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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 computationSun, 14 Dec 2008 15:31:41 -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/14/t1229293953ofwvqugdxxzvw3d.htm/, Retrieved Wed, 15 May 2024 07:29:14 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=33580, Retrieved Wed, 15 May 2024 07:29:14 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact211

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 13:08:46] [6816386b1f3c2f6c0c9f2aa1e5bc9362]
- RMPD  [Mean Plot] [Mean plot - prijs...] [2008-12-12 14:56:05] [6816386b1f3c2f6c0c9f2aa1e5bc9362]
- RMPD    [Tukey lambda PPCC Plot] [PPCC: Bel 20] [2008-12-12 15:02:48] [6816386b1f3c2f6c0c9f2aa1e5bc9362]
- RMP       [ARIMA Backward Selection] [Arima: Bel 20] [2008-12-14 20:11:31] [6816386b1f3c2f6c0c9f2aa1e5bc9362]
F RMPD        [ARIMA Forecasting] [Arima forecasting...] [2008-12-14 22:14:13] [6816386b1f3c2f6c0c9f2aa1e5bc9362]
-   PD            [ARIMA Forecasting] [Arima forecasting...] [2008-12-14 22:31:41] [14a75ec03b2c0d8ddd8b141a7b1594fd] [Current]
-                   [ARIMA Forecasting] [arima forecast do...] [2008-12-15 23:20:43] [73d6180dc45497329efd1b6934a84aba]
-   PD              [ARIMA Forecasting] [Arima forecasting...] [2008-12-19 23:09:36] [6816386b1f3c2f6c0c9f2aa1e5bc9362]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
10967,87
10433,56
10665,78
10666,71
10682,74
10777,22
10052,6
10213,97
10546,82
10767,2
10444,5
10314,68
9042,56
9220,75
9721,84
9978,53
9923,81
9892,56
10500,98
10179,35
10080,48
9492,44
8616,49
8685,4
8160,67
8048,1
8641,21
8526,63
8474,21
7916,13
7977,64
8334,59
8623,36
9098,03
9154,34
9284,73
9492,49
9682,35
9762,12
10124,63
10540,05
10601,61
10323,73
10418,4
10092,96
10364,91
10152,09
10032,8
10204,59
10001,6
10411,75
10673,38
10539,51
10723,78
10682,06
10283,19
10377,18
10486,64
10545,38
10554,27
10532,54
10324,31
10695,25
10827,81
10872,48
10971,19
11145,65
11234,68
11333,88
10997,97
11036,89
11257,35
11533,59
11963,12
12185,15
12377,62
12512,89
12631,48
12268,53
12754,8
13407,75
13480,21
13673,28
13239,71
13557,69
13901,28
13200,58
13406,97
12538,12
12419,57
12193,88
12656,63
12812,48
12056,67
11322,38
11530,75
11114,08
9181,73
8614,55

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'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=33580&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=33580&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=33580&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'Sir Ronald Aylmer Fisher' @ 193.190.124.24






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[87])
7512185.15-------
7612377.62-------
7712512.89-------
7812631.48-------
7912268.53-------
8012754.8-------
8113407.75-------
8213480.21-------
8313673.28-------
8413239.71-------
8513557.69-------
8613901.28-------
8713200.58-------
8813406.9713155.844312489.465413822.22330.23010.44770.9890.4477
8912538.1213152.988212180.037414125.93910.10770.30450.90140.4618
9012419.5713152.805911947.374714358.23710.11660.84120.80170.469
9112193.8813152.794211752.886314552.70210.08970.84770.89220.4733
9212656.6313152.793511582.304514723.28250.26790.88430.69030.4762
9312812.4813152.793411428.516714877.07020.34940.71360.3860.4783
9412056.6713152.793411287.364515018.22230.12470.63970.36540.48
9511322.3813152.793411156.166415149.42050.03620.8590.30470.4813
9611530.7513152.793411033.073115272.51380.06680.95470.4680.4824
9711114.0813152.793410916.745815388.84110.0370.92250.36130.4833
989181.7313152.793410806.178115499.40885e-040.95570.26590.4841
998614.5513152.793410700.590715604.99621e-040.99920.48480.4848

