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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 07:14:00 -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/t1229264117h32xffkg21n72ep.htm/, Retrieved Thu, 09 May 2024 05:45:15 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=33385, Retrieved Thu, 09 May 2024 05:45:15 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact199

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [ARIMA Forecasting] [Paper - Arima For...] [2008-12-14 14:14:00] [98255691c21504803b38711776845ae0] [Current]
-   P     [ARIMA Forecasting] [ARIMA forecasting...] [2008-12-15 14:52:51] [12d343c4448a5f9e527bb31caeac580b]
-  MPD      [ARIMA Forecasting] [paper: 10 Forecast] [2009-12-11 15:59:42] [0f0e461427f61416e46aeda5f4901bed]
-  M D      [ARIMA Forecasting] [] [2009-12-14 19:07:20] [cf890101a20378422561610e0d41fd9c]
-  M D      [ARIMA Forecasting] [] [2009-12-14 19:07:20] [cf890101a20378422561610e0d41fd9c]
-   P         [ARIMA Forecasting] [] [2009-12-17 10:19:20] [cf890101a20378422561610e0d41fd9c]
- R PD          [ARIMA Forecasting] [] [2010-12-21 14:02:55] [4f85667043e8913570b3eb8f368f82b2]
- R PD          [ARIMA Forecasting] [] [2010-12-21 14:02:55] [4f85667043e8913570b3eb8f368f82b2]
- R  D          [ARIMA Forecasting] [] [2010-12-22 10:55:23] [4f85667043e8913570b3eb8f368f82b2]
-  MPD      [ARIMA Forecasting] [univariate arima ...] [2009-12-15 20:49:36] [ba905ddf7cdf9ecb063c35348c4dab2e]
-   PD        [ARIMA Forecasting] [arima] [2009-12-24 18:21:27] [ba905ddf7cdf9ecb063c35348c4dab2e]
-  MPD      [ARIMA Forecasting] [Paper ARIMA forec...] [2009-12-18 09:44:08] [4395c69e961f9a13a0559fd2f0a72538]
- RMPD      [ARIMA Backward Selection] [] [2009-12-18 12:43:09] [5edbdb7a459c4059b6c3b063ba86821c]
-    D        [ARIMA Backward Selection] [] [2009-12-18 12:47:20] [5edbdb7a459c4059b6c3b063ba86821c]
-  MPD      [ARIMA Forecasting] [paper 10] [2009-12-20 16:27:27] [4a2be4899cba879e4eea9daa25281df8]
-  M D      [ARIMA Forecasting] [ARIMA Forecasting...] [2009-12-20 21:59:01] [73863f7f907331e734eff34b7de6fc83]
-  MPD      [ARIMA Forecasting] [ARIMA Forecasting...] [2009-12-21 11:34:13] [73863f7f907331e734eff34b7de6fc83]
- RMPD      [ARIMA Forecasting] [] [2009-12-21 16:08:37] [5d3787a0898969f50f64a85def6703e1]
- RMPD      [ARIMA Forecasting] [] [2009-12-21 16:27:37] [5d3787a0898969f50f64a85def6703e1]
- RMPD      [ARIMA Forecasting] [] [2009-12-21 16:29:37] [5d3787a0898969f50f64a85def6703e1]
-  MPD      [ARIMA Forecasting] [ARIMA FORECAST JD...] [2009-12-21 17:10:18] [74be16979710d4c4e7c6647856088456]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
14929387,5
14717825,3
15826281,2
16301309,6
15033016,9
16998460,6
14066462,7
13328937,3
17319718,2
17586426,8
15887037,4
17935679,1
15869489
15892510,9
17556558,1
16791643
15953688,5
18144913,6
14390881
13885708,7
17332571,5
17152595,8
16003877,1
16841467,1
14783398,1
14667847,5
17714362,2
16282088
15014866,2
17722582,4
13876509,4
15495489,6
17799521,1
17920079,1
17248022,4
18813782,4
16249688,3
17823358,5
20424438,3
17814218,7
19699959,6
19776328,1
15679833,1
17119266,5
20092613
20863688,3
20925203,1
21032593
20664684,3
19711511,4
22553293,4
19498332,9
20722827,8
21321275
17960847,7
17789654,9
20003708,5
