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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 computationWed, 22 Dec 2010 16:40:18 +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/22/t1293036032rdhv4lcr5flw43v.htm/, Retrieved Sun, 05 May 2024 22:13:57 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=114390, Retrieved Sun, 05 May 2024 22:13:57 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact178

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Standard Deviation-Mean Plot] [SMP prof bach] [2008-12-15 22:25:20] [bc937651ef42bf891200cf0e0edc7238]
- RM    [Variance Reduction Matrix] [VRM prof bach] [2008-12-15 22:31:00] [bc937651ef42bf891200cf0e0edc7238]
- RMP     [(Partial) Autocorrelation Function] [ARIMA Prof bach A...] [2008-12-15 22:38:57] [bc937651ef42bf891200cf0e0edc7238]
- RMP       [ARIMA Backward Selection] [Arima backward se...] [2008-12-19 17:26:16] [bc937651ef42bf891200cf0e0edc7238]
- RMP         [ARIMA Forecasting] [ARIMA forecast pr...] [2008-12-20 11:34:44] [bc937651ef42bf891200cf0e0edc7238]
-  MPD          [ARIMA Forecasting] [] [2010-12-21 19:37:30] [94f4aa1c01e87d8321fffb341ed4df07]
-    D              [ARIMA Forecasting] [] [2010-12-22 16:40:18] [d1991ab4912b5ede0ff54c26afa5d84c] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
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
3970,10
4138,52
4199,75
4290,89
4443,91
4502,64
4356,98
4591,27
4696,96
4621,40
4562,84
4202,52
4296,49
4435,23
4105,18
4116,68
3844,49
3720,98
3674,40
3857,62
3801,06
3504,37
3032,60
3047,03
2962,34
2197,82
2014,45
1862,83
1905,41

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=114390&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=114390&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114390&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[37])
254443.91-------
264502.64-------
274356.98-------
284591.27-------
294696.96-------
304621.4-------
314562.84-------
324202.52-------
334296.49-------
344435.23-------
354105.18-------
364116.68-------
373844.49-------
383720.983805.30863527.92844082.68880.27560.390900.3909
393674.43799.66853378.21324221.12380.28010.64280.00480.4174
403857.623798.85663267.82944329.88390.41410.6770.00170.4331
413801.063798.73983176.73444420.74510.49710.42640.00230.4427
423504.373798.72293097.38964500.05630.20540.49740.01070.4491
433032.63798.72053026.15514571.2860.0260.77240.02630.4538
443047.033798.72022960.95654636.48380.03930.96350.17240.4574
452962.343798.72012900.47814696.96210.0340.94950.13870.4602
462197.823798.72012843.82254753.61775e-040.9570.09570.4626
472014.453798.72012790.34514807.09523e-040.99910.27570.4646
481862.833798.72012739.56434857.87592e-040.99950.27810.4663
491905.413798.72012691.10924906.3314e-040.99970.46770.4677

