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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_arimabackwardselection.wasp
Title produced by softwareARIMA Backward Selection
Date of computationFri, 23 Dec 2016 09:52:47 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Dec/23/t1482484348zx10qjuxfle0nre.htm/, Retrieved Wed, 30 Apr 2025 04:14:40 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=302795, Retrieved Wed, 30 Apr 2025 04:14:40 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact126

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [ARIMA Backward Selection] [ARIMA Backward Se...] [2016-12-23 08:52:47] [02b5df5aa2382aa6805f6181aa5e25f1] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
3800
4150
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2700
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6800

Tables (Output of Computation)





Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time5 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time5 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302795&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]5 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=302795&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302795&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 Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time5 seconds
R ServerBig Analytics Cloud Computing Center






ARIMA Parameter Estimation and Backward Selection
Iterationar1ar2ar3sar1sar2
Estimates ( 1 )0.12980.50050.3501-0.8028-0.6531
(p-val)(0.1843 )(0 )(3e-04 )(0 )(0 )
Estimates ( 2 )00.54680.4311-0.7729-0.6232
(p-val)(NA )(0 )(0 )(0 )(0 )
Estimates ( 3 )NANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )
Estimates ( 4 )NANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )
Estimates ( 5 )NANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )
Estimates ( 6 )NANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )
Estimates ( 7 )NANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )
Estimates ( 8 )NANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )
Estimates ( 9 )NANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )

\begin{tabular}{lllllllll}
\hline
ARIMA Parameter Estimation and Backward Selection \tabularnewline
Iteration & ar1 & ar2 & ar3 & sar1 & sar2 \tabularnewline
Estimates ( 1 ) & 0.1298 & 0.5005 & 0.3501 & -0.8028 & -0.6531 \tabularnewline
(p-val) & (0.1843 ) & (0 ) & (3e-04 ) & (0 ) & (0 ) \tabularnewline
Estimates ( 2 ) & 0 & 0.5468 & 0.4311 & -0.7729 & -0.6232 \tabularnewline
(p-val) & (NA ) & (0 ) & (0 ) & (0 ) & (0 ) \tabularnewline
Estimates ( 3 ) & NA & NA & NA & NA & NA \tabularnewline
(p-val) & (NA ) & (NA ) & (NA ) & (NA ) & (NA ) \tabularnewline
Estimates ( 4 ) & NA & NA & NA & NA & NA \tabularnewline
(p-val) & (NA ) & (NA ) & (NA ) & (NA ) & (NA ) \tabularnewline
Estimates ( 5 ) & NA & NA & NA & NA & NA \tabularnewline
(p-val) & (NA ) & (NA ) & (NA ) & (NA ) & (NA ) \tabularnewline
Estimates ( 6 ) & NA & NA & NA & NA & NA \tabularnewline
(p-val) & (NA ) & (NA ) & (NA ) & (NA ) & (NA ) \tabularnewline
Estimates ( 7 ) & NA & NA & NA & NA & NA \tabularnewline
(p-val) & (NA ) & (NA ) & (NA ) & (NA ) & (NA ) \tabularnewline
Estimates ( 8 ) & NA & NA & NA & NA & NA \tabularnewline
(p-val) & (NA ) & (NA ) & (NA ) & (NA ) & (NA ) \tabularnewline
Estimates ( 9 ) & NA & NA & NA & NA & NA \tabularnewline
(p-val) & (NA ) & (NA ) & (NA ) & (NA ) & (NA ) \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302795&T=1