21169851,7
20422839,4
19810562,3

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'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 & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=33385&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=33385&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=33385&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'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[48])
3618813782.4000000-------
3716249688.3-------
3817823358.5-------
3920424438.3-------
4017814218.7-------
4119699959.6-------
4219776328.1-------
4315679833.1-------
4417119266.5000000-------
4520092613-------
4620863688.3-------
4720925203.1-------
4821032593-------
4920664684.318837596.911717016689.914220712939.0320.02810.01090.99660.0109
5019711511.420480374.272518409361.899522616249.64580.24020.43280.99260.3062
5122553293.423187081.464920843767.322125603741.49230.30360.99760.98750.9597
5219498332.920470845.339118048029.779322982986.73870.2240.05210.98090.3306
5320722827.822434151.325119778956.899325187239.56990.11150.98170.97420.8408
542132127522513552.264219703141.124125433490.11710.21180.88530.96690.8399
5517960847.718241595.113315477342.854921137828.06050.42470.01860.95850.0295
5617789654.919745898.05216780358.373622851700.94550.10850.870.95130.2084
5720003708.522842311.812519605631.25226223002.54120.04990.99830.94460.853
5821169851.723643247.447620243869.47127196206.61470.08620.97770.93740.9251
5920422839.423707111.776720182387.024227396788.28040.04050.91110.93030.9223
6019810562.323818592.103920170410.527427642931.52520.020.95910.92330.9233

\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 & 18813782.4000000 & - & - & - & - & - & - & - \tabularnewline
37 & 16249688.3 & - & - & - & - & - & - & - \tabularnewline
38 & 17823358.5 & - & - & - & - & - & - & - \tabularnewline
39 & 20424438.3 & - & - & - & - & - & - & - \tabularnewline
40 & 17814218.7 & - & - & - & - & - & - & - \tabularnewline
41 & 19699959.6 & - & - & - & - & - & - & - \tabularnewline
42 & 19776328.1 & - & - & - & - & - & - & - \tabularnewline
43 & 15679833.1 & - & - & - & - & - & - & - \tabularnewline
44 & 17119266.5000000 & - & - & - & - & - & - & - \tabularnewline
45 & 20092613 & - & - & - & - & - & - & - \tabularnewline
46 & 20863688.3 & - & - & - & - & - & - & - \tabularnewline
47 & 20925203.1 & - & - & - & - & - & - & - \tabularnewline
48 & 21032593 & - & - & - & - & - & - & - \tabularnewline
49 & 20664684.3 & 18837596.9117 & 17016689.9142 & 20712939.032 & 0.0281 & 0.0109 & 0.9966 & 0.0109 \tabularnewline
50 & 19711511.4 & 20480374.2725 & 18409361.8995 & 22616249.6458 & 0.2402 & 0.4328 & 0.9926 & 0.3062 \tabularnewline
51 & 22553293.4 & 23187081.4649 & 20843767.3221 & 25603741.4923 & 0.3036 & 0.9976 & 0.9875 & 0.9597 \tabularnewline
52 & 19498332.9 & 20470845.3391 & 18048029.7793 & 22982986.7387 & 0.224 & 0.0521 & 0.9809 & 0.3306 \tabularnewline
53 & 20722827.8 & 22434151.3251 & 19778956.8993 & 25187239.5699 & 0.1115 & 0.9817 & 0.9742 & 0.8408 \tabularnewline
54 & 21321275 & 22513552.2642 & 19703141.1241 & 25433490.1171 & 0.2118 & 0.8853 & 0.9669 & 0.8399 \tabularnewline
55 & 17960847.7 & 18241595.1133 & 15477342.8549 & 21137828.0605 & 0.4247 & 0.0186 & 0.9585 & 0.0295 \tabularnewline