\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[37]) \tabularnewline
25 & 4443.91 & - & - & - & - & - & - & - \tabularnewline
26 & 4502.64 & - & - & - & - & - & - & - \tabularnewline
27 & 4356.98 & - & - & - & - & - & - & - \tabularnewline
28 & 4591.27 & - & - & - & - & - & - & - \tabularnewline
29 & 4696.96 & - & - & - & - & - & - & - \tabularnewline
30 & 4621.4 & - & - & - & - & - & - & - \tabularnewline
31 & 4562.84 & - & - & - & - & - & - & - \tabularnewline
32 & 4202.52 & - & - & - & - & - & - & - \tabularnewline
33 & 4296.49 & - & - & - & - & - & - & - \tabularnewline
34 & 4435.23 & - & - & - & - & - & - & - \tabularnewline
35 & 4105.18 & - & - & - & - & - & - & - \tabularnewline
36 & 4116.68 & - & - & - & - & - & - & - \tabularnewline
37 & 3844.49 & - & - & - & - & - & - & - \tabularnewline
38 & 3720.98 & 3805.3086 & 3527.9284 & 4082.6888 & 0.2756 & 0.3909 & 0 & 0.3909 \tabularnewline
39 & 3674.4 & 3799.6685 & 3378.2132 & 4221.1238 & 0.2801 & 0.6428 & 0.0048 & 0.4174 \tabularnewline
40 & 3857.62 & 3798.8566 & 3267.8294 & 4329.8839 & 0.4141 & 0.677 & 0.0017 & 0.4331 \tabularnewline
41 & 3801.06 & 3798.7398 & 3176.7344 & 4420.7451 & 0.4971 & 0.4264 & 0.0023 & 0.4427 \tabularnewline
42 & 3504.37 & 3798.7229 & 3097.3896 & 4500.0563 & 0.2054 & 0.4974 & 0.0107 & 0.4491 \tabularnewline
43 & 3032.6 & 3798.7205 & 3026.1551 & 4571.286 & 0.026 & 0.7724 & 0.0263 & 0.4538 \tabularnewline
44 & 3047.03 & 3798.7202 & 2960.9565 & 4636.4838 & 0.0393 & 0.9635 & 0.1724 & 0.4574 \tabularnewline
45 & 2962.34 & 3798.7201 & 2900.4781 & 4696.9621 & 0.034 & 0.9495 & 0.1387 & 0.4602 \tabularnewline
46 & 2197.82 & 3798.7201 & 2843.8225 & 4753.6177 & 5e-04 & 0.957 & 0.0957 & 0.4626 \tabularnewline
47 & 2014.45 & 3798.7201 & 2790.3451 & 4807.0952 & 3e-04 & 0.9991 & 0.2757 & 0.4646 \tabularnewline
48 & 1862.83 & 3798.7201 & 2739.5643 & 4857.8759 & 2e-04 & 0.9995 & 0.2781 & 0.4663 \tabularnewline
49 & 1905.41 & 3798.7201 & 2691.1092 & 4906.331 & 4e-04 & 0.9997 & 0.4677 & 0.4677 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114390&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[37])[/C][/ROW]
[ROW][C]25[/C][C]4443.91[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]26[/C][C]4502.64[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]27[/C][C]4356.98[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]28[/C][C]4591.27[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]29[/C][C]4696.96[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]30[/C][C]4621.4[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]31[/C][C]4562.84[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]32[/C][C]4202.52[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]33[/C][C]4296.49[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]34[/C][C]4435.23[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]35[/C][C]4105.18[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]36[/C][C]4116.68[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]37[/C][C]3844.49[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]38[/C][C]3720.98[/C][C]3805.3086[/C][C]3527.9284[/C][C]4082.6888[/C][C]0.2756[/C][C]0.3909[/C][C]0[/C][C]0.3909[/C][/ROW]