\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[87]) \tabularnewline
75 & 12185.15 & - & - & - & - & - & - & - \tabularnewline
76 & 12377.62 & - & - & - & - & - & - & - \tabularnewline
77 & 12512.89 & - & - & - & - & - & - & - \tabularnewline
78 & 12631.48 & - & - & - & - & - & - & - \tabularnewline
79 & 12268.53 & - & - & - & - & - & - & - \tabularnewline
80 & 12754.8 & - & - & - & - & - & - & - \tabularnewline
81 & 13407.75 & - & - & - & - & - & - & - \tabularnewline
82 & 13480.21 & - & - & - & - & - & - & - \tabularnewline
83 & 13673.28 & - & - & - & - & - & - & - \tabularnewline
84 & 13239.71 & - & - & - & - & - & - & - \tabularnewline
85 & 13557.69 & - & - & - & - & - & - & - \tabularnewline
86 & 13901.28 & - & - & - & - & - & - & - \tabularnewline
87 & 13200.58 & - & - & - & - & - & - & - \tabularnewline
88 & 13406.97 & 13155.8443 & 12489.4654 & 13822.2233 & 0.2301 & 0.4477 & 0.989 & 0.4477 \tabularnewline
89 & 12538.12 & 13152.9882 & 12180.0374 & 14125.9391 & 0.1077 & 0.3045 & 0.9014 & 0.4618 \tabularnewline
90 & 12419.57 & 13152.8059 & 11947.3747 & 14358.2371 & 0.1166 & 0.8412 & 0.8017 & 0.469 \tabularnewline
91 & 12193.88 & 13152.7942 & 11752.8863 & 14552.7021 & 0.0897 & 0.8477 & 0.8922 & 0.4733 \tabularnewline
92 & 12656.63 & 13152.7935 & 11582.3045 & 14723.2825 & 0.2679 & 0.8843 & 0.6903 & 0.4762 \tabularnewline
93 & 12812.48 & 13152.7934 & 11428.5167 & 14877.0702 & 0.3494 & 0.7136 & 0.386 & 0.4783 \tabularnewline
94 & 12056.67 & 13152.7934 & 11287.3645 & 15018.2223 & 0.1247 & 0.6397 & 0.3654 & 0.48 \tabularnewline
95 & 11322.38 & 13152.7934 & 11156.1664 & 15149.4205 & 0.0362 & 0.859 & 0.3047 & 0.4813 \tabularnewline
96 & 11530.75 & 13152.7934 & 11033.0731 & 15272.5138 & 0.0668 & 0.9547 & 0.468 & 0.4824 \tabularnewline
97 & 11114.08 & 13152.7934 & 10916.7458 & 15388.8411 & 0.037 & 0.9225 & 0.3613 & 0.4833 \tabularnewline
98 & 9181.73 & 13152.7934 & 10806.1781 & 15499.4088 & 5e-04 & 0.9557 & 0.2659 & 0.4841 \tabularnewline
99 & 8614.55 & 13152.7934 & 10700.5907 & 15604.9962 & 1e-04 & 0.9992 & 0.4848 & 0.4848 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=33580&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[87])[/C][/ROW]
[ROW][C]75[/C][C]12185.15[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]76[/C][C]12377.62[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]77[/C][C]12512.89[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]78[/C][C]12631.48[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]79[/C][C]12268.53[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]80[/C][C]12754.8[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]81[/C][C]13407.75[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]82[/C][C]13480.21[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]83[/C][C]13673.28[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]84[/C][C]13239.71[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]85[/C][C]13557.69[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]86[/C][C]13901.28[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]87[/C][C]13200.58[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]88[/C][C]13406.97[/C][C]13155.8443[/C][C]12489.4654[/C][C]13822.2233[/C][C]0.2301[/C][C]0.4477[/C][C]0.989[/C][C]0.4477[/C][/ROW]
