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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_arimabackwardselection.wasp
Title produced by softwareARIMA Backward Selection
Date of computationSun, 07 Dec 2008 07:04:55 -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/07/t1228658812uixiosauqyxcirv.htm/, Retrieved Sun, 19 May 2024 10:44:08 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=29993, Retrieved Sun, 19 May 2024 10:44:08 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact234

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F       [ARIMA Backward Selection] [] [2008-12-07 14:04:55] [d41d8cd98f00b204e9800998ecf8427e] [Current]
- RMPD    [(Partial) Autocorrelation Function] [] [2008-12-08 19:08:17] [a4ee3bef49b119f4bd2e925060c84f5e]
- RMPD    [(Partial) Autocorrelation Function] [] [2008-12-08 19:23:30] [a4ee3bef49b119f4bd2e925060c84f5e]
-   PD    [ARIMA Backward Selection] [] [2008-12-08 19:29:21] [a4ee3bef49b119f4bd2e925060c84f5e]
F RMPD    [Standard Deviation-Mean Plot] [] [2008-12-08 19:35:41] [a4ee3bef49b119f4bd2e925060c84f5e]
F   P       [Standard Deviation-Mean Plot] [] [2008-12-09 08:33:18] [888addc516c3b812dd7be4bd54caa358]
F RMPD    [Variance Reduction Matrix] [] [2008-12-08 19:37:16] [a4ee3bef49b119f4bd2e925060c84f5e]
F RMPD    [(Partial) Autocorrelation Function] [] [2008-12-08 19:38:58] [a4ee3bef49b119f4bd2e925060c84f5e]
- RMPD      [ARIMA Forecasting] [] [2008-12-13 11:19:07] [a4ee3bef49b119f4bd2e925060c84f5e]
-   P         [ARIMA Forecasting] [] [2008-12-14 12:52:58] [a4ee3bef49b119f4bd2e925060c84f5e]
-   P         [ARIMA Forecasting] [] [2008-12-14 12:57:19] [a4ee3bef49b119f4bd2e925060c84f5e]
F               [ARIMA Forecasting] [step 1] [2008-12-15 20:19:09] [2b46c8b774ad566be9a33a8da3812a44]
- RMPD        [ARIMA Backward Selection] [] [2008-12-14 13:52:19] [a4ee3bef49b119f4bd2e925060c84f5e]
- RMP           [ARIMA Forecasting] [ARIMA Forecast To...] [2008-12-15 10:56:57] [b635de6fc42b001d22cbe6e730fec936]
-   P     [ARIMA Backward Selection] [] [2008-12-08 19:40:36] [ffbe22449df335faef31f462015daa42]
- RMPD    [Spectral Analysis] [] [2008-12-08 19:40:26] [a4ee3bef49b119f4bd2e925060c84f5e]
F RMPD    [Spectral Analysis] [] [2008-12-08 19:43:41] [a4ee3bef49b119f4bd2e925060c84f5e]
F RMPD    [(Partial) Autocorrelation Function] [] [2008-12-08 19:44:59] [a4ee3bef49b119f4bd2e925060c84f5e]
Feedback Forum
2008-12-15 23:04:23 [Kenny Simons] [reply] 
Hier is de student de mist in gegaan. De parameters zijn verkeerd ingevuld. Je moet ze eerst op maximum zetten om zo tot een goed arima model te komen.

De parameters moesten als volgt ingevuld worden:
 Lambda = 0,5
 d = 1
 D = 1
 Seiz. = 12
 Max p = 3
 Max q = 1
 Max P = 2
 Max Q = 1

Als je dit had gedaan, had je deze link bekomen:
http://www.freestatistics.org/blog/index.php?v=date/2008/Dec/15/t1229309753yabwpsgalun4dp1.htm


De arima backward methode helpt ons na te gaan of de gevonden parameters in step 1 tot step 4 correct gekozen zijn.

Dit model kunnen we als volgt interpreteren.
 Elke rij is een model.
 De waarden in de blokjes stellen de -waarde voor.
 De kleine driehoekjes in de blokjes geven de p-waarde weer. Deze kunnen 4 kleuren hebben:
-Groen: P-waarde = 0
-Bruin: P-waarde =tussen 0,01 / 0,05
-Rood: P-waarde = tussen 0,05 / 0,1
-Zwart: P-waarde = tussen 0,1 / 1
 De onderste rijen dus het onderste model is het beste.

In de eerste rij zie je dat AR 3 niet significant is, omdat het driehoekje een zwarte kleur heeft.
In de 2e rij zien we dat parameter AR3 verdwenen is. Nu zijn de SAR-parameters niet significant. Deze moeten we laten vallen..

In de 3e rij is Sar 2 verdwenen omdat deze de hoogste waarde van de twee had. Sar 1 nog steeds een zwart driehoekje. Hierdoor zien we naar de 4e en laatste rij.

In de 4e rij kunnen we aflezen met welk model we te maken hebben. In dit geval gaat het over een AR2 , MA1 en SMA1 Proces.