[TABLE]
[ROW][C]ARIMA Parameter Estimation and Backward Selection[/C][/ROW]
[ROW][C]Iteration[/C][C]ar1[/C][C]ar2[/C][C]ar3[/C][C]sar1[/C][C]sar2[/C][/ROW]
[ROW][C]Estimates ( 1 )[/C][C]0.1298[/C][C]0.5005[/C][C]0.3501[/C][C]-0.8028[/C][C]-0.6531[/C][/ROW]
[ROW][C](p-val)[/C][C](0.1843 )[/C][C](0 )[/C][C](3e-04 )[/C][C](0 )[/C][C](0 )[/C][/ROW]
[ROW][C]Estimates ( 2 )[/C][C]0[/C][C]0.5468[/C][C]0.4311[/C][C]-0.7729[/C][C]-0.6232[/C][/ROW]
[ROW][C](p-val)[/C][C](NA )[/C][C](0 )[/C][C](0 )[/C][C](0 )[/C][C](0 )[/C][/ROW]
[ROW][C]Estimates ( 3 )[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][/ROW]
[ROW][C](p-val)[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][/ROW]
[ROW][C]Estimates ( 4 )[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][/ROW]
[ROW][C](p-val)[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][/ROW]
[ROW][C]Estimates ( 5 )[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][/ROW]
[ROW][C](p-val)[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][/ROW]
[ROW][C]Estimates ( 6 )[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][/ROW]
[ROW][C](p-val)[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][/ROW]
[ROW][C]Estimates ( 7 )[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][/ROW]
[ROW][C](p-val)[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][/ROW]
[ROW][C]Estimates ( 8 )[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][/ROW]
[ROW][C](p-val)[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][/ROW]
[ROW][C]Estimates ( 9 )[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][/ROW]
[ROW][C](p-val)[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302795&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302795&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
Iterationar1ar2ar3sar1sar2
Estimates ( 1 )0.12980.50050.3501-0.8028-0.6531
(p-val)(0.1843 )(0 )(3e-04 )(0 )(0 )
Estimates ( 2 )00.54680.4311-0.7729-0.6232
(p-val)(NA )(0 )(0 )(0 )(0 )
Estimates ( 3 )NANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )
Estimates ( 4 )NANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )
Estimates ( 5 )NANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )
Estimates ( 6 )NANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )
Estimates ( 7 )NANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )
Estimates ( 8 )NANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )
Estimates ( 9 )NANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )






Estimated ARIMA Residuals
Value
4.04988635601438
200.128544764042
25.3455733629124
-12.0517921717416
-3.32448228633865
200.359695104304
-17.6986976975548
-177.070093286367
44.6321615455857
139.120436995858
134.119377606013
147.822161633021
65.3181805366416
-56.6413922907025
-25.1478814687587
-278.282655191834
261.894929780943
-131.704001442763
-18.4576437221995
-111.488505669327
227.037480908984
71.7361652652435
-4.28462722415898
140.322068210923
-20.4741763280959
-101.369670853645
-26.5339969688944
58.4606968653933
-79.4445872677949
22.5870427163622
-62.6087416904545
-235.426827211737
135.121627431528
205.550562339149
151.027938903416
78.1023512148791
-193.748647326429
-214.424602816098
57.8849178378525
156.433108487835
-113.982144451836
-100.944148123011
94.726044062837
8.24777306118131
80.4147044852488
164.78809012152
86.573729134926
-67.2896779061694
-93.6712585200621
48.91505063981
49.8223000744911
-52.0911458282708
585.254932991989
236.246304032456
55.5008974795646
-315.070034024992
-157.172983705038
100.243212281386
100.395108225757
29.373404030931
-39.2525519930741
28.7173523699939
243.165014352342
317.740439746521
-106.557695548596
-30.9276243981349
-50.9292413623607
-399.871023463398
86.3666623110802
273.784950278701
62.9067633268405
-45.1198751665252
-26.2384330253117
11.8984358246171
48.9683970509259
335.807490238186
-344.546314385183
-246.680353122714
382.354424077064
-326.814737988102
-151.633274626389
300.589554472328
291.321379024351
54.6905571336565
-106.310672486491
136.434321640186
142.531602266292
-733.031066172237
245.756006309673
-126.735821208131
119.469377682395
-671.425461777233
196.066464383268
215.994966106878
308.09890272452
235.564189947085
-97.7247132909661
-90.0451974430935
-50.8036863090174
274.620531458159
-367.971087613153
43.80784495014
-69.5643620951523