[ROW][C]89[/C][C]12538.12[/C][C]13152.9882[/C][C]12180.0374[/C][C]14125.9391[/C][C]0.1077[/C][C]0.3045[/C][C]0.9014[/C][C]0.4618[/C][/ROW]
[ROW][C]90[/C][C]12419.57[/C][C]13152.8059[/C][C]11947.3747[/C][C]14358.2371[/C][C]0.1166[/C][C]0.8412[/C][C]0.8017[/C][C]0.469[/C][/ROW]
[ROW][C]91[/C][C]12193.88[/C][C]13152.7942[/C][C]11752.8863[/C][C]14552.7021[/C][C]0.0897[/C][C]0.8477[/C][C]0.8922[/C][C]0.4733[/C][/ROW]
[ROW][C]92[/C][C]12656.63[/C][C]13152.7935[/C][C]11582.3045[/C][C]14723.2825[/C][C]0.2679[/C][C]0.8843[/C][C]0.6903[/C][C]0.4762[/C][/ROW]
[ROW][C]93[/C][C]12812.48[/C][C]13152.7934[/C][C]11428.5167[/C][C]14877.0702[/C][C]0.3494[/C][C]0.7136[/C][C]0.386[/C][C]0.4783[/C][/ROW]
[ROW][C]94[/C][C]12056.67[/C][C]13152.7934[/C][C]11287.3645[/C][C]15018.2223[/C][C]0.1247[/C][C]0.6397[/C][C]0.3654[/C][C]0.48[/C][/ROW]
[ROW][C]95[/C][C]11322.38[/C][C]13152.7934[/C][C]11156.1664[/C][C]15149.4205[/C][C]0.0362[/C][C]0.859[/C][C]0.3047[/C][C]0.4813[/C][/ROW]
[ROW][C]96[/C][C]11530.75[/C][C]13152.7934[/C][C]11033.0731[/C][C]15272.5138[/C][C]0.0668[/C][C]0.9547[/C][C]0.468[/C][C]0.4824[/C][/ROW]
[ROW][C]97[/C][C]11114.08[/C][C]13152.7934[/C][C]10916.7458[/C][C]15388.8411[/C][C]0.037[/C][C]0.9225[/C][C]0.3613[/C][C]0.4833[/C][/ROW]
[ROW][C]98[/C][C]9181.73[/C][C]13152.7934[/C][C]10806.1781[/C][C]15499.4088[/C][C]5e-04[/C][C]0.9557[/C][C]0.2659[/C][C]0.4841[/C][/ROW]
[ROW][C]99[/C][C]8614.55[/C][C]13152.7934[/C][C]10700.5907[/C][C]15604.9962[/C][C]1e-04[/C][C]0.9992[/C][C]0.4848[/C][C]0.4848[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=33580&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=33580&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[87])
7512185.15-------
7612377.62-------
7712512.89-------
7812631.48-------
7912268.53-------
8012754.8-------
8113407.75-------
8213480.21-------
8313673.28-------
8413239.71-------
8513557.69-------
8613901.28-------
8713200.58-------
8813406.9713155.844312489.465413822.22330.23010.44770.9890.4477
8912538.1213152.988212180.037414125.93910.10770.30450.90140.4618
9012419.5713152.805911947.374714358.23710.11660.84120.80170.469
9112193.8813152.794211752.886314552.70210.08970.84770.89220.4733
9212656.6313152.793511582.304514723.28250.26790.88430.69030.4762
9312812.4813152.793411428.516714877.07020.34940.71360.3860.4783
9412056.6713152.793411287.364515018.22230.12470.63970.36540.48
9511322.3813152.793411156.166415149.42050.03620.8590.30470.4813
9611530.7513152.793411033.073115272.51380.06680.95470.4680.4824
9711114.0813152.793410916.745815388.84110.0370.92250.36130.4833
989181.7313152.793410806.178115499.40885e-040.95570.26590.4841
998614.5513152.793410700.590715604.99621e-040.99920.48480.4848