Als we het model nu met de bekomen parameters uitschrijven, bekomen we dit:

(1-1B-2B²) 12√Yt = (1- ϑB)(1-ϑ1B12)et

Vervolgens controleren we nog de assumpties.

Als we de grafiek van de residual autocorrelation function bezien, merken we op dat er geen seizoenaliteit, geen LT-trend en geen patroon meer zichtbaar is. Er is slechts 1 coëfficiënt dat niet binnen het betrouwbaarheidsinterval ligt, maar dit is geen probleem omdat we werken met een betrouwbaarheid van 95%. Op 200 coëfficiënten wil dit zeggen dat er 10 buiten het interval kunnen/mogen liggen. Er is dus geen autocorrelatie meer.

Op de grafiek van de residual cumulative periodogram zien we dat de lijn nu perfect binnen het betrouwbaarheidsinterval ligt. Het histogram en de density plot geven beide een normaalverdeling weer.

We kunnen dus besluiten dat het model nu in orde is, want er is geen autocorrelatie meer en er is nu een normaalverdeling.

Post a new message

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
235.1
280.7
264.6
240.7
201.4
240.8
241.1
223.8
206.1
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347.4
338.3
327.7
351.6
396.6
438.8
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363.5
378.8
357
369
464.8
479.1
431.3
366.5
326.3
355.1
331.6
261.3
249
205.5
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232.3
193.8
177
213.2
207.2
180.6
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234
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178.2
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343.3
292.9
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572.5

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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 & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=29993&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]3 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=29993&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29993&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 time3 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






ARIMA Parameter Estimation and Backward Selection
Iterationar1sma1
Estimates ( 1 )0.1409-0.7401
(p-val)(0.0084 )(0 )
Estimates ( 2 )0-1.3201
(p-val)(NA )(0 )
Estimates ( 3 )NANA
(p-val)(NA )(NA )

\begin{tabular}{lllllllll}
\hline
ARIMA Parameter Estimation and Backward Selection \tabularnewline
Iteration & ar1 & sma1 \tabularnewline
Estimates ( 1 ) & 0.1409 & -0.7401 \tabularnewline
(p-val) & (0.0084 ) & (0 ) \tabularnewline
Estimates ( 2 ) & 0 & -1.3201 \tabularnewline
(p-val) & (NA ) & (0 ) \tabularnewline
Estimates ( 3 ) & NA & NA \tabularnewline
(p-val) & (NA ) & (NA ) \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=29993&T=1

[TABLE]
[ROW][C]ARIMA Parameter Estimation and Backward Selection[/C][/ROW]
[ROW][C]Iteration[/C][C]ar1[/C][C]sma1[/C][/ROW]
[ROW][C]Estimates ( 1 )[/C][C]0.1409[/C][C]-0.7401[/C][/ROW]
[ROW][C](p-val)[/C][C](0.0084 )[/C][C](0 )[/C][/ROW]
[ROW][C]Estimates ( 2 )[/C][C]0[/C][C]-1.3201[/C][/ROW]
[ROW][C](p-val)[/C][C](NA )[/C][C](0 )[/C][/ROW]
[ROW][C]Estimates ( 3 )[/C][C]NA[/C][C]NA[/C][/ROW]
[ROW][C](p-val)[/C][C](NA )[/C][C](NA )[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=29993&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29993&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:

ARIMA Parameter Estimation and Backward Selection
Iterationar1sma1
Estimates ( 1 )0.1409-0.7401
(p-val)(0.0084 )(0 )
Estimates ( 2 )0-1.3201
(p-val)(NA )(0 )
Estimates ( 3 )NANA
(p-val)(NA )(NA )






Estimated ARIMA Residuals
Value
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-0.416095271072094
0.570091475053155
0.164171215279737
-0.278099004584488
-0.399903216466279
0.276065270828965
-0.183484082576004
0.0280995958703195
-0.394707404846936
0.173134025255439
-0.313189246872826
-0.224516542030629
-0.307507179684471
0.218795074675831
0.0349649733807163
-0.149094221114195
-0.119261753593472
-0.874999310092227
-0.0785986922164093
-0.303394341488209
0.220058101524419
-0.279879278614641
0.169165626550553
-0.324900079217714
-0.138864653389882
0.0159725276535892
-0.0667083453817329
0.256508087990534
-0.707579663337128
0.661797573069472
0.140027138042760
0.623406892872159
-0.0605449757970465
-0.289251457742578
-0.11732503796901
0.352905542208752
0.131851019302699
0.392751706823959
-0.124577696020257
1.00294374806918
0.0229117324672210
1.04005469568175
0.875138129106983
1.99625594245141
-0.34648456714327
0.747753308228602
-0.101523789369636
0.271923420497328
-1.08123150968054
0.0948204714650919
-0.118334876118100
-0.268104159187353
-0.00173199018612319
-0.615882809239734
-0.087988056865133
-0.514612378368584
-0.429601880041536
-0.377455697479242
-0.169897398272989
-0.552165379195016
0.207377755873382
0.424034771741994
0.287310058261187
-0.497955457699965
0.177117991968696
0.0443419813167771
-0.208815440722914
-0.622451281907236
0.427149650602193
-0.456641973269615
-0.79200077081928
0.000852829419739935
0.0483062127677115
-0.490665002722778
0.442784527838166
-0.455228583822449
0.0782893841690099
-0.205445155590349
-0.924915865190904
0.150927614291425
-0.518612459318498
0.252148581391821
-0.398414242738324
0.302205274747805
-0.719455908749632
0.912605450528232
-0.50596772932521
0.103473122629045
-0.271841862352215
-0.0029377226106754
0.444033971646533