\begin{tabular}{lllllllll}
\hline
Estimated ARIMA Residuals \tabularnewline
Value \tabularnewline
4.04988635601438 \tabularnewline
200.128544764042 \tabularnewline
25.3455733629124 \tabularnewline
-12.0517921717416 \tabularnewline
-3.32448228633865 \tabularnewline
200.359695104304 \tabularnewline
-17.6986976975548 \tabularnewline
-177.070093286367 \tabularnewline
44.6321615455857 \tabularnewline
139.120436995858 \tabularnewline
134.119377606013 \tabularnewline
147.822161633021 \tabularnewline
65.3181805366416 \tabularnewline
-56.6413922907025 \tabularnewline
-25.1478814687587 \tabularnewline
-278.282655191834 \tabularnewline
261.894929780943 \tabularnewline
-131.704001442763 \tabularnewline
-18.4576437221995 \tabularnewline
-111.488505669327 \tabularnewline
227.037480908984 \tabularnewline
71.7361652652435 \tabularnewline
-4.28462722415898 \tabularnewline
140.322068210923 \tabularnewline
-20.4741763280959 \tabularnewline
-101.369670853645 \tabularnewline
-26.5339969688944 \tabularnewline
58.4606968653933 \tabularnewline
-79.4445872677949 \tabularnewline
22.5870427163622 \tabularnewline
-62.6087416904545 \tabularnewline
-235.426827211737 \tabularnewline
135.121627431528 \tabularnewline
205.550562339149 \tabularnewline
151.027938903416 \tabularnewline
78.1023512148791 \tabularnewline
-193.748647326429 \tabularnewline
-214.424602816098 \tabularnewline
57.8849178378525 \tabularnewline
156.433108487835 \tabularnewline
-113.982144451836 \tabularnewline
-100.944148123011 \tabularnewline
94.726044062837 \tabularnewline
8.24777306118131 \tabularnewline
80.4147044852488 \tabularnewline
164.78809012152 \tabularnewline
86.573729134926 \tabularnewline
-67.2896779061694 \tabularnewline
-93.6712585200621 \tabularnewline
48.91505063981 \tabularnewline
49.8223000744911 \tabularnewline
-52.0911458282708 \tabularnewline
585.254932991989 \tabularnewline
236.246304032456 \tabularnewline
55.5008974795646 \tabularnewline
-315.070034024992 \tabularnewline
-157.172983705038 \tabularnewline
100.243212281386 \tabularnewline
100.395108225757 \tabularnewline
29.373404030931 \tabularnewline
-39.2525519930741 \tabularnewline
28.7173523699939 \tabularnewline
243.165014352342 \tabularnewline
317.740439746521 \tabularnewline
-106.557695548596 \tabularnewline
-30.9276243981349 \tabularnewline
-50.9292413623607 \tabularnewline
-399.871023463398 \tabularnewline
86.3666623110802 \tabularnewline
273.784950278701 \tabularnewline
62.9067633268405 \tabularnewline
-45.1198751665252 \tabularnewline
-26.2384330253117 \tabularnewline
11.8984358246171 \tabularnewline
48.9683970509259 \tabularnewline
335.807490238186 \tabularnewline
-344.546314385183 \tabularnewline
-246.680353122714 \tabularnewline
382.354424077064 \tabularnewline
-326.814737988102 \tabularnewline
-151.633274626389 \tabularnewline
300.589554472328 \tabularnewline
291.321379024351 \tabularnewline
54.6905571336565 \tabularnewline
-106.310672486491 \tabularnewline
136.434321640186 \tabularnewline
142.531602266292 \tabularnewline
-733.031066172237 \tabularnewline
245.756006309673 \tabularnewline
-126.735821208131 \tabularnewline
119.469377682395 \tabularnewline
-671.425461777233 \tabularnewline
196.066464383268 \tabularnewline
215.994966106878 \tabularnewline
308.09890272452 \tabularnewline
235.564189947085 \tabularnewline
-97.7247132909661 \tabularnewline
-90.0451974430935 \tabularnewline
-50.8036863090174 \tabularnewline
274.620531458159 \tabularnewline
-367.971087613153 \tabularnewline
43.80784495014 \tabularnewline
-69.5643620951523 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302795&T=2