Univariate ARIMA Extrapolation Forecast Performance
time% S.E.PEMAPESq.EMSERMSE
880.02580.01910.001663064.10055255.341772.4937
890.0377-0.04670.0039378062.925531505.2438177.4972
900.0468-0.05570.0046537634.843244802.9036211.667
910.0543-0.07290.0061919516.576626.375276.8147
920.0609-0.03770.0031246178.205320514.8504143.2301
930.0669-0.02590.0022115813.23689651.103198.24
940.0724-0.08330.00691201486.5869100123.8822316.4236
950.0775-0.13920.01163350413.3459279201.1122528.3948
960.0822-0.12330.01032631024.9075219252.0756468.2436
970.0867-0.1550.01294156352.4732346362.7061588.5259
980.091-0.30190.025215769344.81091314112.06761146.3473
990.0951-0.3450.028820595653.48231716304.45691310.078

\begin{tabular}{lllllllll}
\hline
Univariate ARIMA Extrapolation Forecast Performance \tabularnewline
time & % S.E. & PE & MAPE & Sq.E & MSE & RMSE \tabularnewline
88 & 0.0258 & 0.0191 & 0.0016 & 63064.1005 & 5255.3417 & 72.4937 \tabularnewline
89 & 0.0377 & -0.0467 & 0.0039 & 378062.9255 & 31505.2438 & 177.4972 \tabularnewline
90 & 0.0468 & -0.0557 & 0.0046 & 537634.8432 & 44802.9036 & 211.667 \tabularnewline
91 & 0.0543 & -0.0729 & 0.0061 & 919516.5 & 76626.375 & 276.8147 \tabularnewline
92 & 0.0609 & -0.0377 & 0.0031 & 246178.2053 & 20514.8504 & 143.2301 \tabularnewline
93 & 0.0669 & -0.0259 & 0.0022 & 115813.2368 & 9651.1031 & 98.24 \tabularnewline
94 & 0.0724 & -0.0833 & 0.0069 & 1201486.5869 & 100123.8822 & 316.4236 \tabularnewline
95 & 0.0775 & -0.1392 & 0.0116 & 3350413.3459 & 279201.1122 & 528.3948 \tabularnewline
96 & 0.0822 & -0.1233 & 0.0103 & 2631024.9075 & 219252.0756 & 468.2436 \tabularnewline
97 & 0.0867 & -0.155 & 0.0129 & 4156352.4732 & 346362.7061 & 588.5259 \tabularnewline
98 & 0.091 & -0.3019 & 0.0252 & 15769344.8109 & 1314112.0676 & 1146.3473 \tabularnewline
99 & 0.0951 & -0.345 & 0.0288 & 20595653.4823 & 1716304.4569 & 1310.078 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=33580&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]88[/C][C]0.0258[/C][C]0.0191[/C][C]0.0016[/C][C]63064.1005[/C][C]5255.3417[/C][C]72.4937[/C][/ROW]
[ROW][C]89[/C][C]0.0377[/C][C]-0.0467[/C][C]0.0039[/C][C]378062.9255[/C][C]31505.2438[/C][C]177.4972[/C][/ROW]
[ROW][C]90[/C][C]0.0468[/C][C]-0.0557[/C][C]0.0046[/C][C]537634.8432[/C][C]44802.9036[/C][C]211.667[/C][/ROW]
[ROW][C]91[/C][C]0.0543[/C][C]-0.0729[/C][C]0.0061[/C][C]919516.5[/C][C]76626.375[/C][C]276.8147[/C][/ROW]
[ROW][C]92[/C][C]0.0609[/C][C]-0.0377[/C][C]0.0031[/C][C]246178.2053[/C][C]20514.8504[/C][C]143.2301[/C][/ROW]
[ROW][C]93[/C][C]0.0669[/C][C]-0.0259[/C][C]0.0022[/C][C]115813.2368[/C][C]9651.1031[/C][C]98.24[/C][/ROW]
[ROW][C]94[/C][C]0.0724[/C][C]-0.0833[/C][C]0.0069[/C][C]1201486.5869[/C][C]100123.8822[/C][C]316.4236[/C][/ROW]
[ROW][C]95[/C][C]0.0775[/C][C]-0.1392[/C][C]0.0116[/C][C]3350413.3459[/C][C]279201.1122[/C][C]528.3948[/C][/ROW]
[ROW][C]96[/C][C]0.0822[/C][C]-0.1233[/C][C]0.0103[/C][C]2631024.9075[/C][C]219252.0756[/C][C]468.2436[/C][/ROW]
[ROW][C]97[/C][C]0.0867[/C][C]-0.155[/C][C]0.0129[/C][C]4156352.4732[/C][C]346362.7061[/C][C]588.5259[/C][/ROW]
[ROW][C]98[/C][C]0.091[/C][C]-0.3019[/C][C]0.0252[/C][C]15769344.8109[/C][C]1314112.0676[/C][C]1146.3473[/C][/ROW]
[ROW][C]99[/C][C]0.0951[/C][C]-0.345[/C][C]0.0288[/C][C]20595653.4823[/C][C]1716304.4569[/C][C]1310.078[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=33580&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=33580&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
880.02580.01910.001663064.10055255.341772.4937
890.0377-0.04670.0039378062.925531505.2438177.4972
900.0468-0.05570.0046537634.843244802.9036211.667
910.0543-0.07290.0061919516.576626.375276.8147
920.0609-0.03770.0031246178.205320514.8504143.2301
930.0669-0.02590.0022115813.23689651.103198.24
940.0724-0.08330.00691201486.5869100123.8822316.4236
950.0775-0.13920.01163350413.3459279201.1122528.3948
960.0822-0.12330.01032631024.9075219252.0756468.2436
970.0867-0.1550.01294156352.4732346362.7061588.5259
980.091-0.30190.025215769344.81091314112.06761146.3473
990.0951-0.3450.028820595653.48231716304.45691310.078


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')