434621.4-------
444562.84-------
454202.52-------
464296.49-------
474435.23-------
484105.18-------
494116.683982.35123741.52364223.17880.13710.15870.0060.1587
503844.493982.35123577.99384386.70850.2520.25750.01260.2758
513720.983982.35123463.68774501.01470.16160.69880.02460.3213
523674.43982.35123370.37184594.33050.1620.79870.11510.347
533857.623982.35123289.51234675.190.36210.80820.04250.3641
543801.063982.35123217.15014747.55220.32120.62530.03360.3765
553504.373982.35123151.06334813.63910.12990.66550.06590.3861
563032.63982.35123089.85664874.84570.01850.85310.10120.3937
573047.033982.35123032.58624932.11610.02680.9750.32480.3999
582962.343982.35122978.57814986.12420.02320.96610.26980.4052
592197.823982.35122927.33115037.37125e-040.9710.20010.4097
602014.453982.35122878.46075086.24172e-040.99920.41370.4137






Univariate ARIMA Extrapolation Forecast Performance
time% S.E.PEMAPESq.EMSERMSE
490.03090.03370.002818044.23271503.686138.7774
500.0518-0.03460.002919005.70411583.808739.7971
510.0664-0.06560.005568314.89225692.907775.4514
520.0784-0.07730.006494833.92747902.827388.8978
530.0888-0.03130.002615557.86651296.488936.0068
540.098-0.04550.003832866.49082738.874252.3343
550.1065-0.120.01228466.005519038.8338137.9813
560.1143-0.23850.0199902027.298275168.9415274.1695
570.1217-0.23490.0196874825.704172902.142270.004
580.1286-0.25610.02131040422.801286701.9001294.4519
590.1352-0.44810.03733184551.5216265379.2935515.1498
600.1414-0.49420.04123872635.0423322719.5869568.0841

\begin{tabular}{lllllllll}
\hline
Univariate ARIMA Extrapolation Forecast Performance \tabularnewline
time & % S.E. & PE & MAPE & Sq.E & MSE & RMSE \tabularnewline
49 & 0.0309 & 0.0337 & 0.0028 & 18044.2327 & 1503.6861 & 38.7774 \tabularnewline
50 & 0.0518 & -0.0346 & 0.0029 & 19005.7041 & 1583.8087 & 39.7971 \tabularnewline
51 & 0.0664 & -0.0656 & 0.0055 & 68314.8922 & 5692.9077 & 75.4514 \tabularnewline
52 & 0.0784 & -0.0773 & 0.0064 & 94833.9274 & 7902.8273 & 88.8978 \tabularnewline
53 & 0.0888 & -0.0313 & 0.0026 & 15557.8665 & 1296.4889 & 36.0068 \tabularnewline
54 & 0.098 & -0.0455 & 0.0038 & 32866.4908 & 2738.8742 & 52.3343 \tabularnewline
55 & 0.1065 & -0.12 & 0.01 & 228466.0055 & 19038.8338 & 137.9813 \tabularnewline
56 & 0.1143 & -0.2385 & 0.0199 & 902027.2982 & 75168.9415 & 274.1695 \tabularnewline
57 & 0.1217 & -0.2349 & 0.0196 & 874825.7041 & 72902.142 & 270.004 \tabularnewline
58 & 0.1286 & -0.2561 & 0.0213 & 1040422.8012 & 86701.9001 & 294.4519 \tabularnewline
59 & 0.1352 & -0.4481 & 0.0373 & 3184551.5216 & 265379.2935 & 515.1498 \tabularnewline
60 & 0.1414 & -0.4942 & 0.0412 & 3872635.0423 & 322719.5869 & 568.0841 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36074&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]0.0309[/C][C]0.0337[/C][C]0.0028[/C][C]18044.2327[/C][C]1503.6861[/C][C]38.7774[/C][/ROW]
[ROW][C]50[/C][C]0.0518[/C][C]-0.0346[/C][C]0.0029[/C][C]19005.7041[/C][C]1583.8087[/C][C]39.7971[/C][/ROW]
[ROW][C]51[/C][C]0.0664[/C][C]-0.0656[/C][C]0.0055[/C][C]68314.8922[/C][C]5692.9077[/C][C]75.4514[/C][/ROW]
[ROW][C]52[/C][C]0.0784[/C][C]-0.0773[/C][C]0.0064[/C][C]94833.9274[/C][C]7902.8273[/C][C]88.8978[/C][/ROW]
[ROW][C]53[/C][C]0.0888[/C][C]-0.0313[/C][C]0.0026[/C][C]15557.8665[/C][C]1296.4889[/C][C]36.0068[/C][/ROW]
[ROW][C]54[/C][C]0.098[/C][C]-0.0455[/C][C]0.0038[/C][C]32866.4908[/C][C]2738.8742[/C][C]52.3343[/C][/ROW]
[ROW][C]55[/C][C]0.1065[/C][C]-0.12[/C][C]0.01[/C][C]228466.0055[/C][C]19038.8338[/C][C]137.9813[/C][/ROW]
[ROW][C]56[/C][C]0.1143[/C][C]-0.2385[/C][C]0.0199[/C][C]902027.2982[/C][C]75168.9415[/C][C]274.1695[/C][/ROW]
[ROW][C]57[/C][C]0.1217[/C][C]-0.2349[/C][C]0.0196[/C][C]874825.7041[/C][C]72902.142[/C][C]270.004[/C][/ROW]
[ROW][C]58[/C][C]0.1286[/C][C]-0.2561[/C][C]0.0213[/C][C]1040422.8012[/C][C]86701.9001[/C][C]294.4519[/C][/ROW]
[ROW][C]59[/C][C]0.1352[/C][C]-0.4481[/C][C]0.0373[/C][C]3184551.5216[/C][C]265379.2935[/C][C]515.1498[/C][/ROW]
[ROW][C]60[/C][C]0.1414[/C][C]-0.4942[/C][C]0.0412[/C][C]3872635.0423[/C][C]322719.5869[/C][C]568.0841[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36074&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36074&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
490.03090.03370.002818044.23271503.686138.7774
500.0518-0.03460.002919005.70411583.808739.7971
510.0664-0.06560.005568314.89225692.907775.4514
520.0784-0.07730.006494833.92747902.827388.8978
530.0888-0.03130.002615557.86651296.488936.0068
540.098-0.04550.003832866.49082738.874252.3343
550.1065-0.120.01228466.005519038.8338137.9813
560.1143-0.23850.0199902027.298275168.9415274.1695
570.1217-0.23490.0196874825.704172902.142270.004
580.1286-0.25610.02131040422.801286701.9001294.4519
590.1352-0.44810.03733184551.5216265379.2935515.1498
600.1414-0.49420.04123872635.0423322719.5869568.0841


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 = 0 ; 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')