[TABLE]
[ROW][C]Estimated ARIMA Residuals[/C][/ROW]
[ROW][C]Value[/C][/ROW]
[ROW][C]4.04988635601438[/C][/ROW]
[ROW][C]200.128544764042[/C][/ROW]
[ROW][C]25.3455733629124[/C][/ROW]
[ROW][C]-12.0517921717416[/C][/ROW]
[ROW][C]-3.32448228633865[/C][/ROW]
[ROW][C]200.359695104304[/C][/ROW]
[ROW][C]-17.6986976975548[/C][/ROW]
[ROW][C]-177.070093286367[/C][/ROW]
[ROW][C]44.6321615455857[/C][/ROW]
[ROW][C]139.120436995858[/C][/ROW]
[ROW][C]134.119377606013[/C][/ROW]
[ROW][C]147.822161633021[/C][/ROW]
[ROW][C]65.3181805366416[/C][/ROW]
[ROW][C]-56.6413922907025[/C][/ROW]
[ROW][C]-25.1478814687587[/C][/ROW]
[ROW][C]-278.282655191834[/C][/ROW]
[ROW][C]261.894929780943[/C][/ROW]
[ROW][C]-131.704001442763[/C][/ROW]
[ROW][C]-18.4576437221995[/C][/ROW]
[ROW][C]-111.488505669327[/C][/ROW]
[ROW][C]227.037480908984[/C][/ROW]
[ROW][C]71.7361652652435[/C][/ROW]
[ROW][C]-4.28462722415898[/C][/ROW]
[ROW][C]140.322068210923[/C][/ROW]
[ROW][C]-20.4741763280959[/C][/ROW]
[ROW][C]-101.369670853645[/C][/ROW]
[ROW][C]-26.5339969688944[/C][/ROW]
[ROW][C]58.4606968653933[/C][/ROW]
[ROW][C]-79.4445872677949[/C][/ROW]
[ROW][C]22.5870427163622[/C][/ROW]
[ROW][C]-62.6087416904545[/C][/ROW]
[ROW][C]-235.426827211737[/C][/ROW]
[ROW][C]135.121627431528[/C][/ROW]
[ROW][C]205.550562339149[/C][/ROW]
[ROW][C]151.027938903416[/C][/ROW]
[ROW][C]78.1023512148791[/C][/ROW]
[ROW][C]-193.748647326429[/C][/ROW]
[ROW][C]-214.424602816098[/C][/ROW]
[ROW][C]57.8849178378525[/C][/ROW]
[ROW][C]156.433108487835[/C][/ROW]
[ROW][C]-113.982144451836[/C][/ROW]
[ROW][C]-100.944148123011[/C][/ROW]
[ROW][C]94.726044062837[/C][/ROW]
[ROW][C]8.24777306118131[/C][/ROW]
[ROW][C]80.4147044852488[/C][/ROW]
[ROW][C]164.78809012152[/C][/ROW]
[ROW][C]86.573729134926[/C][/ROW]
[ROW][C]-67.2896779061694[/C][/ROW]
[ROW][C]-93.6712585200621[/C][/ROW]
[ROW][C]48.91505063981[/C][/ROW]
[ROW][C]49.8223000744911[/C][/ROW]
[ROW][C]-52.0911458282708[/C][/ROW]
[ROW][C]585.254932991989[/C][/ROW]
[ROW][C]236.246304032456[/C][/ROW]
[ROW][C]55.5008974795646[/C][/ROW]
[ROW][C]-315.070034024992[/C][/ROW]
[ROW][C]-157.172983705038[/C][/ROW]
[ROW][C]100.243212281386[/C][/ROW]
[ROW][C]100.395108225757[/C][/ROW]
[ROW][C]29.373404030931[/C][/ROW]
[ROW][C]-39.2525519930741[/C][/ROW]
[ROW][C]28.7173523699939[/C][/ROW]
[ROW][C]243.165014352342[/C][/ROW]
[ROW][C]317.740439746521[/C][/ROW]
[ROW][C]-106.557695548596[/C][/ROW]
[ROW][C]-30.9276243981349[/C][/ROW]
[ROW][C]-50.9292413623607[/C][/ROW]
[ROW][C]-399.871023463398[/C][/ROW]
[ROW][C]86.3666623110802[/C][/ROW]
[ROW][C]273.784950278701[/C][/ROW]
[ROW][C]62.9067633268405[/C][/ROW]
[ROW][C]-45.1198751665252[/C][/ROW]
[ROW][C]-26.2384330253117[/C][/ROW]
[ROW][C]11.8984358246171[/C][/ROW]
[ROW][C]48.9683970509259[/C][/ROW]
[ROW][C]335.807490238186[/C][/ROW]
[ROW][C]-344.546314385183[/C][/ROW]
[ROW][C]-246.680353122714[/C][/ROW]
[ROW][C]382.354424077064[/C][/ROW]
[ROW][C]-326.814737988102[/C][/ROW]
[ROW][C]-151.633274626389[/C][/ROW]
[ROW][C]300.589554472328[/C][/ROW]
[ROW][C]291.321379024351[/C][/ROW]