\begin{tabular}{lllllllll}
\hline
Estimated ARIMA Residuals \tabularnewline
Value \tabularnewline
-0.0447155215240564 \tabularnewline
-0.0704353335375155 \tabularnewline
0.204383035977208 \tabularnewline
0.343590856822772 \tabularnewline
1.53235641053271 \tabularnewline
-0.353774667018016 \tabularnewline
0.840661799348455 \tabularnewline
-0.510091240295515 \tabularnewline
-0.121597537342134 \tabularnewline
1.25937055354956 \tabularnewline
-1.46759577784405 \tabularnewline
-0.0404146406610601 \tabularnewline
-0.0598145297172682 \tabularnewline
-0.943696848936777 \tabularnewline
-0.560032921800867 \tabularnewline
-0.920236494446471 \tabularnewline
-0.576158571064935 \tabularnewline
-0.320715841179214 \tabularnewline
-1.01845999165732 \tabularnewline
-0.96638381555172 \tabularnewline
0.462812147107481 \tabularnewline
-1.05639305174936 \tabularnewline
0.886147550388205 \tabularnewline
-0.359724879152859 \tabularnewline
-1.49383981570117 \tabularnewline
-1.06007138090481 \tabularnewline
0.140326740829799 \tabularnewline
-0.364768617855696 \tabularnewline
0.0290662907965497 \tabularnewline
0.224624595008922 \tabularnewline
-0.321414595262205 \tabularnewline
0.359001705705696 \tabularnewline
0.804481632795936 \tabularnewline
0.13784795227238 \tabularnewline
0.301251178750939 \tabularnewline
-1.05493250175468 \tabularnewline
-0.0269559123770988 \tabularnewline
-0.253998013731939 \tabularnewline
-0.435613597309457 \tabularnewline
0.515305002088366 \tabularnewline
0.328132754897662 \tabularnewline
-0.284598105069671 \tabularnewline
0.214086701144757 \tabularnewline
0.552582014711514 \tabularnewline
-0.468778480412715 \tabularnewline
-0.246672604053907 \tabularnewline
-0.117686316427589 \tabularnewline
-0.177983538458835 \tabularnewline
0.444704772296298 \tabularnewline
-1.10402113922085 \tabularnewline
0.453994545714176 \tabularnewline
0.634133615437254 \tabularnewline
-0.494679134003473 \tabularnewline
-0.245077650687217 \tabularnewline
-0.092919208679261 \tabularnewline
0.245080526996974 \tabularnewline
0.809380263143736 \tabularnewline
0.450508231641225 \tabularnewline
0.995643891366349 \tabularnewline
1.05760914117721 \tabularnewline
1.43420080486901 \tabularnewline
0.678016193899131 \tabularnewline
0.720596032986933 \tabularnewline
0.132256650210588 \tabularnewline
0.0744547737613371 \tabularnewline
-0.937121070542617 \tabularnewline
0.109555616223195 \tabularnewline
0.393333145235029 \tabularnewline
0.0326453281791595 \tabularnewline
-0.819001881895963 \tabularnewline
-0.226315562541894 \tabularnewline
-0.53978612098446 \tabularnewline
-0.426494724036775 \tabularnewline
-0.611682356535021 \tabularnewline
-0.148356064724198 \tabularnewline
0.324019238253844 \tabularnewline
-0.852668635956679 \tabularnewline
-0.0155161556620593 \tabularnewline
-0.682207847558002 \tabularnewline
0.546328954446236 \tabularnewline
-0.53172494172034 \tabularnewline
0.706953039006389 \tabularnewline
-0.0635394462523348 \tabularnewline
0.0693714733142069 \tabularnewline
-0.808363930579449 \tabularnewline
-0.0545046416719144 \tabularnewline
0.584713443053854 \tabularnewline
-0.619370562648199 \tabularnewline
1.12423968325724 \tabularnewline
0.247767835680543 \tabularnewline
-0.434011932107338 \tabularnewline
-0.791707166690393 \tabularnewline
-0.221957251080234 \tabularnewline
0.0821672487557488 \tabularnewline
0.862523507509944 \tabularnewline
-0.0830032277649072 \tabularnewline
-0.380117242455725 \tabularnewline
-0.485141072539303 \tabularnewline
-0.283150430851938 \tabularnewline
0.190997609389973 \tabularnewline
0.510526427249245 \tabularnewline
0.579163259486582 \tabularnewline
-0.648966997001509 \tabularnewline
0.0539830294228536 \tabularnewline
0.308924857713502 \tabularnewline
0.477292098640667 \tabularnewline
0.888370264286018 \tabularnewline
0.275399112124137 \tabularnewline
0.942912193685502 \tabularnewline
1.29213582512030 \tabularnewline
0.383852472244307 \tabularnewline
0.410559876388898 \tabularnewline
-0.223450942603087 \tabularnewline
-0.0846734546320959 \tabularnewline
0.161469026910882 \tabularnewline
-0.185650009402128 \tabularnewline
-0.997250489625638 \tabularnewline
-0.130395671304672 \tabularnewline
-1.1425456416149 \tabularnewline