56 & 17789654.9 & 19745898.052 & 16780358.3736 & 22851700.9455 & 0.1085 & 0.87 & 0.9513 & 0.2084 \tabularnewline
57 & 20003708.5 & 22842311.8125 & 19605631.252 & 26223002.5412 & 0.0499 & 0.9983 & 0.9446 & 0.853 \tabularnewline
58 & 21169851.7 & 23643247.4476 & 20243869.471 & 27196206.6147 & 0.0862 & 0.9777 & 0.9374 & 0.9251 \tabularnewline
59 & 20422839.4 & 23707111.7767 & 20182387.0242 & 27396788.2804 & 0.0405 & 0.9111 & 0.9303 & 0.9223 \tabularnewline
60 & 19810562.3 & 23818592.1039 & 20170410.5274 & 27642931.5252 & 0.02 & 0.9591 & 0.9233 & 0.9233 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=33385&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]18813782.4000000[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]37[/C][C]16249688.3[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]38[/C][C]17823358.5[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]39[/C][C]20424438.3[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]40[/C][C]17814218.7[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]41[/C][C]19699959.6[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]42[/C][C]19776328.1[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]43[/C][C]15679833.1[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]44[/C][C]17119266.5000000[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]45[/C][C]20092613[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]46[/C][C]20863688.3[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]47[/C][C]20925203.1[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]48[/C][C]21032593[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]49[/C][C]20664684.3[/C][C]18837596.9117[/C][C]17016689.9142[/C][C]20712939.032[/C][C]0.0281[/C][C]0.0109[/C][C]0.9966[/C][C]0.0109[/C][/ROW]
[ROW][C]50[/C][C]19711511.4[/C][C]20480374.2725[/C][C]18409361.8995[/C][C]22616249.6458[/C][C]0.2402[/C][C]0.4328[/C][C]0.9926[/C][C]0.3062[/C][/ROW]
[ROW][C]51[/C][C]22553293.4[/C][C]23187081.4649[/C][C]20843767.3221[/C][C]25603741.4923[/C][C]0.3036[/C][C]0.9976[/C][C]0.9875[/C][C]0.9597[/C][/ROW]
[ROW][C]52[/C][C]19498332.9[/C][C]20470845.3391[/C][C]18048029.7793[/C][C]22982986.7387[/C][C]0.224[/C][C]0.0521[/C][C]0.9809[/C][C]0.3306[/C][/ROW]
[ROW][C]53[/C][C]20722827.8[/C][C]22434151.3251[/C][C]19778956.8993[/C][C]25187239.5699[/C][C]0.1115[/C][C]0.9817[/C][C]0.9742[/C][C]0.8408[/C][/ROW]
[ROW][C]54[/C][C]21321275[/C][C]22513552.2642[/C][C]19703141.1241[/C][C]25433490.1171[/C][C]0.2118[/C][C]0.8853[/C][C]0.9669[/C][C]0.8399[/C][/ROW]
[ROW][C]55[/C][C]17960847.7[/C][C]18241595.1133[/C][C]15477342.8549[/C][C]21137828.0605[/C][C]0.4247[/C][C]0.0186[/C][C]0.9585[/C][C]0.0295[/C][/ROW]
[ROW][C]56[/C][C]17789654.9[/C][C]19745898.052[/C][C]16780358.3736[/C][C]22851700.9455[/C][C]0.1085[/C][C]0.87[/C][C]0.9513[/C][C]0.2084[/C][/ROW]
[ROW][C]57[/C][C]20003708.5[/C][C]22842311.8125[/C][C]19605631.252[/C][C]26223002.5412[/C][C]0.0499[/C][C]0.9983[/C][C]0.9446[/C][C]0.853[/C][/ROW]
[ROW][C]58[/C][C]21169851.7[/C][C]23643247.4476[/C][C]20243869.471[/C][C]27196206.6147[/C][C]0.0862[/C][C]0.9777[/C][C]0.9374[/C][C]0.9251[/C][/ROW]
[ROW][C]59[/C][C]20422839.4[/C][C]23707111.7767[/C][C]20182387.0242[/C][C]27396788.2804[/C][C]0.0405[/C][C]0.9111[/C][C]0.9303[/C][C]0.9223[/C][/ROW]