[ROW][C]39[/C][C]3674.4[/C][C]3799.6685[/C][C]3378.2132[/C][C]4221.1238[/C][C]0.2801[/C][C]0.6428[/C][C]0.0048[/C][C]0.4174[/C][/ROW]
[ROW][C]40[/C][C]3857.62[/C][C]3798.8566[/C][C]3267.8294[/C][C]4329.8839[/C][C]0.4141[/C][C]0.677[/C][C]0.0017[/C][C]0.4331[/C][/ROW]
[ROW][C]41[/C][C]3801.06[/C][C]3798.7398[/C][C]3176.7344[/C][C]4420.7451[/C][C]0.4971[/C][C]0.4264[/C][C]0.0023[/C][C]0.4427[/C][/ROW]
[ROW][C]42[/C][C]3504.37[/C][C]3798.7229[/C][C]3097.3896[/C][C]4500.0563[/C][C]0.2054[/C][C]0.4974[/C][C]0.0107[/C][C]0.4491[/C][/ROW]
[ROW][C]43[/C][C]3032.6[/C][C]3798.7205[/C][C]3026.1551[/C][C]4571.286[/C][C]0.026[/C][C]0.7724[/C][C]0.0263[/C][C]0.4538[/C][/ROW]
[ROW][C]44[/C][C]3047.03[/C][C]3798.7202[/C][C]2960.9565[/C][C]4636.4838[/C][C]0.0393[/C][C]0.9635[/C][C]0.1724[/C][C]0.4574[/C][/ROW]
[ROW][C]45[/C][C]2962.34[/C][C]3798.7201[/C][C]2900.4781[/C][C]4696.9621[/C][C]0.034[/C][C]0.9495[/C][C]0.1387[/C][C]0.4602[/C][/ROW]
[ROW][C]46[/C][C]2197.82[/C][C]3798.7201[/C][C]2843.8225[/C][C]4753.6177[/C][C]5e-04[/C][C]0.957[/C][C]0.0957[/C][C]0.4626[/C][/ROW]
[ROW][C]47[/C][C]2014.45[/C][C]3798.7201[/C][C]2790.3451[/C][C]4807.0952[/C][C]3e-04[/C][C]0.9991[/C][C]0.2757[/C][C]0.4646[/C][/ROW]
[ROW][C]48[/C][C]1862.83[/C][C]3798.7201[/C][C]2739.5643[/C][C]4857.8759[/C][C]2e-04[/C][C]0.9995[/C][C]0.2781[/C][C]0.4663[/C][/ROW]
[ROW][C]49[/C][C]1905.41[/C][C]3798.7201[/C][C]2691.1092[/C][C]4906.331[/C][C]4e-04[/C][C]0.9997[/C][C]0.4677[/C][C]0.4677[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114390&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114390&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[37])
254443.91-------
264502.64-------
274356.98-------
284591.27-------
294696.96-------
304621.4-------
314562.84-------
324202.52-------
334296.49-------
344435.23-------
354105.18-------
364116.68-------
373844.49-------
383720.983805.30863527.92844082.68880.27560.390900.3909
393674.43799.66853378.21324221.12380.28010.64280.00480.4174
403857.623798.85663267.82944329.88390.41410.6770.00170.4331
413801.063798.73983176.73444420.74510.49710.42640.00230.4427
423504.373798.72293097.38964500.05630.20540.49740.01070.4491
433032.63798.72053026.15514571.2860.0260.77240.02630.4538
443047.033798.72022960.95654636.48380.03930.96350.17240.4574
452962.343798.72012900.47814696.96210.0340.94950.13870.4602
462197.823798.72012843.82254753.61775e-040.9570.09570.4626
472014.453798.72012790.34514807.09523e-040.99910.27570.4646
481862.833798.72012739.56434857.87592e-040.99950.27810.4663
491905.413798.72012691.10924906.3314e-040.99970.46770.4677