0.613694776752398 \tabularnewline
-0.737563575778369 \tabularnewline
-0.289046086431741 \tabularnewline
-0.541765352631671 \tabularnewline
-1.21861331890744 \tabularnewline
-0.0314489266512679 \tabularnewline
0.281601030586419 \tabularnewline
-0.107273412238293 \tabularnewline
0.310766256079911 \tabularnewline
0.101931792189831 \tabularnewline
0.656666904719546 \tabularnewline
0.0340324419631722 \tabularnewline
-0.705310820471469 \tabularnewline
-0.330496994774258 \tabularnewline
-0.852386956096837 \tabularnewline
1.32366107768567 \tabularnewline
-0.676834698215901 \tabularnewline
-0.0721047086552707 \tabularnewline
1.04457534206299 \tabularnewline
-0.459635044865709 \tabularnewline
0.514906743922494 \tabularnewline
-0.596001339118493 \tabularnewline
1.07470980911778 \tabularnewline
-0.0280535872241519 \tabularnewline
1.00457752939272 \tabularnewline
-0.0356759078313158 \tabularnewline
0.572325621503041 \tabularnewline
-0.382091670595813 \tabularnewline
-0.101106295807447 \tabularnewline
0.0270830764522009 \tabularnewline
0.153771150800864 \tabularnewline
-0.314165086362222 \tabularnewline
-0.368703395851731 \tabularnewline
-0.263908287260354 \tabularnewline
-0.244672938006823 \tabularnewline
-0.788572404401233 \tabularnewline
-0.102757662409262 \tabularnewline
-0.450019667387897 \tabularnewline
-0.506070053578337 \tabularnewline
-0.0264313516513532 \tabularnewline
-0.0474501779488537 \tabularnewline
0.733069645821482 \tabularnewline
-0.764349012245764 \tabularnewline
-0.318783974804085 \tabularnewline
0.98984421684828 \tabularnewline
-0.396176938099767 \tabularnewline
-0.351265682407397 \tabularnewline
0.562980683049922 \tabularnewline
-0.396500264895954 \tabularnewline
0.415283051033411 \tabularnewline
0.409018908026867 \tabularnewline
-0.759783351314399 \tabularnewline
0.0953242608886003 \tabularnewline
0.200844689806792 \tabularnewline
0.289013819537990 \tabularnewline
-0.370393193568025 \tabularnewline
-0.266857272780982 \tabularnewline
0.111485903022112 \tabularnewline
0.102093687796911 \tabularnewline
0.259876193496945 \tabularnewline
-0.546144405098477 \tabularnewline
0.0179986397895542 \tabularnewline
-0.34334799093622 \tabularnewline
-0.0390777533675878 \tabularnewline
0.122273710656280 \tabularnewline
-0.546647414433681 \tabularnewline
1.16075568293815 \tabularnewline
-1.33273154129292 \tabularnewline
0.577692888175691 \tabularnewline
-0.0412600595925113 \tabularnewline
0.107304430940684 \tabularnewline
-0.698022015539628 \tabularnewline
0.147779525049814 \tabularnewline
-0.451162965635083 \tabularnewline
0.510861998586957 \tabularnewline
-0.75506314755249 \tabularnewline
0.614701027328518 \tabularnewline
-0.435280139956835 \tabularnewline
0.749961051161294 \tabularnewline
-0.664198700815297 \tabularnewline
-0.0166626883737108 \tabularnewline
-0.123187966655755 \tabularnewline
-0.120713421073439 \tabularnewline
-0.282812631417830 \tabularnewline
-0.464078564304735 \tabularnewline
-0.331824937665995 \tabularnewline
-0.56365474644945 \tabularnewline
0.427247824587208 \tabularnewline
0.111932195721085 \tabularnewline
0.658072618767547 \tabularnewline
0.447345881423942 \tabularnewline
-0.359123992724486 \tabularnewline
0.02719071640604 \tabularnewline
-0.142186926517785 \tabularnewline
0.195316608883191 \tabularnewline
-0.424691357639979 \tabularnewline
0.243709232157433 \tabularnewline
-0.189858915617572 \tabularnewline
0.0127605561143377 \tabularnewline
-0.0628438902607073 \tabularnewline
0.0307944383600589 \tabularnewline
-0.332661901374049 \tabularnewline
1.57746375845208 \tabularnewline
0.0411717673291143 \tabularnewline
-0.249821606573593 \tabularnewline
0.76094178295504 \tabularnewline
0.313841457022639 \tabularnewline
-0.856920728288364 \tabularnewline
-0.560225922113031 \tabularnewline
-0.434578532506293 \tabularnewline
0.59403090165304 \tabularnewline
-0.479955903355932 \tabularnewline
-0.392590459365407 \tabularnewline
-0.140787878768313 \tabularnewline
1.62683111542213 \tabularnewline
-0.0898451189552398 \tabularnewline
-0.591124282052134 \tabularnewline
0.255940634060494 \tabularnewline
-0.186139886421883 \tabularnewline
-0.217899036721367 \tabularnewline
-0.418187448010847 \tabularnewline