[ROW][C]60[/C][C]19810562.3[/C][C]23818592.1039[/C][C]20170410.5274[/C][C]27642931.5252[/C][C]0.02[/C][C]0.9591[/C][C]0.9233[/C][C]0.9233[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=33385&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=33385&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])
3618813782.4000000-------
3716249688.3-------
3817823358.5-------
3920424438.3-------
4017814218.7-------
4119699959.6-------
4219776328.1-------
4315679833.1-------
4417119266.5000000-------
4520092613-------
4620863688.3-------
4720925203.1-------
4821032593-------
4920664684.318837596.911717016689.914220712939.0320.02810.01090.99660.0109
5019711511.420480374.272518409361.899522616249.64580.24020.43280.99260.3062
5122553293.423187081.464920843767.322125603741.49230.30360.99760.98750.9597
5219498332.920470845.339118048029.779322982986.73870.2240.05210.98090.3306
5320722827.822434151.325119778956.899325187239.56990.11150.98170.97420.8408
542132127522513552.264219703141.124125433490.11710.21180.88530.96690.8399
5517960847.718241595.113315477342.854921137828.06050.42470.01860.95850.0295
5617789654.919745898.05216780358.373622851700.94550.10850.870.95130.2084
5720003708.522842311.812519605631.25226223002.54120.04990.99830.94460.853
5821169851.723643247.447620243869.47127196206.61470.08620.97770.93740.9251
5920422839.423707111.776720182387.024227396788.28040.04050.91110.93030.9223
6019810562.323818592.103920170410.527427642931.52520.020.95910.92330.9233






Univariate ARIMA Extrapolation Forecast Performance
time% S.E.PEMAPESq.EMSERMSE
490.05080.0970.00813338248324553.6278187360379.466527434.6977
500.0532-0.03750.0031591150116703.42149262509725.2851221951.5932
510.0532-0.02730.0023401687311247.47233473942603.956182958.8549
520.0626-0.04750.004945780444110.39378815037009.1994280740.1592
530.0626-0.07630.00642928628207563.05244052350630.254494016.5489
540.0662-0.0530.00441421525074662.09118460422888.507344180.7997
550.081-0.01540.001378819110068.02916568259172.335881044.7973
560.0802-0.09910.00833826887269687.6318907272473.967564718.7552
570.0755-0.12430.01048057668765458.11671472397121.51819434.1933
580.0767-0.10460.00876117686524222.43509807210351.87714007.8503
590.0794-0.13850.011510786445044653.6898870420387.803948087.7704
600.0819-0.16830.01416064302908771.21338691909064.271157018.5431

\begin{tabular}{lllllllll}
\hline
Univariate ARIMA Extrapolation Forecast Performance \tabularnewline
time & % S.E. & PE & MAPE & Sq.E & MSE & RMSE \tabularnewline
49 & 0.0508 & 0.097 & 0.0081 & 3338248324553.6 & 278187360379.466 & 527434.6977 \tabularnewline
50 & 0.0532 & -0.0375 & 0.0031 & 591150116703.421 & 49262509725.2851 & 221951.5932 \tabularnewline
51 & 0.0532 & -0.0273 & 0.0023 & 401687311247.472 & 33473942603.956 & 182958.8549 \tabularnewline
52 & 0.0626 & -0.0475 & 0.004 & 945780444110.393 & 78815037009.1994 & 280740.1592 \tabularnewline
53 & 0.0626 & -0.0763 & 0.0064 & 2928628207563.05 & 244052350630.254 & 494016.5489 \tabularnewline
54 & 0.0662 & -0.053 & 0.0044 & 1421525074662.09 & 118460422888.507 & 344180.7997 \tabularnewline
55 & 0.081 & -0.0154 & 0.0013 & 78819110068.0291 & 6568259172.3358 & 81044.7973 \tabularnewline