[ROW][C]54.6905571336565[/C][/ROW]
[ROW][C]-106.310672486491[/C][/ROW]
[ROW][C]136.434321640186[/C][/ROW]
[ROW][C]142.531602266292[/C][/ROW]
[ROW][C]-733.031066172237[/C][/ROW]
[ROW][C]245.756006309673[/C][/ROW]
[ROW][C]-126.735821208131[/C][/ROW]
[ROW][C]119.469377682395[/C][/ROW]
[ROW][C]-671.425461777233[/C][/ROW]
[ROW][C]196.066464383268[/C][/ROW]
[ROW][C]215.994966106878[/C][/ROW]
[ROW][C]308.09890272452[/C][/ROW]
[ROW][C]235.564189947085[/C][/ROW]
[ROW][C]-97.7247132909661[/C][/ROW]
[ROW][C]-90.0451974430935[/C][/ROW]
[ROW][C]-50.8036863090174[/C][/ROW]
[ROW][C]274.620531458159[/C][/ROW]
[ROW][C]-367.971087613153[/C][/ROW]
[ROW][C]43.80784495014[/C][/ROW]
[ROW][C]-69.5643620951523[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302795&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302795&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
4.04988635601438
200.128544764042
25.3455733629124
-12.0517921717416
-3.32448228633865
200.359695104304
-17.6986976975548
-177.070093286367
44.6321615455857
139.120436995858
134.119377606013
147.822161633021
65.3181805366416
-56.6413922907025
-25.1478814687587
-278.282655191834
261.894929780943
-131.704001442763
-18.4576437221995
-111.488505669327
227.037480908984
71.7361652652435
-4.28462722415898
140.322068210923
-20.4741763280959
-101.369670853645
-26.5339969688944
58.4606968653933
-79.4445872677949
22.5870427163622
-62.6087416904545
-235.426827211737
135.121627431528
205.550562339149
151.027938903416
78.1023512148791
-193.748647326429
-214.424602816098
57.8849178378525
156.433108487835
-113.982144451836
-100.944148123011
94.726044062837
8.24777306118131
80.4147044852488
164.78809012152
86.573729134926
-67.2896779061694
-93.6712585200621
48.91505063981
49.8223000744911
-52.0911458282708
585.254932991989
236.246304032456
55.5008974795646
-315.070034024992
-157.172983705038
100.243212281386
100.395108225757
29.373404030931
-39.2525519930741
28.7173523699939
243.165014352342
317.740439746521
-106.557695548596
-30.9276243981349
-50.9292413623607
-399.871023463398
86.3666623110802
273.784950278701
62.9067633268405
-45.1198751665252
-26.2384330253117
11.8984358246171
48.9683970509259
335.807490238186
-344.546314385183
-246.680353122714
382.354424077064
-326.814737988102
-151.633274626389
300.589554472328
291.321379024351
54.6905571336565
-106.310672486491
136.434321640186
142.531602266292
-733.031066172237
245.756006309673
-126.735821208131
119.469377682395
-671.425461777233
196.066464383268
215.994966106878
308.09890272452
235.564189947085
-97.7247132909661
-90.0451974430935
-50.8036863090174
274.620531458159
-367.971087613153
43.80784495014
-69.5643620951523


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = FALSE ; par2 = 1 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = 3 ; par7 = 0 ; par8 = 2 ; par9 = 0 ;
Parameters (R input):
par1 = FALSE ; par2 = 1 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = 3 ; par7 = 0 ; par8 = 2 ; par9 = 0 ;
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')