0.0374135252614398 \tabularnewline
-0.0681287746719672 \tabularnewline
0.202104146355373 \tabularnewline
0.340977029887173 \tabularnewline
-0.376871775547671 \tabularnewline
0.640535818790618 \tabularnewline
0.519695497931741 \tabularnewline
-0.118822039322625 \tabularnewline
0.89543048293497 \tabularnewline
-0.288253050722115 \tabularnewline
-0.752335480935497 \tabularnewline
0.0205531920527481 \tabularnewline
0.834469605339556 \tabularnewline
0.712937218033068 \tabularnewline
0.390848233276471 \tabularnewline
0.35708561683383 \tabularnewline
0.0258669133438303 \tabularnewline
0.394058265596066 \tabularnewline
0.592108651353634 \tabularnewline
0.0864722858475862 \tabularnewline
0.55088091280636 \tabularnewline
0.0651245516928922 \tabularnewline
0.622406167071036 \tabularnewline
0.165318992612725 \tabularnewline
0.0616265379709319 \tabularnewline
-0.363152348919614 \tabularnewline
0.00263954954740357 \tabularnewline
-0.284997586234302 \tabularnewline
-0.147777810393251 \tabularnewline
-0.416095271072094 \tabularnewline
0.570091475053155 \tabularnewline
0.164171215279737 \tabularnewline
-0.278099004584488 \tabularnewline
-0.399903216466279 \tabularnewline
0.276065270828965 \tabularnewline
-0.183484082576004 \tabularnewline
0.0280995958703195 \tabularnewline
-0.394707404846936 \tabularnewline
0.173134025255439 \tabularnewline
-0.313189246872826 \tabularnewline
-0.224516542030629 \tabularnewline
-0.307507179684471 \tabularnewline
0.218795074675831 \tabularnewline
0.0349649733807163 \tabularnewline
-0.149094221114195 \tabularnewline
-0.119261753593472 \tabularnewline
-0.874999310092227 \tabularnewline
-0.0785986922164093 \tabularnewline
-0.303394341488209 \tabularnewline
0.220058101524419 \tabularnewline
-0.279879278614641 \tabularnewline
0.169165626550553 \tabularnewline
-0.324900079217714 \tabularnewline
-0.138864653389882 \tabularnewline
0.0159725276535892 \tabularnewline
-0.0667083453817329 \tabularnewline
0.256508087990534 \tabularnewline
-0.707579663337128 \tabularnewline
0.661797573069472 \tabularnewline
0.140027138042760 \tabularnewline
0.623406892872159 \tabularnewline
-0.0605449757970465 \tabularnewline
-0.289251457742578 \tabularnewline
-0.11732503796901 \tabularnewline
0.352905542208752 \tabularnewline
0.131851019302699 \tabularnewline
0.392751706823959 \tabularnewline
-0.124577696020257 \tabularnewline
1.00294374806918 \tabularnewline
0.0229117324672210 \tabularnewline
1.04005469568175 \tabularnewline
0.875138129106983 \tabularnewline
1.99625594245141 \tabularnewline
-0.34648456714327 \tabularnewline
0.747753308228602 \tabularnewline
-0.101523789369636 \tabularnewline
0.271923420497328 \tabularnewline
-1.08123150968054 \tabularnewline
0.0948204714650919 \tabularnewline
-0.118334876118100 \tabularnewline
-0.268104159187353 \tabularnewline
-0.00173199018612319 \tabularnewline
-0.615882809239734 \tabularnewline
-0.087988056865133 \tabularnewline
-0.514612378368584 \tabularnewline
-0.429601880041536 \tabularnewline
-0.377455697479242 \tabularnewline
-0.169897398272989 \tabularnewline
-0.552165379195016 \tabularnewline
0.207377755873382 \tabularnewline
0.424034771741994 \tabularnewline
0.287310058261187 \tabularnewline
-0.497955457699965 \tabularnewline
0.177117991968696 \tabularnewline
0.0443419813167771 \tabularnewline
-0.208815440722914 \tabularnewline
-0.622451281907236 \tabularnewline
0.427149650602193 \tabularnewline
-0.456641973269615 \tabularnewline
-0.79200077081928 \tabularnewline
0.000852829419739935 \tabularnewline
0.0483062127677115 \tabularnewline
-0.490665002722778 \tabularnewline
0.442784527838166 \tabularnewline
-0.455228583822449 \tabularnewline
0.0782893841690099 \tabularnewline
-0.205445155590349 \tabularnewline
-0.924915865190904 \tabularnewline
0.150927614291425 \tabularnewline
-0.518612459318498 \tabularnewline
0.252148581391821 \tabularnewline
-0.398414242738324 \tabularnewline
0.302205274747805 \tabularnewline
-0.719455908749632 \tabularnewline
0.912605450528232 \tabularnewline
-0.50596772932521 \tabularnewline
0.103473122629045 \tabularnewline
-0.271841862352215 \tabularnewline
-0.0029377226106754 \tabularnewline
0.444033971646533 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=29993&T=2