56 & 0.0802 & -0.0991 & 0.0083 & 3826887269687.6 & 318907272473.967 & 564718.7552 \tabularnewline
57 & 0.0755 & -0.1243 & 0.0104 & 8057668765458.11 & 671472397121.51 & 819434.1933 \tabularnewline
58 & 0.0767 & -0.1046 & 0.0087 & 6117686524222.43 & 509807210351.87 & 714007.8503 \tabularnewline
59 & 0.0794 & -0.1385 & 0.0115 & 10786445044653.6 & 898870420387.803 & 948087.7704 \tabularnewline
60 & 0.0819 & -0.1683 & 0.014 & 16064302908771.2 & 1338691909064.27 & 1157018.5431 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=33385&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]0.0508[/C][C]0.097[/C][C]0.0081[/C][C]3338248324553.6[/C][C]278187360379.466[/C][C]527434.6977[/C][/ROW]
[ROW][C]50[/C][C]0.0532[/C][C]-0.0375[/C][C]0.0031[/C][C]591150116703.421[/C][C]49262509725.2851[/C][C]221951.5932[/C][/ROW]
[ROW][C]51[/C][C]0.0532[/C][C]-0.0273[/C][C]0.0023[/C][C]401687311247.472[/C][C]33473942603.956[/C][C]182958.8549[/C][/ROW]
[ROW][C]52[/C][C]0.0626[/C][C]-0.0475[/C][C]0.004[/C][C]945780444110.393[/C][C]78815037009.1994[/C][C]280740.1592[/C][/ROW]
[ROW][C]53[/C][C]0.0626[/C][C]-0.0763[/C][C]0.0064[/C][C]2928628207563.05[/C][C]244052350630.254[/C][C]494016.5489[/C][/ROW]
[ROW][C]54[/C][C]0.0662[/C][C]-0.053[/C][C]0.0044[/C][C]1421525074662.09[/C][C]118460422888.507[/C][C]344180.7997[/C][/ROW]
[ROW][C]55[/C][C]0.081[/C][C]-0.0154[/C][C]0.0013[/C][C]78819110068.0291[/C][C]6568259172.3358[/C][C]81044.7973[/C][/ROW]
[ROW][C]56[/C][C]0.0802[/C][C]-0.0991[/C][C]0.0083[/C][C]3826887269687.6[/C][C]318907272473.967[/C][C]564718.7552[/C][/ROW]
[ROW][C]57[/C][C]0.0755[/C][C]-0.1243[/C][C]0.0104[/C][C]8057668765458.11[/C][C]671472397121.51[/C][C]819434.1933[/C][/ROW]
[ROW][C]58[/C][C]0.0767[/C][C]-0.1046[/C][C]0.0087[/C][C]6117686524222.43[/C][C]509807210351.87[/C][C]714007.8503[/C][/ROW]
[ROW][C]59[/C][C]0.0794[/C][C]-0.1385[/C][C]0.0115[/C][C]10786445044653.6[/C][C]898870420387.803[/C][C]948087.7704[/C][/ROW]
[ROW][C]60[/C][C]0.0819[/C][C]-0.1683[/C][C]0.014[/C][C]16064302908771.2[/C][C]1338691909064.27[/C][C]1157018.5431[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=33385&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=33385&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
490.05080.0970.00813338248324553.6278187360379.466527434.6977
500.0532-0.03750.0031591150116703.42149262509725.2851221951.5932
510.0532-0.02730.0023401687311247.47233473942603.956182958.8549
520.0626-0.04750.004945780444110.39378815037009.1994280740.1592
530.0626-0.07630.00642928628207563.05244052350630.254494016.5489
540.0662-0.0530.00441421525074662.09118460422888.507344180.7997
550.081-0.01540.001378819110068.02916568259172.335881044.7973
560.0802-0.09910.00833826887269687.6318907272473.967564718.7552
570.0755-0.12430.01048057668765458.11671472397121.51819434.1933
580.0767-0.10460.00876117686524222.43509807210351.87714007.8503
590.0794-0.13850.011510786445044653.6898870420387.803948087.7704
600.0819-0.16830.01416064302908771.21338691909064.271157018.5431


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 12 ; par2 = 0.7 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = 0 ; par7 = 1 ; par8 = 0 ; par9 = 0 ; par10 = FALSE ;
Parameters (R input):
par1 = 12 ; par2 = 0.7 ; par3 = 1 ; par4 = 1 ; 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')