Univariate ARIMA Extrapolation Forecast Performance
time% S.E.PEMAPESq.EMSERMSE
380.0372-0.02220.00187111.317592.609724.3436
390.0566-0.0330.002715692.20211307.683536.1619
400.07130.01550.00133453.1331287.761116.9635
410.08356e-041e-045.38350.44860.6698
420.0942-0.07750.006586643.65427220.304584.9724
430.1038-0.20170.0168586940.65148911.7209221.1599
440.1125-0.19790.0165565038.113647086.5095216.9943
450.1206-0.22020.0183699531.706958294.3089241.4421
460.1283-0.42140.03512562881.1746213573.4312462.1401
470.1354-0.46970.03913183619.8355265301.653515.0744
480.1423-0.50960.04253747670.5283312305.8774558.8433
490.1488-0.49840.04153584623.1827298718.5986546.5516

\begin{tabular}{lllllllll}
\hline
Univariate ARIMA Extrapolation Forecast Performance \tabularnewline
time & % S.E. & PE & MAPE & Sq.E & MSE & RMSE \tabularnewline
38 & 0.0372 & -0.0222 & 0.0018 & 7111.317 & 592.6097 & 24.3436 \tabularnewline
39 & 0.0566 & -0.033 & 0.0027 & 15692.2021 & 1307.6835 & 36.1619 \tabularnewline
40 & 0.0713 & 0.0155 & 0.0013 & 3453.1331 & 287.7611 & 16.9635 \tabularnewline
41 & 0.0835 & 6e-04 & 1e-04 & 5.3835 & 0.4486 & 0.6698 \tabularnewline
42 & 0.0942 & -0.0775 & 0.0065 & 86643.6542 & 7220.3045 & 84.9724 \tabularnewline
43 & 0.1038 & -0.2017 & 0.0168 & 586940.651 & 48911.7209 & 221.1599 \tabularnewline
44 & 0.1125 & -0.1979 & 0.0165 & 565038.1136 & 47086.5095 & 216.9943 \tabularnewline
45 & 0.1206 & -0.2202 & 0.0183 & 699531.7069 & 58294.3089 & 241.4421 \tabularnewline
46 & 0.1283 & -0.4214 & 0.0351 & 2562881.1746 & 213573.4312 & 462.1401 \tabularnewline
47 & 0.1354 & -0.4697 & 0.0391 & 3183619.8355 & 265301.653 & 515.0744 \tabularnewline
48 & 0.1423 & -0.5096 & 0.0425 & 3747670.5283 & 312305.8774 & 558.8433 \tabularnewline
49 & 0.1488 & -0.4984 & 0.0415 & 3584623.1827 & 298718.5986 & 546.5516 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114390&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]38[/C][C]0.0372[/C][C]-0.0222[/C][C]0.0018[/C][C]7111.317[/C][C]592.6097[/C][C]24.3436[/C][/ROW]
[ROW][C]39[/C][C]0.0566[/C][C]-0.033[/C][C]0.0027[/C][C]15692.2021[/C][C]1307.6835[/C][C]36.1619[/C][/ROW]
[ROW][C]40[/C][C]0.0713[/C][C]0.0155[/C][C]0.0013[/C][C]3453.1331[/C][C]287.7611[/C][C]16.9635[/C][/ROW]
[ROW][C]41[/C][C]0.0835[/C][C]6e-04[/C][C]1e-04[/C][C]5.3835[/C][C]0.4486[/C][C]0.6698[/C][/ROW]
[ROW][C]42[/C][C]0.0942[/C][C]-0.0775[/C][C]0.0065[/C][C]86643.6542[/C][C]7220.3045[/C][C]84.9724[/C][/ROW]
[ROW][C]43[/C][C]0.1038[/C][C]-0.2017[/C][C]0.0168[/C][C]586940.651[/C][C]48911.7209[/C][C]221.1599[/C][/ROW]
[ROW][C]44[/C][C]0.1125[/C][C]-0.1979[/C][C]0.0165[/C][C]565038.1136[/C][C]47086.5095[/C][C]216.9943[/C][/ROW]
[ROW][C]45[/C][C]0.1206[/C][C]-0.2202[/C][C]0.0183[/C][C]699531.7069[/C][C]58294.3089[/C][C]241.4421[/C][/ROW]
[ROW][C]46[/C][C]0.1283[/C][C]-0.4214[/C][C]0.0351[/C][C]2562881.1746[/C][C]213573.4312[/C][C]462.1401[/C][/ROW]
[ROW][C]47[/C][C]0.1354[/C][C]-0.4697[/C][C]0.0391[/C][C]3183619.8355[/C][C]265301.653[/C][C]515.0744[/C][/ROW]
[ROW][C]48[/C][C]0.1423[/C][C]-0.5096[/C][C]0.0425[/C][C]3747670.5283[/C][C]312305.8774[/C][C]558.8433[/C][/ROW]
[ROW][C]49[/C][C]0.1488[/C][C]-0.4984[/C][C]0.0415[/C][C]3584623.1827[/C][C]298718.5986[/C][C]546.5516[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114390&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114390&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
380.0372-0.02220.00187111.317592.609724.3436
390.0566-0.0330.002715692.20211307.683536.1619
400.07130.01550.00133453.1331287.761116.9635
410.08356e-041e-045.38350.44860.6698
420.0942-0.07750.006586643.65427220.304584.9724
430.1038-0.20170.0168586940.65148911.7209221.1599
440.1125-0.19790.0165565038.113647086.5095216.9943
450.1206-0.22020.0183699531.706958294.3089241.4421
460.1283-0.42140.03512562881.1746213573.4312462.1401
470.1354-0.46970.03913183619.8355265301.653515.0744
480.1423-0.50960.04253747670.5283312305.8774558.8433
490.1488-0.49840.04153584623.1827298718.5986546.5516


Figures (Output of Computation)

Input Parameters & R Code

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