[TABLE]
[ROW][C]Estimated ARIMA Residuals[/C][/ROW]
[ROW][C]Value[/C][/ROW]
[ROW][C]-0.0447155215240564[/C][/ROW]
[ROW][C]-0.0704353335375155[/C][/ROW]
[ROW][C]0.204383035977208[/C][/ROW]
[ROW][C]0.343590856822772[/C][/ROW]
[ROW][C]1.53235641053271[/C][/ROW]
[ROW][C]-0.353774667018016[/C][/ROW]
[ROW][C]0.840661799348455[/C][/ROW]
[ROW][C]-0.510091240295515[/C][/ROW]
[ROW][C]-0.121597537342134[/C][/ROW]
[ROW][C]1.25937055354956[/C][/ROW]
[ROW][C]-1.46759577784405[/C][/ROW]
[ROW][C]-0.0404146406610601[/C][/ROW]
[ROW][C]-0.0598145297172682[/C][/ROW]
[ROW][C]-0.943696848936777[/C][/ROW]
[ROW][C]-0.560032921800867[/C][/ROW]
[ROW][C]-0.920236494446471[/C][/ROW]
[ROW][C]-0.576158571064935[/C][/ROW]
[ROW][C]-0.320715841179214[/C][/ROW]
[ROW][C]-1.01845999165732[/C][/ROW]
[ROW][C]-0.96638381555172[/C][/ROW]
[ROW][C]0.462812147107481[/C][/ROW]
[ROW][C]-1.05639305174936[/C][/ROW]
[ROW][C]0.886147550388205[/C][/ROW]
[ROW][C]-0.359724879152859[/C][/ROW]
[ROW][C]-1.49383981570117[/C][/ROW]
[ROW][C]-1.06007138090481[/C][/ROW]
[ROW][C]0.140326740829799[/C][/ROW]
[ROW][C]-0.364768617855696[/C][/ROW]
[ROW][C]0.0290662907965497[/C][/ROW]
[ROW][C]0.224624595008922[/C][/ROW]
[ROW][C]-0.321414595262205[/C][/ROW]
[ROW][C]0.359001705705696[/C][/ROW]
[ROW][C]0.804481632795936[/C][/ROW]
[ROW][C]0.13784795227238[/C][/ROW]
[ROW][C]0.301251178750939[/C][/ROW]
[ROW][C]-1.05493250175468[/C][/ROW]
[ROW][C]-0.0269559123770988[/C][/ROW]
[ROW][C]-0.253998013731939[/C][/ROW]
[ROW][C]-0.435613597309457[/C][/ROW]
[ROW][C]0.515305002088366[/C][/ROW]
[ROW][C]0.328132754897662[/C][/ROW]
[ROW][C]-0.284598105069671[/C][/ROW]
[ROW][C]0.214086701144757[/C][/ROW]
[ROW][C]0.552582014711514[/C][/ROW]
[ROW][C]-0.468778480412715[/C][/ROW]
[ROW][C]-0.246672604053907[/C][/ROW]
[ROW][C]-0.117686316427589[/C][/ROW]
[ROW][C]-0.177983538458835[/C][/ROW]
[ROW][C]0.444704772296298[/C][/ROW]
[ROW][C]-1.10402113922085[/C][/ROW]
[ROW][C]0.453994545714176[/C][/ROW]
[ROW][C]0.634133615437254[/C][/ROW]
[ROW][C]-0.494679134003473[/C][/ROW]
[ROW][C]-0.245077650687217[/C][/ROW]
[ROW][C]-0.092919208679261[/C][/ROW]
[ROW][C]0.245080526996974[/C][/ROW]
[ROW][C]0.809380263143736[/C][/ROW]
[ROW][C]0.450508231641225[/C][/ROW]
[ROW][C]0.995643891366349[/C][/ROW]
[ROW][C]1.05760914117721[/C][/ROW]
[ROW][C]1.43420080486901[/C][/ROW]
[ROW][C]0.678016193899131[/C][/ROW]
[ROW][C]0.720596032986933[/C][/ROW]
[ROW][C]0.132256650210588[/C][/ROW]
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[ROW][C]0.912605450528232[/C][/ROW]
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[ROW][C]0.103473122629045[/C][/ROW]
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[ROW][C]-0.0029377226106754[/C][/ROW]
[ROW][C]0.444033971646533[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=29993&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29993&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:

Estimated ARIMA Residuals
Value
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0.204383035977208
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1.53235641053271
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0.886147550388205
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0.140326740829799
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0.0290662907965497
0.224624595008922
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0.359001705705696
0.804481632795936
0.13784795227238
0.301251178750939
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0.515305002088366
0.328132754897662
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0.214086701144757
0.552582014711514
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0.444704772296298
-1.10402113922085
0.453994545714176
0.634133615437254
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0.245080526996974
0.809380263143736
0.450508231641225
0.995643891366349
1.05760914117721
1.43420080486901
0.678016193899131
0.720596032986933
0.132256650210588
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0.0340324419631722
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1.32366107768567
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1.04457534206299
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1.07470980911778
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1.00457752939272
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Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 36 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ;
Parameters (R input):
par1 = FALSE ; par2 = 0.5 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = 1 ; par7 = 0 ; par8 = 0 ; par9 = 1 ;
R code (references can be found in the software module):
library(lattice)
if (par1 == 'TRUE') par1 <- TRUE
if (par1 == 'FALSE') par1 <- FALSE
par2 <- as.numeric(par2) #Box-Cox lambda transformation parameter
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) #degree (p) of the non-seasonal AR(p) polynomial
par7 <- as.numeric(par7) #degree (q) of the non-seasonal MA(q) polynomial
par8 <- as.numeric(par8) #degree (P) of the seasonal AR(P) polynomial
par9 <- as.numeric(par9) #degree (Q) of the seasonal MA(Q) polynomial
armaGR <- function(arima.out, names, n){
try1 <- arima.out$coef
try2 <- sqrt(diag(arima.out$var.coef))
try.data.frame  <- data.frame(matrix(NA,ncol=4,nrow=length(names)))
dimnames(try.data.frame) <- list(names,c('coef','std','tstat','pv'))
try.data.frame[,1] <- try1
for(i in 1:length(try2)) try.data.frame[which(rownames(try.data.frame)==names(try2)[i]),2] <- try2[i]
try.data.frame[,3] <- try.data.frame[,1] / try.data.frame[,2]
try.data.frame[,4] <- round((1-pt(abs(try.data.frame[,3]),df=n-(length(try2)+1)))*2,5)
vector <- rep(NA,length(names))
vector[is.na(try.data.frame[,4])] <- 0
maxi <- which.max(try.data.frame[,4])
continue <- max(try.data.frame[,4],na.rm=TRUE) > .05
vector[maxi] <- 0
list(summary=try.data.frame,next.vector=vector,continue=continue)
}
arimaSelect <- function(series, order=c(13,0,0), seasonal=list(order=c(2,0,0),period=12), include.mean=F){
nrc <- order[1]+order[3]+seasonal$order[1]+seasonal$order[3]
coeff <- matrix(NA, nrow=nrc*2, ncol=nrc)
pval <- matrix(NA, nrow=nrc*2, ncol=nrc)
mylist <- rep(list(NULL), nrc)
names  <- NULL
if(order[1] > 0) names <- paste('ar',1:order[1],sep='')
if(order[3] > 0) names <- c( names , paste('ma',1:order[3],sep='') )
if(seasonal$order[1] > 0) names <- c(names, paste('sar',1:seasonal$order[1],sep=''))
if(seasonal$order[3] > 0) names <- c(names, paste('sma',1:seasonal$order[3],sep=''))
arima.out <- arima(series, order=order, seasonal=seasonal, include.mean=include.mean, method='ML')
mylist[[1]] <- arima.out
last.arma <- armaGR(arima.out, names, length(series))
mystop <- FALSE
i <- 1
coeff[i,] <- last.arma[[1]][,1]
pval [i,] <- last.arma[[1]][,4]
i <- 2
aic <- arima.out$aic
while(!mystop){
mylist[[i]] <- arima.out
arima.out <- arima(series, order=order, seasonal=seasonal, include.mean=include.mean, method='ML', fixed=last.arma$next.vector)
aic <- c(aic, arima.out$aic)
last.arma <- armaGR(arima.out, names, length(series))
mystop <- !last.arma$continue
coeff[i,] <- last.arma[[1]][,1]
pval [i,] <- last.arma[[1]][,4]
i <- i+1
}
list(coeff, pval, mylist, aic=aic)
}
arimaSelectplot <- function(arimaSelect.out,noms,choix){
noms <- names(arimaSelect.out[[3]][[1]]$coef)
coeff <- arimaSelect.out[[1]]
k <- min(which(is.na(coeff[,1])))-1
coeff <- coeff[1:k,]
pval  <- arimaSelect.out[[2]][1:k,]
aic   <- arimaSelect.out$aic[1:k]
coeff[coeff==0] <- NA
n <- ncol(coeff)
if(missing(choix)) choix <- k
layout(matrix(c(1,1,1,2,
3,3,3,2,
3,3,3,4,
5,6,7,7),nr=4),
widths=c(10,35,45,15),
heights=c(30,30,15,15))
couleurs <- rainbow(75)[1:50]#(50)
ticks <- pretty(coeff)
par(mar=c(1,1,3,1))
plot(aic,k:1-.5,type='o',pch=21,bg='blue',cex=2,axes=F,lty=2,xpd=NA)
points(aic[choix],k-choix+.5,pch=21,cex=4,bg=2,xpd=NA)
title('aic',line=2)
par(mar=c(3,0,0,0))
plot(0,axes=F,xlab='',ylab='',xlim=range(ticks),ylim=c(.1,1))
rect(xleft  = min(ticks) + (0:49)/50*(max(ticks)-min(ticks)),
xright = min(ticks) + (1:50)/50*(max(ticks)-min(ticks)),
ytop   = rep(1,50),
ybottom= rep(0,50),col=couleurs,border=NA)
axis(1,ticks)
rect(xleft=min(ticks),xright=max(ticks),ytop=1,ybottom=0)
text(mean(coeff,na.rm=T),.5,'coefficients',cex=2,font=2)
par(mar=c(1,1,3,1))
image(1:n,1:k,t(coeff[k:1,]),axes=F,col=couleurs,zlim=range(ticks))
for(i in 1:n) for(j in 1:k) if(!is.na(coeff[j,i])) {
if(pval[j,i]<.01)                            symb = 'green'
else if( (pval[j,i]<.05) & (pval[j,i]>=.01)) symb = 'orange'
else if( (pval[j,i]<.1)  & (pval[j,i]>=.05)) symb = 'red'
else                                         symb = 'black'
polygon(c(i+.5   ,i+.2   ,i+.5   ,i+.5),
c(k-j+0.5,k-j+0.5,k-j+0.8,k-j+0.5),
col=symb)
if(j==choix)  {
rect(xleft=i-.5,
xright=i+.5,
ybottom=k-j+1.5,
ytop=k-j+.5,
lwd=4)
text(i,
k-j+1,
round(coeff[j,i],2),
cex=1.2,
font=2)
}
else{
rect(xleft=i-.5,xright=i+.5,ybottom=k-j+1.5,ytop=k-j+.5)
text(i,k-j+1,round(coeff[j,i],2),cex=1.2,font=1)
}
}
axis(3,1:n,noms)
par(mar=c(0.5,0,0,0.5))
plot(0,axes=F,xlab='',ylab='',type='n',xlim=c(0,8),ylim=c(-.2,.8))
cols <- c('green','orange','red','black')
niv  <- c('0','0.01','0.05','0.1')
for(i in 0:3){
polygon(c(1+2*i   ,1+2*i   ,1+2*i-.5   ,1+2*i),
c(.4      ,.7      , .4        , .4),
col=cols[i+1])
text(2*i,0.5,niv[i+1],cex=1.5)
}
text(8,.5,1,cex=1.5)
text(4,0,'p-value',cex=2)
box()
residus <- arimaSelect.out[[3]][[choix]]$res
par(mar=c(1,2,4,1))
acf(residus,main='')
title('acf',line=.5)
par(mar=c(1,2,4,1))
pacf(residus,main='')
title('pacf',line=.5)
par(mar=c(2,2,4,1))
qqnorm(residus,main='')
title('qq-norm',line=.5)
qqline(residus)
residus
}
if (par2 == 0) x <- log(x)
if (par2 != 0) x <- x^par2
(selection <- arimaSelect(x, order=c(par6,par3,par7), seasonal=list(order=c(par8,par4,par9), period=par5)))
bitmap(file='test1.png')
resid <- arimaSelectplot(selection)
dev.off()
resid
bitmap(file='test2.png')
acf(resid,length(resid)/2, main='Residual Autocorrelation Function')
dev.off()
bitmap(file='test3.png')
pacf(resid,length(resid)/2, main='Residual Partial Autocorrelation Function')
dev.off()
bitmap(file='test4.png')
cpgram(resid, main='Residual Cumulative Periodogram')
dev.off()
bitmap(file='test5.png')
hist(resid, main='Residual Histogram', xlab='values of Residuals')
dev.off()
bitmap(file='test6.png')
densityplot(~resid,col='black',main='Residual Density Plot', xlab='values of Residuals')
dev.off()
bitmap(file='test7.png')
qqnorm(resid, main='Residual Normal Q-Q Plot')
qqline(resid)
dev.off()
ncols <- length(selection[[1]][1,])
nrows <- length(selection[[2]][,1])-1
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'ARIMA Parameter Estimation and Backward Selection', ncols+1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Iteration', header=TRUE)
for (i in 1:ncols) {
a<-table.element(a,names(selection[[3]][[1]]$coef)[i],header=TRUE)
}
a<-table.row.end(a)
for (j in 1:nrows) {
a<-table.row.start(a)
mydum <- 'Estimates ('
mydum <- paste(mydum,j)
mydum <- paste(mydum,')')
a<-table.element(a,mydum, header=TRUE)
for (i in 1:ncols) {
a<-table.element(a,round(selection[[1]][j,i],4))
}
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'(p-val)', header=TRUE)
for (i in 1:ncols) {
mydum <- '('
mydum <- paste(mydum,round(selection[[2]][j,i],4),sep='')
mydum <- paste(mydum,')')
a<-table.element(a,mydum)
}
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,'Estimated ARIMA Residuals', 1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Value', 1,TRUE)
a<-table.row.end(a)
for (i in (par4*par5+par3):length(resid)) {
a<-table.row.start(a)
a<-table.element(a,resid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')